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Electromagnetism
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Electricity · Magnetism
Magnetostatics
Ampère’s law · Electric current · Magnetic field · Magnetization · Magnetic flux · Biot–Savart law · Magnetic dipole moment · Gauss's law for magnetism
.
Magnetic field lines represented by the alignment of iron filings.
^ A magnetic field represents stored energy and .
  • Magnetism: quantities, units and relationships 18 September 2009 7:28 UTC info.ee.surrey.ac.uk [Source type: Academic]

^ Treatment with the iron chelator deferiprone also blocked the effects of magnetic fields on brain cell DNA, suggesting the involvement of iron.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

^ Hz magnetic field at 7 mT in the presence of iron cations.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

.The high magnetic permeability of the individual filings causes their magnetic fields to concentrate at their ends.^ The magnetic relative permeability (mu) for Iron at extremely high temperatures and pressures is not accurately known, but it seems to rise with temperature and seems certain to be at least 10,000.
  • http://mb-soft.com/public/tecto2.html 13 January 2010 10:13 UTC mb-soft.com [Source type: FILTERED WITH BAYES]

^ The magnetic field pattern around a bar magnet is created by the superposition of the dipole fields of the individual iron atoms.

^ The increasing magnetic field causes electrons to circulate (current) around the second coil in such a way as to oppose the increasing magnetic field that the first coil is trying to establish.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

.The mutual attraction of opposite poles then results in the formation of elongated clusters of filings along the field lines.^ (In this way, they resemble the field lines of an iron bar magnet, which arch from the north to the south poles.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ E × B d v This predicts something specific about the direction of propagation of a light wave: it must be along the line perpendicular to the electric and magnetic fields.

^ Moreover, the shifting magnetic field outside the star must drive electrical currents along arched magnetic field lines.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

However, these lines do not precisely represent the field lines of the magnet, as the presence of the iron filings somewhat alters its magnetic field.
.Magnetic fields surround magnetic materials and electric currents and are detected by the force they exert on other magnetic materials and moving electric charges.^ This electric field is not created by charges .

^ In particular, the fact that electric currents create magnetic fields.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

.The magnetic field at any given point is specified by both a direction and a magnitude (or strength); as such it is a vector field.^ Infer the direction of the magnetic field.

^ The magnetic field varies in both magnitude and direction (i.e., it is a vector field) in a volume of space around a magnet or around a loop of current.
  • "MAGNETIC UFO" 13 January 2010 10:13 UTC brumac.8k.com [Source type: Academic]

^ The electric field at point P is , and the magnetic field is .

[1]
.For the physics of magnetic materials, see magnetism and magnet, more specifically ferromagnetism, paramagnetism, and diamagnetism.^ FIELD OF THE INVENTION [0001] The present invention relates to a magnetic field control method and a magnetic field generator, and more specifically, to a magnetic field control method and a magnetic field generator in which an orientation of a magnetic field at a target position is changed to an arbitrary direction.
  • Magnetic Field Control Method and Magnetic Field Generator - Patent application 13 January 2010 10:13 UTC www.faqs.org [Source type: Reference]

^ Diamagnetic materials have the interesting property that they are repelled from regions of strong magnetic field, and it is therefore possible to levitate a diamagnetic object above a magnet, as in figure h .

^ Diamagnetism is generally a much weaker effect than paramagnetism, and is easily masked if there is any trace of contamination from a paramagnetic material.

.For constant magnetic fields, such as are generated by magnetic materials and steady currents, see magnetostatics.^ Magnetic fields curl around currents.

^ The torque on a current loop in a magnetic field.

^ The magnetic field generator according to claim 3 or 4, wherein at least one of the magnetic field generating units is constituted by a plurality of permanent magnets and a holding member holding the permanent magnets.
  • Magnetic Field Control Method and Magnetic Field Generator - Patent application 13 January 2010 10:13 UTC www.faqs.org [Source type: Reference]

.A changing magnetic field generates an electric field and a changing electric field results in a magnetic field.^ The relationship between the change in the magnetic field, and the electric field it produces.

^ Do we have infinite energy in the resulting magnetic field?

^ What is the difference between an electric field and a magnetic field?
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

(See electromagnetism.)
.In view of special relativity, the electric and magnetic fields are two interrelated aspects of a single object, called the electromagnetic field.^ Melatonin aspects of exposure to low frequency electric and magnetic fields.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

^ Geometry of the electric and magnetic fields .

^ Prove that in an electromagnetic wave, half the energy is in the electric field and half in the magnetic field.

.A pure electric field in one reference frame is observed as a combination of both an electric field and a magnetic field in a moving reference frame.^ Where is the moving charge responsible for this magnetic field?

^ In her frame of reference, it's the bar magnet that is moving.

^ Or an example where the fields are purely electric in one frame, but purely magnetic in another?

.In modern physics, the magnetic (and electric) fields are understood to be due to a photon field; in the language of the Standard Model the electromagnetic force is mediated by photons.^ H-field alias magnetizing force .
  • Magnetism: quantities, units and relationships 18 September 2009 7:28 UTC info.ee.surrey.ac.uk [Source type: Academic]

^ Geometry of the electric and magnetic fields .

^ Prove that in an electromagnetic wave, half the energy is in the electric field and half in the magnetic field.

.Most often this microscopic description is not needed because the simpler classical theory covered in this article is sufficient; the difference is negligible under most circumstances.^ This article proposes a comprehensive theory that logically explains ALL the peculiar findings, as well as a mathematically and physically logical description of the source itself.
  • http://mb-soft.com/public/tecto2.html 13 January 2010 10:13 UTC mb-soft.com [Source type: FILTERED WITH BAYES]

Contents

B and H

Alternative names for B
name used by
magnetic flux density electrical engineers
magnetic induction applied mathematicians
electrical engineers
magnetic field physicists
Alternative names for H
name used by
magnetic field intensity electrical engineers
magnetic field strength electrical engineers
auxiliary magnetic field physicists
magnetizing field physicists
.The term magnetic field is used for two different vector fields, denoted B and H.^ What is the difference between an electric field and a magnetic field?
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ We can also anticipate that the magnetic field will be a vector.

^ Magnetic Grid Layer After extensive research into magnetic fields and the use of magnets in alternative health care, engineers designed a magnetic grid pattern with two distinct benefits: First, the field distribution is even, so that all parts of the body benefit equally.
  • MAGNETIC FIELD THERAPY - MAGNETIC MATTRESS PADS 13 January 2010 10:13 UTC www.shoppingsolution.com [Source type: General]

[2] There are many alternative names for both, though. (See sidebar.) .To avoid confusion, this article uses B-field and H-field for these fields, and uses magnetic field where either or both fields apply.^ B = 0 Maxwell's Equation for B You could argue that B indicates better the strength of a magnetic field than does the 'magnetic field strength' H! This is one reason why modern authors tend not to use these names and stick instead with 'B field' and 'H field'.
  • Magnetism: quantities, units and relationships 18 September 2009 7:28 UTC info.ee.surrey.ac.uk [Source type: Academic]

^ Now perhaps we can use reasoning with the same flavor to show that changing magnetic fields produce curly electric fields.

^ These data further support a role of free radicals on the effects of magnetic fields.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

.The B-field can be defined in many equivalent ways based on the effects it has on its environment.^ MR ( magnetoresistive ) A technology based on the effect where electrical resistance in a material changes when brought in contact with a magnetic field .
  • Pro Audio Reference M 13 January 2010 10:13 UTC www.rane.com [Source type: FILTERED WITH BAYES]

^ Based on counts of supernovae within many other galaxies like the Milky Way, this rate is estimated in the range of 1 per 100 years.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ This hypothesis could have an important implication for the possible health effects associated with exposure to extremely low-frequency magnetic fields in the public and occupational environments.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

.For instance, a particle having an electric charge, q, and moving in a B-field with a velocity, v, experiences a force, F, called the Lorentz force (see below).^ This electric field is not created by charges .

^ Where is the moving charge responsible for this magnetic field?

^ Definition in terms of the force on a moving particle .

In SI units, the Lorentz force equation is
\mathbf{F}=q\left(\mathbf{v}	imes\mathbf{B}\right)
where × is the vector cross product. .The B-field is measured in teslas in SI units and in gauss in cgs units.^ The unit of magnetic field, the tesla, is named after Serbian-American inventor Nikola Tesla.

^ Although the relationship E ≤ftrightarrow q between electric fields and their sources is unalterably locked in by Gauss's law, that's not what we see in practical measurements.

^ Early in the nineteenth century, Carl Friedrich Gauss (1833; 1839) used many measurements from all over the world to characterize the earth’s field.
  • The Earth’s Magnetic Field is Still Losing Energy 13 January 2010 10:13 UTC www.creationresearch.org [Source type: Academic]

An alternate working definition of the B-field can be given in terms of the torque on a magnetic dipole placed in a B-field:
\boldsymbol{	au}=\mathbf{m_m}	imes\mathbf{B}
for a .magnetic dipole moment m (in ampere-square meters).^ Example 1: The magnetic dipole moment of an atom .

^ The distant field of a square dipole turns out to be simple, and is no different from the distant field of any other dipole with the same dipole moment.

^ Apparently, nearly all the atoms in such a magnet are oriented randomly, and do not contribute to the magnet's dipole moment.

.Although views have shifted over the years, B is now understood as being the fundamental quantity, while H is a derived field.^ Now, in the last 20 years or so, the magnetic field has become erratic.
  • A Weakening Magnetic Field and Emerging Sunspot Cycle 24... What Does This Mean for Planet Earth and All Species? | KnowTheLies.com - The Truth is Hidden in Plain View... 13 January 2010 10:13 UTC www.knowthelies.com [Source type: FILTERED WITH BAYES]

^ For these reasons, let's look at an alternative method of defining the magnetic field which, although not as fundamental or mathematically simple, may be more appealing.

^ The effect occurs only when the magnetic field is changing, and it appears to be proportional to the derivative ∂ B /∂ t , which is in one direction when the field is being established, and in the opposite direction when it collapses.

H is defined as a modification of B due to magnetic fields produced by material media, such that (in SI):
\mathbf{H}\ \equiv \ \frac{\mathbf{B}}{\mu_0}-\mathbf{M},
where .M is the magnetization of the material and μ0 is the permeability of free space (or magnetic constant).^ H = B / μ 0 - M Sommerfeld Field Equation This formula applies generally, even if the materials within the field have non-uniform permeability or a permanent magnetic moment .
  • Magnetism: quantities, units and relationships 18 September 2009 7:28 UTC info.ee.surrey.ac.uk [Source type: Academic]

^ The result is that when a magnetic field enters a high-permeability material, it tends to twist abruptly to one side, and the pattern of the field tends to be channeled through the material like water through a funnel.

^ A magnetically permeable material is placed at the center of a solenoid.

[3] .The H-field is measured in amperes per meter (A/m) in SI units, and in oersteds (Oe) in cgs units.^ H = F m / l e ampere-turns per metre The field produces magnetic flux density - .
  • Magnetism: quantities, units and relationships 18 September 2009 7:28 UTC info.ee.surrey.ac.uk [Source type: Academic]

^ The oval lines are contours of constant current density (amperes per square meter).
  • The Earth’s Magnetic Field is Still Losing Energy 13 January 2010 10:13 UTC www.creationresearch.org [Source type: Academic]

^ Exposed to an electric field E , a conductor responds with a current per unit cross-sectional area J =σ E .

[4]
.In materials for which M is proportional to B the relationship between B and H can be cast into the simpler form: H = B/μ, where μ is a material dependent parameter called the permeability.^ In fact, if you can treat the permeability as being linear, then the constants N , l e , μ and A e can be lumped together into one constant for the winding which is called (surprise!
  • Magnetism: quantities, units and relationships 18 September 2009 7:28 UTC info.ee.surrey.ac.uk [Source type: Academic]

^ L = N × d Φ / d I Equation TMO If the core material's permeability is considered constant then the relation between flux and current is linear and so: .
  • Magnetism: quantities, units and relationships 18 September 2009 7:28 UTC info.ee.surrey.ac.uk [Source type: Academic]

.In free space, there is no magnetization, M, so that H = B/μ0.^ A charged particle is in a region of space in which there is a uniform magnetic field .

^ On page 667, I proved that H ||,1 = H ||,2 at the boundary between two substances if there is no free current and the fields are static.

^ All the compasses pointed north indicating that there was no large magnetic anomaly in the area.
  • "MAGNETIC UFO" 13 January 2010 10:13 UTC brumac.8k.com [Source type: Academic]

.For many materials, though, there is no simple relationship between B and M.^ Though studies are being done to see if there is a link between it and tumors of the brain and central nervous system, there is no definitive link between the two, the institute says on its Web site.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ On page 667, I proved that H ||,1 = H ||,2 at the boundary between two substances if there is no free current and the fields are static.

^ There is no difference between the “stuff” in one end of the magnet and the other, q .

.For example, ferromagnetic materials and superconductors have a magnetization that is a multiple-valued function of B due to hysteresis.^ Since the hysteresis curve is nonlinear, and is not a function (it has more than one value of M for a particular value of B ), a ferromagnetic material does not have a single, well-defined value of the permeability μ; a value like 4,000 for transformer iron represents some kind of a rough average.

^ Ferromagnetism is a phenomenon in which a material tends to organize itself so that it has a nonvanishing magnetic field.

[5]
See History below for further discussion.

The magnetic field and permanent magnets

.Permanent magnets are objects that produce their own persistent magnetic fields.^ A changing electric field can produce a magnetic field.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ Now perhaps we can use reasoning with the same flavor to show that changing magnetic fields produce curly electric fields.

^ If the current is a DC (direct current), the magnetic field is steady, like that form a permanent magnet.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

.All permanent magnets have both a north and a south pole.^ Suppose, for example, that the axis of the coil is aligned with the magnetic north-south.

^ Today, the magnetic field focuses space radiation towards the far north and south where few people live.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ The rotating Iron Core would necessarily have its rotational axis on the line connecting the North and South Magnetic Poles.
  • http://mb-soft.com/public/tecto2.html 13 January 2010 10:13 UTC mb-soft.com [Source type: FILTERED WITH BAYES]

.They are made of ferromagnetic materials such as iron and nickel that have been magnetized.^ Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ I suggested that if such motions were fast enough, they could cause magnetic polarity reversals.
  • The Earth’s Magnetic Field is Still Losing Energy 13 January 2010 10:13 UTC www.creationresearch.org [Source type: Academic]

^ Diamagnetic materials have the interesting property that they are repelled from regions of strong magnetic field, and it is therefore possible to levitate a diamagnetic object above a magnet, as in figure h .

.The strength of a magnet is represented by its magnetic moment, m; for simple magnets, m points in the direction of a line drawn from the south to the north pole of the magnet.^ That is, it is not a simple field with just a north and south pole, like a bar magnet.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ Today, the magnetic field focuses space radiation towards the far north and south where few people live.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ The bizarre implication was that at some point the entire global magnetic field had done a sudden 180-degree flip, completely reversing direction.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

.For more details about magnets see magnetization below and the article ferromagnetism.^ Let's assume a magnetic field of this form, and see what Maxwell's equations tell us about it.

^ For more information, see my review article, Physics in Ultra-strong Magnetic Fields .
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ Learn More About Current Research From Europe From Our New Report on Pulsed Magnetic Therapy Download for Free by Clicking Here .

Force on a magnet due to a non-uniform B

.Like magnetic poles brought near each other repel while opposite poles attract.^ Worse yet, the various movements of the location of the two Magnetic Poles often seem to have no relationship with each other.
  • http://mb-soft.com/public/tecto2.html 13 January 2010 10:13 UTC mb-soft.com [Source type: FILTERED WITH BAYES]

^ That is, it is not a simple field with just a north and south pole, like a bar magnet.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ But as they were well aware, magnetic north keeps moving, wandering about near the pole as the field gradually changes.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

.This is a specific example of a general rule that magnets are attracted (or repulsed depending on the orientation of the magnet) to regions of higher magnetic field.^ However, Barnes also argues strenuously against the standard theory of dynamo action generating the Earth's magnetic field.
  • Creation Science and the Earth's MagneticField 13 January 2010 10:13 UTC www.talkorigins.org [Source type: FILTERED WITH BAYES]

^ Or an example where the fields are purely electric in one frame, but purely magnetic in another?

^ All matter on Earth assists in creating this field and so becomes charged with this magnetic resonance, displaying different results, dependant on the substance.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

.For example, opposite poles attract because each magnet is pulled into the larger magnetic field near the pole of the other; the force is attractive because for each magnet m is in the same direction as the magnetic field B of the other.^ Infer the direction of the magnetic field.

^ In example 9 , the outer loop has a current in the opposite direction, so it contributes a field that is into the page.

^ And this magnet, because a magnetic field is a force field, will align itself with the Earth's magnetic field.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

.Reversing the direction of m reverses the resultant force.^ Make a sketch showing the direction of motion and the direction of the field, and show that the resulting force is in the right direction to produce circular motion.

^ Furthermore, reversing the current I in our example would have reversed the force, which would only make sense if the magnetic field had a direction in space that could be reversed.

^ When an object experiences a force with constant magnitude, which is always perpendicular to the direction of its motion, the result is that it travels in a circle.

.Magnets with m opposite to B are pushed into regions of lower magnetic field, provided that the magnet, and therefore, m does not flip due to magnetic torque.^ The torque on a current loop in a magnetic field.

^ Has the earth’s magnetic field ever flipped?
  • The Earth’s Magnetic Field is Still Losing Energy 13 January 2010 10:13 UTC www.creationresearch.org [Source type: Academic]

^ So, what does this sighting have to do with a magnetic field?
  • "MAGNETIC UFO" 13 January 2010 10:13 UTC brumac.8k.com [Source type: Academic]

.This corresponds to the like poles of two magnets being brought together.^ Becuase the magnet has two poles, then the particle would be a magnetic dipole.
  • Rosemary Ainslie | A Magnetic Field Model 13 January 2010 10:13 UTC www.energeticforum.com [Source type: General]

^ Worse yet, the various movements of the location of the two Magnetic Poles often seem to have no relationship with each other.
  • http://mb-soft.com/public/tecto2.html 13 January 2010 10:13 UTC mb-soft.com [Source type: FILTERED WITH BAYES]

^ Having two poles, one north and one south, it has the same shape as the field from a tiny but powerful bar magnet right at the center of the sphere.
  • The Earth’s Magnetic Field is Still Losing Energy 13 January 2010 10:13 UTC www.creationresearch.org [Source type: Academic]

.The ability of a nonuniform magnetic field to sort differently oriented dipoles is the basis of the Stern–Gerlach experiment, which established the quantum mechanical nature of the magnetic dipoles associated with atoms and electrons.^ But the nature of the field is evident in all magnetic fields.
  • Rosemary Ainslie | A Magnetic Field Model 13 January 2010 10:13 UTC www.energeticforum.com [Source type: General]

^ Dipole field around a magnetized sphere.
  • The Earth’s Magnetic Field is Still Losing Energy 13 January 2010 10:13 UTC www.creationresearch.org [Source type: Academic]

^ What is the difference between an electric field and a magnetic field?
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

[6][7]
Mathematically, the force on a magnet having a magnetic moment m is:[8]
\mathbf{F} = \mathbf{
abla} \left(\mathbf{m}\cdot\mathbf{B}\right),
where the .gradient is the change of the quantity m · B per unit distance and the direction is that of maximum increase of m · B.^ As the gradiometer rod was turned away from the direction of maximum frequency (maximum gradient), i.e., rotated to the left, right, upward or downward, the frequency decreased considerably.
  • "MAGNETIC UFO" 13 January 2010 10:13 UTC brumac.8k.com [Source type: Academic]

^ But when we multiply electric field by distance, what we get is an indication of the amount of work per unit charge done on a test charge that has been moved through that distance.

^ The upward direction of the maximum gradient suggests that the source may have been at or above the tops the pine trees.
  • "MAGNETIC UFO" 13 January 2010 10:13 UTC brumac.8k.com [Source type: Academic]

.(The dot product m · B = mBcos(θ), where m and B represent the magnitude of the m and B vectors and θ is the angle between them.^ The energy density of a light wave is related to the magnitudes of the fields in a specific way --- it depends on the squares of their magnitudes, E 2 and B 2 , which are the same as the dot products E ⋅ E and B ⋅ B .

^ A dot product is zero when the vectors are perpendicular, so only the top and bottom edges contribute to Γ.

^ A circulation is defined by breaking up a loop into tiny segments, d s , and adding up the dot products of these distance vectors with the field.

) .This equation is strictly only valid for magnets of zero size, but it can often be used as an approximation for not too large magnets.^ An infinite magnetic circulation Γ B can only be produced by an infinite magnetic field, so without the ∂Φ E /∂ t term, Maxwell's equations predict nonsense: the edge of the surface would experience an infinite magnetic field at one instant, and zero magnetic field at all other times.

^ An easy way to approach this is to use the fact that vB has the same units as E , which can be seen by comparing the equations for magnetic and electric forces used above.

^ It only tells us that we can't make them using magnetic monopoles.

.The magnetic force on larger magnets is determined by dividing them into smaller regions having their own m then summing up the forces on each of these regions.^ Plugging all these values into the equation gives a result of a Magnetic Flux of around 4 * 10 25 Maxwells.
  • http://mb-soft.com/public/tecto2.html 13 January 2010 10:13 UTC mb-soft.com [Source type: FILTERED WITH BAYES]

^ This is because the current in the coil sets up its own magnetic field, and that field exerts a torque on the magnet.

^ The charge by itself up above the wire is like a test charge, being used to determine the magnetic and electric fields created by the wire.

.The force between two magnets is quite complicated and depends on the orientation of both magnets and the distance of the magnets relative to each other.^ Find the induced magnetic field at a point between the plates, at a distance R from the axis.

^ As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

^ There are two primary methods by which one can generate a mathematical description of the Earth's magnetic field, or any other field for that matter.
  • Creation Science and the Earth's MagneticField 13 January 2010 10:13 UTC www.talkorigins.org [Source type: FILTERED WITH BAYES]

.The force is particularly sensitive to rotations of the magnets due to magnetic torque.^ One solution to this problem relies on the fact that the force experienced by a charged particle in an electric field, F E =q E , is independent of its velocity, but the force due to a magnetic field, F B =q v × B , isn't.

^ The magnetic force on the lone charge q due to the current I is .

^ This would therefore mean that the only remaining rotation that could induce a magnetic field today would be due to the daily rotation of the Earth.
  • http://mb-soft.com/public/tecto2.html 13 January 2010 10:13 UTC mb-soft.com [Source type: FILTERED WITH BAYES]

.In many cases, the force and the torque on a magnet can be modeled quite well by assuming a 'magnetic charge' at the poles of each magnet and using a magnetic equivalent to Coulomb's law.^ These lodestones have been charged by the Earth, and thus are harmoniously in tune with the human bodies' frequencies as well, they have for thousands of years been successfully used in the healing arts.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ The simple dipole model can be used to calculate the equivalent source strength, Bo, from the gradient measured by J's instrument if the distance to the source is known or assumed.
  • "MAGNETIC UFO" 13 January 2010 10:13 UTC brumac.8k.com [Source type: Academic]

^ When charged particles are moving, they make magnetic fields as well.

.In this model, each magnetic pole is a source of an H-field that is stronger near the pole.^ Magnetic fields have no sources or sinks.

^ The fact that this theory suggests that the Earth's Magnetic Field measured at the surface (or in space) is a result of the vector sum of two much stronger but generally opposing source fields, enables straightforward explanation of many of the peculiar characteristics measured in the Earth's Magnetic Field.
  • http://mb-soft.com/public/tecto2.html 13 January 2010 10:13 UTC mb-soft.com [Source type: FILTERED WITH BAYES]

^ For instance, what should happen to the radius when the magnetic field is made stronger?

.An external H-field exerts a force in the direction of H on a north pole and opposite to H on a south pole.^ Today, the magnetic field focuses space radiation towards the far north and south where few people live.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ By symmetry, the field in this plane cannot have any component in the radial direction (inward toward the dipole, or outward away from it); it is perpendicular to the plane, and in the opposite direction compared to the dipole vector.

^ This same problem applies equally to explaining the short-term variations in both magnetic field strength and direction and in explaining erratic magnetic pole migration.
  • http://mb-soft.com/public/tecto2.html 13 January 2010 10:13 UTC mb-soft.com [Source type: FILTERED WITH BAYES]

.In a nonuniform magnetic field, each pole sees a different field and is subject to a different force.^ What is the difference between an electric field and a magnetic field?
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

^ If the velocity vector is initially perpendicular to the field, then the curve of its motion will remain in the plane perpendicular to the field, so the magnitude of the magnetic force on it will stay the same.

.The difference in the two forces moves the magnet in the direction of increasing magnetic field and may also cause a net torque.^ Where is the moving charge responsible for this magnetic field?

^ Infer the direction of the magnetic field.

^ The torque on a current loop in a magnetic field.

.Unfortunately, the idea of "poles" does not accurately reflect what happens inside a magnet (see ferromagnetism).^ The present premise does NOT require this, and includes a mechanism for explaining the separation of the Geographic and Magnetic Poles.
  • http://mb-soft.com/public/tecto2.html 13 January 2010 10:13 UTC mb-soft.com [Source type: FILTERED WITH BAYES]

^ We, and all other living things, are surrounded by a magnetic field extending out into space from our bodies, and the fields from the brain reflect what is happening in the brain.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

.For instance, a small magnet placed inside of a larger magnet feels a force in the opposite direction.^ Humans have an innate ability to sense the direction of magnetic north, and this ability can be blocked by placing a bar magnet against a person's forehead for only fifteen minutes!
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ DANIEL LATHROP: We apply a large magnetic field on the sodium flow inside the sphere, and you can get a feel for how strong the magnetic field is.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ My 1990 paper shows that as upwelling core fluid expels magnetic flux, it also generates loops of new lines of force in the reversed direction.
  • The Earth’s Magnetic Field is Still Losing Energy 13 January 2010 10:13 UTC www.creationresearch.org [Source type: Academic]

.The more physically correct description of magnetism involves atomic sized loops of current distributed throughout the magnet.^ The torque on a current loop in a magnetic field.

^ A much more useful building block is a square current loop.

^ Likewise, as shown in figure f , if we could find the magnetic field of a square dipole, then we could find the field of any planar loop of current by adding the contributions to the field from all the squares.

[9]

Torque on a magnet due to a B-field

.In the presence of an external magnetic field B, a magnet will experience a torque that tends to align its poles with the direction of B.^ Infer the direction of the magnetic field.

^ The torque on a current loop in a magnetic field.

^ A compass needle in a magnetic field experiences a torque which tends to align it with the field.

.The torque on a magnet due to an external magnetic field is easy to observe by placing two magnets near each other while allowing one to rotate.^ The torque on a current loop in a magnetic field.

^ Roughly speaking, it looks like the field of one big dipole, especially farther away from the magnet.

^ As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

The torque τ on a small magnet is proportional both to the applied B-field and to the magnetic moment m of the magnet:
\boldsymbol{	au}=\mathbf{m}	imes\mathbf{B}, \,
where × represents the vector cross product. .The torque τ will tend to align the magnet's poles with the B-field lines.^ The torque on a current loop in a magnetic field.

^ A compass needle in a magnetic field experiences a torque which tends to align it with the field.

^ A dipole tends to align itself to the surrounding magnetic field.

.This phenomenon explains why the magnetic needle of a compass points toward the Earth's north pole.^ However, a compass needle doesn't point at true north, at the real geographical North Pole, instead it points at magnetic north.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ It's what makes our compasses point north.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ Today the Earth's magnetic field runs from south to north—which is why compass needles point towards the North Pole—and recent lava flows record a field pointing north.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

.By definition, the direction of the local magnetic field is the direction that the north pole of a compass (or of any magnet) tends to point.^ It's what makes our compasses point north.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ Infer the direction of the magnetic field.

^ A compass needle in a magnetic field experiences a torque which tends to align it with the field.

.Magnetic torque is used to drive simple electric motors.^ An electric motorized clock, plugged into a wall socket, produces an amazingly high magnetic field because of the small electric motor that runs it.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ Now perhaps we can use reasoning with the same flavor to show that changing magnetic fields produce curly electric fields.

^ The charge by itself up above the wire is like a test charge, being used to determine the magnetic and electric fields created by the wire.

.In one simple motor design, a magnet is fixed to a freely rotating shaft (forming a rotor) and subjected to a magnetic field from an array of electromagnets—called the stator.^ A magnetic field in the form of a sine wave.

^ Roughly speaking, it looks like the field of one big dipole, especially farther away from the magnet.

^ These data further support a role of free radicals on the effects of magnetic fields.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

.By continuously switching the electrical current through each of the electromagnets, thereby flipping the polarity of their magnetic fields, the stator keeps like poles next to the rotor; The resultant magnetic torque is transferred to the shaft.^ In particular, the fact that electric currents create magnetic fields.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

^ Scientists believe that just as the electric currents produce the magnetic field, so the magnetic field produces the electric currents.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

.The inverse process, changing mechanical motion to electrical energy, is accomplished by the inverse of the above mechanism in the electric generator.^ These processes use artificial electrical energy, which has within its structure a frequency composition different to that of nature.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ Summing up, we propose that magnetic fields initiate an iron-dependent free radical generation process in cells, which can lead to genotoxic changes and/or cell death.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

^ Simply stated, it has been shown that turbulent motions within an electrically conductive fluid will generate magnetic fields.
  • Creation Science and the Earth's MagneticField 13 January 2010 10:13 UTC www.talkorigins.org [Source type: FILTERED WITH BAYES]

.See Rotating magnetic fields below for an example using this effect with electromagnets.^ We're already seeing acute effects that are noticed within minutes of using a cell phone.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ MR ( magnetoresistive ) A technology based on the effect where electrical resistance in a material changes when brought in contact with a magnetic field .
  • Pro Audio Reference M 13 January 2010 10:13 UTC www.rane.com [Source type: FILTERED WITH BAYES]

^ As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

Visualizing the magnetic field using field lines

.
Magnetic field lines shown by iron filings.
^ Treatment with the iron chelator deferiprone also blocked the effects of magnetic fields on brain cell DNA, suggesting the involvement of iron.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

^ Hz magnetic field at 7 mT in the presence of iron cations.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

^ The magnetic field pattern around a bar magnet is created by the superposition of the dipole fields of the individual iron atoms.

The field lines are not precisely the same as the isolated magnet; the magnetization of the filings alters the field somewhat.
.Mapping out the strength and direction of the magnetic field is simple in principle.^ The arrows map the magnetic field B .

^ Infer the direction of the magnetic field.

^ Milligauss is a unit of flux density , not magnetic field strength, but the difference is not important.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

.First, measure the strength and direction of the magnetic field at a large number of locations.^ Infer the direction of the magnetic field.

^ In addition to this, the STRENGTH of the measured magnetic field also has a number of variations and drifts.
  • http://mb-soft.com/public/tecto2.html 13 January 2010 10:13 UTC mb-soft.com [Source type: FILTERED WITH BAYES]

^ MARIO ACUNA: So here is my spring, here's my magnet, and if I pass an electrical current through my spring and measure the disturbance of my magnet, which is inside, then I can transmit back to Earth the information about the strength and the direction of the field we are trying to measure.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

.Then mark each location with an arrow (called a vector) pointing in the direction of the local magnetic field with a length proportional to the strength of the magnetic field.^ Infer the direction of the magnetic field.

^ The arrows map the magnetic field B .

^ Its strength is proportional to the rate at which the field changes.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

An alternative method of visualizing the magnetic field which greatly simplifies the diagram while containing the same information is to 'connect' the arrows to form "magnetic field lines".
.
Compasses reveal the direction of the local magnetic field.
^ Infer the direction of the magnetic field.

^ The current is at right angles to the direction of the changing magnetic field, and is strongest near the extremities of a person.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ The bizarre implication was that at some point the entire global magnetic field had done a sudden 180-degree flip, completely reversing direction.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

As seen here, the magnetic field points towards a magnet's south pole and away from its north pole.
.Various physical phenomena have the effect of displaying magnetic field lines.^ MR ( magnetoresistive ) A technology based on the effect where electrical resistance in a material changes when brought in contact with a magnetic field .
  • Pro Audio Reference M 13 January 2010 10:13 UTC www.rane.com [Source type: FILTERED WITH BAYES]

^ Treatment with the iron chelator deferiprone also blocked the effects of magnetic fields on brain cell DNA, suggesting the involvement of iron.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

^ Because the other studies reporting effects of magnetic fields on DNA were carried out under continuous exposure conditions, the results of Ivancsits et al.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

.For example, iron filings placed in a magnetic field line up in such a way as to visually show the orientation of the magnetic field (see figure to left).^ Figure 1a shows the magnetic lines of force outside a magnetized sphere.
  • The Earth’s Magnetic Field is Still Losing Energy 13 January 2010 10:13 UTC www.creationresearch.org [Source type: Academic]

^ Figure b shows a mysterious curly magnetic field.

^ As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

.Magnetic fields lines are also visually displayed in polar auroras, in which plasma particle dipole interactions create visible streaks of light that line up with the local direction of Earth's magnetic field.^ The earth's magnetic field impacts climate .
  • A Weakening Magnetic Field and Emerging Sunspot Cycle 24... What Does This Mean for Planet Earth and All Species? | KnowTheLies.com - The Truth is Hidden in Plain View... 13 January 2010 10:13 UTC www.knowthelies.com [Source type: FILTERED WITH BAYES]

^ Infer the direction of the magnetic field.

^ Recent trends in the earth’s magnetic field.
  • The Earth’s Magnetic Field is Still Losing Energy 13 January 2010 10:13 UTC www.creationresearch.org [Source type: Academic]

.Field lines provide a simple way to depict or draw the magnetic field (or any other vector field).^ We can also anticipate that the magnetic field will be a vector.

^ In reception, both conductors are bathed in the same electric and magnetic fields, so an emf that adds current on one side subtracts current from the other side, resulting in cancellation.

^ If this single particle qualifies as a current, then it should be surrounded by a curly magnetic field, just like any other current.

.The magnetic field can be estimated at any point (whether on a field line or not) using the direction and density of the field lines nearby.^ Infer the direction of the magnetic field.

^ The electric field at point P is , and the magnetic field is .

^ As it spins, the nearby magnetic field changes.

[10] .A higher density of nearby field lines indicates a larger magnetic field.^ As it spins, the nearby magnetic field changes.

^ These data indicate an interaction between intensity and duration of exposure on biologic effects of magnetic fields.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

^ If the sample is initially unmagnetized, 1, and a field H is externally applied, the magnetization increases, 2, but eventually becomes saturated, 3, so that higher fields do not result in any further magnetization, 4.

.Field lines are also a good qualitative tool for visualizing magnetic forces.^ Figure 1a shows the magnetic lines of force outside a magnetized sphere.
  • The Earth’s Magnetic Field is Still Losing Energy 13 January 2010 10:13 UTC www.creationresearch.org [Source type: Academic]

^ For a purely dipolar field, the equation r = R sin 2 q relates the radius r and colatitude q of each point on a given line of force, R being the value of r where the line of force intersects the equatorial plane.
  • The Earth’s Magnetic Field is Still Losing Energy 13 January 2010 10:13 UTC www.creationresearch.org [Source type: Academic]

^ It is that a magnetic field is a primary force in the same way as gravity is seen as a primry force.
  • Rosemary Ainslie | A Magnetic Field Model 13 January 2010 10:13 UTC www.energeticforum.com [Source type: General]

.In ferromagnetic substances like iron and in plasmas, magnetic forces can be understood by imagining that the field lines exert a tension, (like a rubber band) along their length, and a pressure perpendicular to their length on neighboring field lines.^ Treatment with the iron chelator deferiprone also blocked the effects of magnetic fields on brain cell DNA, suggesting the involvement of iron.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

^ Hz magnetic field at 7 mT in the presence of iron cations.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

^ If the current is a DC (direct current), the magnetic field is steady, like that form a permanent magnet.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

.'Unlike' poles of magnets attract because they are linked by many field lines; 'like' poles repel because their field lines do not meet, but run parallel, pushing on each other.^ Roughly speaking, it looks like the field of one big dipole, especially farther away from the magnet.

^ They actually trap in...they record the Earth's magnetic field.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ An electric motorized clock, plugged into a wall socket, produces an amazingly high magnetic field because of the small electric motor that runs it.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

.The direction of a magnetic field line can be revealed using a compass.^ Infer the direction of the magnetic field.

^ Describe the direction of the magnetic field that would be produced, at its center, by the loop in the x - y plane alone.

^ Acting like microscopic compass needles, they record not only how strong the field is, but also in what direction it is pointing.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

.A compass placed near the north pole of a magnet points away from that pole—like poles repel.^ It's what makes our compasses point north.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ Roughly speaking, it looks like the field of one big dipole, especially farther away from the magnet.

^ For reasons not fully understood, CMEs in even-numbered solar cycles (like 24) tend to hit Earth with a leading edge that is magnetized north.
  • A Weakening Magnetic Field and Emerging Sunspot Cycle 24... What Does This Mean for Planet Earth and All Species? | KnowTheLies.com - The Truth is Hidden in Plain View... 13 January 2010 10:13 UTC www.knowthelies.com [Source type: FILTERED WITH BAYES]

.The opposite occurs for a compass placed near a magnet's south pole.^ When the Voyager II space probe flew past Uranus and Neptune, the apparent north and south magnetic poles were sizably offset from where the rotational pole was in earlier recordings.
  • A Weakening Magnetic Field and Emerging Sunspot Cycle 24... What Does This Mean for Planet Earth and All Species? | KnowTheLies.com - The Truth is Hidden in Plain View... 13 January 2010 10:13 UTC www.knowthelies.com [Source type: FILTERED WITH BAYES]

^ That is, it is not a simple field with just a north and south pole, like a bar magnet.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ But as they were well aware, magnetic north keeps moving, wandering about near the pole as the field gradually changes.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

.The magnetic field points away from a magnet near its north pole and towards a magnet near its south pole.^ That is, it is not a simple field with just a north and south pole, like a bar magnet.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ The electric field at point P is , and the magnetic field is .

^ Today the Earth's magnetic field runs from south to north—which is why compass needles point towards the North Pole—and recent lava flows record a field pointing north.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

.Magnetic field lines outside of a magnet point from the north pole to the south.^ That is, it is not a simple field with just a north and south pole, like a bar magnet.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ The electric field at point P is , and the magnetic field is .

^ (In this way, they resemble the field lines of an iron bar magnet, which arch from the north to the south poles.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

.Not all magnetic fields are describable in terms of poles, though.^ All matter on Earth assists in creating this field and so becomes charged with this magnetic resonance, displaying different results, dependant on the substance.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ "A general type of mathematical argument is described, which applies to all the cases in which dynamo maintenance of a steady magnetic field by motion in a uniform mass is known to be impossible.
  • Creation Science and the Earth's MagneticField 13 January 2010 10:13 UTC www.talkorigins.org [Source type: FILTERED WITH BAYES]

^ They suggests that specific tones described as g-mode vibrations are picked up by the magnetic field at the Sun’s surface.
  • A Weakening Magnetic Field and Emerging Sunspot Cycle 24... What Does This Mean for Planet Earth and All Species? | KnowTheLies.com - The Truth is Hidden in Plain View... 13 January 2010 10:13 UTC www.knowthelies.com [Source type: FILTERED WITH BAYES]

.A straight current-carrying wire, for instance, produces a magnetic field that points neither towards nor away from the wire, but encircles it instead.^ Scientists believe that just as the electric currents produce the magnetic field, so the magnetic field produces the electric currents.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ Any wire that carries an AC electrical current produces magnetic fields.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ The v oltage on a wire produces electric fields.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

B-field lines never end

.Field lines are a useful way to represent any vector field and often reveal sophisticated properties of fields quite simply.^ The Russian National Academy of Sciences doesn't give us a time-line, but the change from what was known and accepted to the way it is now represents a 1000 percent increase.
  • A Weakening Magnetic Field and Emerging Sunspot Cycle 24... What Does This Mean for Planet Earth and All Species? | KnowTheLies.com - The Truth is Hidden in Plain View... 13 January 2010 10:13 UTC www.knowthelies.com [Source type: FILTERED WITH BAYES]

^ A vector going into the page is represented using the tailfeathers of the arrow.

^ (The minus sign simply represents the right-handed relationship of the fields relative to their direction of propagation.

.One important property of the B-field is that it is a solenoidal vector field.^ We could, for example, have two solenoidal coils, one in the outgoing line and one in the return line, interwound with one another with their windings oriented so that their differential-mode fields would cancel.

^ In chapter 10 , one of the most important goals was to learn how to calculate the electric field for a given charge distribution.

^ Assume they are long enough to act like ideal solenoids, so that each one only contributes significantly to the field inside itself, and the interior fields are nearly uniform.

.In field line terms, this means that magnetic field lines neither start nor end: They always either form closed curves ("loops"), or extend to and from infinity.^ The torque on a current loop in a magnetic field.

^ A magnetic field in the form of a sine wave.

^ NARRATOR: As Mars Global Surveyor started to send back data, it soon became clear to Mario and the team that today Mars has no overall magnetic field.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

To date no exception to this rule has been found. (See magnetic monopole below.)
.Magnetic field exits a magnet near its north pole and enters near its south pole but inside the magnet B-field lines return from the south pole back to the north.^ That is, it is not a simple field with just a north and south pole, like a bar magnet.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ (In this way, they resemble the field lines of an iron bar magnet, which arch from the north to the south poles.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ It appears to orbit, north to south and back to north.
  • Rosemary Ainslie | A Magnetic Field Model 13 January 2010 10:13 UTC www.energeticforum.com [Source type: General]

[11] .If a B-field line enters a magnet somewhere it has to leave somewhere else; it is not allowed to have an end point.^ The electric field at point P is , and the magnetic field is .

^ The bizarre implication was that at some point the entire global magnetic field had done a sudden 180-degree flip, completely reversing direction.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ In the language of space physics, a north-pointing solar magnetic field is called a "northern IMF" and it is synonymous with shields up.
  • A Weakening Magnetic Field and Emerging Sunspot Cycle 24... What Does This Mean for Planet Earth and All Species? | KnowTheLies.com - The Truth is Hidden in Plain View... 13 January 2010 10:13 UTC www.knowthelies.com [Source type: FILTERED WITH BAYES]

.For this reason, magnetic poles always come in N and S pairs.^ (Recall that the radio beams in an ordinary pulsar come from a rotation-driven outflow of charged particles above the magnetic poles.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

.Cutting a magnet in half results in two separate magnets each with both a north and a south pole.^ Suppose, for example, that the axis of the coil is aligned with the magnetic north-south.

^ Today, the magnetic field focuses space radiation towards the far north and south where few people live.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ Two separate physical reasons for a proportionality to length result in an overall proportionality to length squared, which is the same as the area of the loop.

.Magnetic fields are produced by electric currents, which can be macroscopic currents in wires, or microscopic currents associated with electrons in atomic orbits.^ An electric current flowing in a wire or coil produces its own magnetic field.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ In particular, the fact that electric currents create magnetic fields.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ The magnetic field of a long, straight wire.

.The magnetic field B is defined in terms of force on moving charge in the Lorentz force law.^ Where is the moving charge responsible for this magnetic field?

^ Definition in terms of the force on a moving particle .

^ Likewise, we want to define a magnetic field, B .

.The interaction of magnetic field with charge leads to many practical applications.^ Where is the moving charge responsible for this magnetic field?

^ Thus the magnetic field acts like a "bottle," holding charged particles.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ Modify the calculation on page 617 to determine the component of the magnetic field of a sheet of charge that is perpendicular to the sheet.

.The SI unit for magnetic field is the tesla, which can be seen from the magnetic part of the Lorentz force law Fmag = (qv × B) to be equivalent to (newton × second)/(coulomb × metre).^ GARY GLATZMAIER: Now this movie will show part of a simulation that spans a magnetic field reversal.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ If the velocity vector is initially perpendicular to the field, then the curve of its motion will remain in the plane perpendicular to the field, so the magnitude of the magnetic force on it will stay the same.

^ In the same way I proposed that a magnetic flux field may also comprise particles being the smallest part of the whole field.
  • Rosemary Ainslie | A Magnetic Field Model 13 January 2010 10:13 UTC www.energeticforum.com [Source type: General]

.A smaller magnetic field unit is the gauss (1 tesla = 10,000 gauss).^ The field must be roughly 10 14 Gauss or more to cause the deep-crust solid to fail.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ In this frame of reference, the earth is moving, and therefore the local magnetic field is changing in strength by 10 -9 T/s.

Magnetic monopole (hypothetical)

.A magnetic monopole is a hypothetical particle (or class of particles) that has, as its name suggests, only one magnetic pole (either a north pole or a south pole).^ Today, the magnetic field focuses space radiation towards the far north and south where few people live.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ (Recall that the radio beams in an ordinary pulsar come from a rotation-driven outflow of charged particles above the magnetic poles.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ Maine The only American state whose name is just one syllable.
  • Pro Audio Reference M 13 January 2010 10:13 UTC www.rane.com [Source type: FILTERED WITH BAYES]

.In other words, it would possess a "magnetic charge" analogous to electric charge.^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

^ This buildup of charge would start to quench both currents due to electrical forces, but the current in the right side of the wire, which is driven by the weaker magnetic field, would be the first to stop.

^ From arguments about relative motion, we concluded that moving electric charges create magnetic fields.

.Modern interest in this concept stems from particle theories, notably Grand Unified Theories and superstring theories, that predict either the existence or the possibility of magnetic monopoles.^ Both possibilities are probable, and in either event they would lose their structure as a string and collapse into a field of dissassociated particles, half of which would be manifest as truants.
  • Rosemary Ainslie | A Magnetic Field Model 13 January 2010 10:13 UTC www.energeticforum.com [Source type: General]

^ Diamagnetic materials have the interesting property that they are repelled from regions of strong magnetic field, and it is therefore possible to levitate a diamagnetic object above a magnet, as in figure h .

^ Perhaps some exotic form of matter exists, composed of particles that are magnetic monopoles.

.These theories and others have inspired extensive efforts to search for monopoles.^ For these admittedly subjective reasons, there have been several searches for magnetic monopoles.

.Despite these efforts, no magnetic monopole has been observed to date.^ No magnetic monopoles .

^ For these admittedly subjective reasons, there have been several searches for magnetic monopoles.

[12]
In recent research materials known as spin ices can simulate monopoles, but do not contain actual monopoles.

H-field lines begin and end near magnetic poles

.Outside a magnet H-field lines are identical to B-field lines, but inside they point in opposite directions.^ They actually trap in...they record the Earth's magnetic field.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ MARIO ACUNA: So here is my spring, here's my magnet, and if I pass an electrical current through my spring and measure the disturbance of my magnet, which is inside, then I can transmit back to Earth the information about the strength and the direction of the field we are trying to measure.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ So it's really currents inside the Earth's liquid metal core that we think gives rise to the magnetic field.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

.Whether inside or out of a magnet, H-field lines start near the S pole and end near the N. The H-field, therefore, is analogous to the electric field E which starts as a positive charge and ends at a negative charge.^ This electric field is not created by charges .

^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

^ Where is the moving charge responsible for this magnetic field?

.It is tempting, therefore, to model magnets in terms of magnetic charges localized near the poles.^ In this frame of reference, the earth is moving, and therefore the local magnetic field is changing in strength by 10 -9 T/s.

^ (Recall that the radio beams in an ordinary pulsar come from a rotation-driven outflow of charged particles above the magnetic poles.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ E 1 = 0 In frame 1, any force experienced by the lone charge must therefore be attributed solely to magnetism.

.Unfortunately, this model is incorrect; it often fails when determining the magnetic field inside of magnets for instance.^ Determine the electric and magnetic fields.

^ Modify the calculation on page 617 to determine the component of the magnetic field of a sheet of charge that is perpendicular to the sheet.

^ So it's really currents inside the Earth's liquid metal core that we think gives rise to the magnetic field.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

.(See #Force on a magnet due to a non-uniform B above.^ Assume that no other forces are present besides the possible electrical and magnetic ones, and that the fields, if they are present, are uniform.

^ A charged particle of mass m and charge q moves in a circle due to a uniform magnetic field of magnitude B , which points perpendicular to the plane of the circle.

^ The magnetic force on the lone charge q due to the current I is .

)

The magnetic field and electrical currents

.Currents of electrical charges both generate a magnetic field and feel a force due to magnetic B-fields.^ This electric field is not created by charges .

^ In particular, the fact that electric currents create magnetic fields.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

Magnetic field due to moving charges and electrical currents

Right hand grip rule: current (I) flowing through a conductor in the direction indicated by the white arrow produces a magnetic field (B) around the conductor as shown by the red arrows.
.All moving charged particles produce magnetic fields.^ But the nature of the field is evident in all magnetic fields.
  • Rosemary Ainslie | A Magnetic Field Model 13 January 2010 10:13 UTC www.energeticforum.com [Source type: General]

^ Where is the moving charge responsible for this magnetic field?

^ A charged particle is in a region of space in which there is a uniform magnetic field .

[13] .Moving point charges, such as electrons, produce complicated but well known magnetic fields that depend on the charge, velocity, and acceleration of the particles.^ The electric field at point P is , and the magnetic field is .

^ When charged particles are moving, they make magnetic fields as well.

^ But magnetism deflects charged particles.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

[14]
.Magnetic field lines form in concentric circles around a cylindrical current-carrying conductor, such as a length of wire.^ Any wire that carries an AC electrical current produces magnetic fields.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ We have a circling atomic current inside the circling current in the wires.

^ What is the magnetic field inside a long, straight wire in which the current density is j ?

.The direction of such a magnetic field can be determined by using the "right hand grip rule" (see figure at right).^ In general, determine these plus and minus signs using the right-hand rule shown in the figure.

^ Determine the electric and magnetic fields.

^ If possible, determine the direction of the magnetic or electric field.

.The strength of the magnetic field decreases in inverse proportion to the square of the distance from the conductor (inverse-square law).^ Its strength is proportional to the rate at which the field changes.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ Milligauss is a unit of flux density , not magnetic field strength, but the difference is not important.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ Find the induced magnetic field at a point between the plates, at a distance R from the axis.

[citation needed]
.Bending a current-carrying wire into a loop concentrates the magnetic field inside the loop while weakening it outside.^ Any wire that carries an AC electrical current produces magnetic fields.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ We have a circling atomic current inside the circling current in the wires.

^ What is the magnetic field inside a long, straight wire in which the current density is j ?

.Bending a wire into multiple closely-spaced loops to form a coil or "solenoid" enhances this effect.^ Problem 33 dealt with the dependence of a transformer's gain on the number of loops of wire in the input solenoid.

^ A type of electromagnetic transducer that operates by having a mechanical device move a coil of wire in a magnetic filed to convert the mechanical movement into an electrical current.
  • Pro Audio Reference M 13 January 2010 10:13 UTC www.rane.com [Source type: FILTERED WITH BAYES]

^ Each coil is made of two sets of 40 turns each of #6 wire wound in rectangular loops, with minimum internal dimensions of 0.86 0.543 m.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

.A device so formed around an iron core may act as an electromagnet, generating a strong, well-controlled magnetic field.^ Ultra-strong magnetic fields .
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ Scientists have a theory about how the core generates the magnetic field.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ Strong magnetic fields * .
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

.An infinitely long electromagnet has a uniform magnetic field inside, and no magnetic field outside.^ Magnetic fields have no sources or sinks.

^ What is the magnetic field inside a long, straight wire in which the current density is j ?

^ Do we have infinite energy in the resulting magnetic field?

.A finite length electromagnet produces essentially the same magnetic field as a uniform permanent magnet of the same shape and size, with its strength and polarity determined by the current flowing through the coil.^ Scientists believe that just as the electric currents produce the magnetic field, so the magnetic field produces the electric currents.
  • NOVA | Transcripts | Magnetic Storm | PBS 13 January 2010 10:13 UTC www.pbs.org [Source type: Original source]

^ Any wire that carries an AC electrical current produces magnetic fields.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ In 3, a permanent magnet with double the strength has been used.

[citation needed]
The magnetic field generated by a steady[15] current I (a constant flow of charges in which charge is neither accumulating nor depleting at any point) is described by the Biot–Savart law:
 \mathbf{B} = \frac{\mu_0I}{4\pi}\oint\frac{d\boldsymbol{\ell} 	imes \mathbf{\hat r}}{r^2},
where the integral sums over the entire loop of a wire with .d a particular infinitesimal piece of that loop, μ0 is the magnetic constant, r is the distance between the location of d and the location at which the magnetic field is being calculated, and \scriptstyle\mathbf{\hat r} is a unit vector in the direction of r.^ What is the difference between an electric field and a magnetic field?
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ If a magnet is dropped on a hard floor, the magnetic field is destroyed because the atoms are "shaken up" and their direction is changed, resulting in a random pattern.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ No significant difference between magnetic field and sham in Trolox-treated animals.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

A slightly more general[16][17] way of relating the current I to the B-field is through Ampère's law:
\oint \mathbf{B} \cdot d\boldsymbol{\ell} = \mu_0 I_{\mathrm{enc}},
where the integral is over any arbitrary loop and Ienc is the current enclosed by that loop. .Ampère's law is always valid for steady currents and can be used to calculate the B-field for certain highly symmetric situations such as an infinite wire or an infinite solenoid.^ But we can build just about any static current distribution we like using such a bundle of wires, so it follows that Ampère's law is valid for any static current distribution.

^ Carry out this calculation, using the result for the field of a wire that was established without using Ampère's law.

^ So far, however, we only know how to calculate the magnetic field of a long, straight wire, .

.In a modified form that accounts for time varying electric fields, Ampère's law is one of four Maxwell's equations that describe electricity and magnetism.^ The Φ E equation is Gauss' law: charges make diverging electric fields.

^ What is the velocity of the waves described by Maxwell's equations?

^ The electric field at point P is , and the magnetic field is .

Force due to a B-field on a moving charge

Force on a charged particle

Beam of electrons moving in a circle. Lighting is caused by excitation of atoms of gas in a bulb.
.A charged particle moving in a B-field experiences a sideways force that is proportional to the strength of the magnetic field, the component of the velocity that is perpendicular to the magnetic field and the charge of the particle.^ When charged particles are moving, they make magnetic fields as well.

^ Where is the moving charge responsible for this magnetic field?

^ A charged particle is in a region of space in which there is a uniform magnetic field .

This force is known as the Lorentz force, and is given by
\mathbf{F} = q (\mathbf{v} 	imes \mathbf{B}),
where .F is the force, q is the electric charge of the particle, v is the instantaneous velocity of the particle, and B is the magnetic field (in teslas).^ This electric field is not created by charges .

^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

^ Where is the moving charge responsible for this magnetic field?

.The Lorentz force is always perpendicular to both the velocity of the particle and the magnetic field that created it.^ A changing magnetic field can create an electric field.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ The direction of the force is at right angles both to the direction of the magnetic field and the direction of the current.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ Suppose a charged particle is moving through a region of space in which there is an electric field perpendicular to its velocity vector, and also a magnetic field perpendicular to both the particle's velocity vector and the electric field.

.Neither a stationary particle nor one moving in the direction of the magnetic field lines experiences a force.^ Where is the moving charge responsible for this magnetic field?

^ Definition in terms of the force on a moving particle .

^ Infer the direction of the magnetic field.

.For that reason, charged particles move in a circle (or more generally, in a helix) around magnetic field lines; this is called cyclotron motion.^ Where is the moving charge responsible for this magnetic field?

^ A charged particle is in a region of space in which there is a uniform magnetic field .

^ When charged particles are moving, they make magnetic fields as well.

.Because the magnetic force is always perpendicular to the motion, the magnetic fields can do no work on an isolated charge.^ Because the other studies reporting effects of magnetic fields on DNA were carried out under continuous exposure conditions, the results of Ivancsits et al.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

^ No charge will actually flow through the air gap between them, yet a magnetic field will be created in that gap as if the charge were flowing.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

.It can and does, however, change the particle's direction, even to the extent that a force applied in one direction can cause the particle to drift in a perpendicular direction.^ The magnetic force is always perpendicular to the motion of the particle, so it can never do any work, and a charged particle moving through a magnetic field does not experience any change in its kinetic energy: its velocity vector can change its direction, but not its magnitude.

^ However, having said that there is the chance that, at it's worst - it might entertain a purist to see the bazaar machinations of thought applied by an outsider to the complexity of the forces.
  • Rosemary Ainslie | A Magnetic Field Model 13 January 2010 10:13 UTC www.energeticforum.com [Source type: General]

^ Show that there will be one particular velocity at which the particle can be moving that results in a total force of zero on it.

.It is often claimed that the magnetic force can do work to a non-elementary magnetic dipole, or to charged particles whose motion is constrained by other forces, but this is not the case[18] because the work in those cases is performed by the electric forces of the charges deflected by the magnetic field.^ Note that the magnetic field never does work on a charged particle, because its force is perpendicular to the motion; the electric power is actually coming from the mechanical work that had to be done to spin the coil.

^ This electric field is not created by charges .

^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

Force on current-carrying wire

.The force on a current carrying wire is similar to that of a moving charge as expected since a charge carrying wire is a collection of moving charges.^ The moving charges in the wire attract the moving charges in the electron beam, causing the electrons to curve.

^ Since the charge densities don't cancel, there is an electric field in frame 2, which points into the wire, attracting the lone charge.

^ This buildup of charge would start to quench both currents due to electrical forces, but the current in the right side of the wire, which is driven by the weaker magnetic field, would be the first to stop.

.A current carrying wire feels a sideways force in the presence of a magnetic field.^ Find the magnetic force on the wire.

^ Any wire that carries an AC electrical current produces magnetic fields.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ What is the magnetic field inside a long, straight wire in which the current density is j ?

.The Lorentz force on a macroscopic current is often referred to as the Laplace force.^ There is no induction going on in this frame of reference; the forces that cause the current are just the ordinary magnetic forces experienced by any charged particle moving through a magnetic field.

.
The right-hand rule: Pointing the thumb of the right hand in the direction of the conventional current or moving positive charge and the fingers in the direction of the B-field the force on the current points out of the palm.
^ Where is the moving charge responsible for this magnetic field?

^ By the right-hand rule, the curl points out of the page, i.e., along the positive z axis, so we have .

^ This is in agreement with the right-hand rule.

The force is reversed for a negative charge.

Direction of force

.The direction of force on a positive charge or a current is determined by the right-hand rule.^ Verify the direction of the force using right-hand rules.

^ This agrees with the right-hand rule.

^ Apply the right-hand rule again to find the direction of wire 2's force on wire 1.

See the figure on the right. .Using the right hand and pointing the thumb in the direction of the moving positive charge or positive current and the fingers in the direction of the magnetic field the resulting force on the charge points outwards from the palm.^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

^ Where is the moving charge responsible for this magnetic field?

^ Infer the direction of the magnetic field.

.The force on a negatively charged particle is in the opposite direction.^ In what direction should the particle be moving in order to minimize the total force acting on it?

^ One solution to this problem relies on the fact that the force experienced by a charged particle in an electric field, F E =q E , is independent of its velocity, but the force due to a magnetic field, F B =q v × B , isn't.

^ Magnetic forces are forces between moving charges and other moving charges, so a magnetic field can never accelerate a charged particle starting from rest.

.If both the speed and the charge are reversed then the direction of the force remains the same.^ If the velocity vector is initially perpendicular to the field, then the curve of its motion will remain in the plane perpendicular to the field, so the magnitude of the magnetic force on it will stay the same.

^ The following data give the results of two experiments in which charged particles were released from the same point in space, and the forces on them were measured: .

^ Furthermore, reversing the current I in our example would have reversed the force, which would only make sense if the magnetic field had a direction in space that could be reversed.

.For that reason a magnetic field measurement (by itself) cannot distinguish whether there is a positive charge moving to the right or a negative charge moving to the left.^ When charged particles are moving, they make magnetic fields as well.

^ Magnetic fields are supposed to be made by moving charges, but there don't seem to be any moving charges in this landscape.

^ Where is the moving charge responsible for this magnetic field?

.(Both of these cases produce the same current.^ We can produce these currents by tiling the region between the circles with square current loops, whose currents all cancel each other except at the inner and outer edges.

^ Now if we're convinced that figure h /2 produces a current in the coil, then it seems very plausible that the same will happen in figure h /1, which implies the existence of induction effects.

^ These metals are called ferromagnetic and their single outer electrons each produce a tiny, circulating current due to the electron orbits.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

) .On the other hand, a magnetic field combined with an electric field can distinguish between these, see Hall effect below.^ The relationship between the change in the magnetic field, and the electric field it produces.

^ Geometry of the electric and magnetic fields .

^ A changing magnetic field can create an electric field.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

.An alternative, similar trick to the right hand rule is Fleming's left hand rule.^ Left-handed and right-handed definitions.

^ This is in agreement with the right-hand rule.

^ This agrees with the right-hand rule.

H and B inside and outside of magnetic materials

.The formulas derived for the magnetic field above are correct when dealing with the entire current.^ The torque on a current loop in a magnetic field.

^ Magnetic fields curl around currents.

^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

.A magnetic material placed inside a magnetic field, though, generates its own bound current which can be a challenge to calculate.^ What is the magnetic field inside a long, straight wire in which the current density is j ?

^ The torque on a current loop in a magnetic field.

^ Does the electron experience a magnetic field created by its own current?

.(This bound current is due to the sum of atomic sized current loops and the spin of the subatomic particles such as electrons that make up the material.^ The field of a square-loop dipole is very complicated close up, but luckily for us, we only need to know the current at distances that are large compared to the size of the loop, because we're free to make the squares on our grid as small as we like.

^ Electrons flowing in the other direction achieve high velocities, because such lightweight particles are easy to accelerate.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ These metals are called ferromagnetic and their single outer electrons each produce a tiny, circulating current due to the electron orbits.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

) .The H-field as defined above helps factor out this bound current; but in order to see how it helps to introduce the concept of magnetization first.^ Likewise, we want to define a magnetic field, B .

^ The current in the first wire creates a magnetic field that acts on the current in the second wire.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ The total current is I = I free + I bound , and we define an altered version of the magnetic field, .

Magnetization

.The magnetization field M represents how strongly a region of material is magnetized and is defined as the volume density of the net magnetic dipole moment in that region.^ Example 1: The magnetic dipole moment of an atom .

^ Likewise, we want to define a magnetic field, B .

^ Roughly speaking, it looks like the field of one big dipole, especially farther away from the magnet.

.The unit of magnetization M in SI is ampere-turn per meter which is identical to that of the H-field since the unit of magnetic moment is ampere-turn m2.^ The ambient magnetic field in our laboratory (i.e., when the power supply to the coils was turned off) was 0.14 T. .
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

^ The distant field of a square dipole turns out to be simple, and is no different from the distant field of any other dipole with the same dipole moment.

^ Ordinary incandescent light bulbs (and electric blankets made since 1992) produce very little magnetic field.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

.The direction of the magnetization M is that of the average magnetic dipole moment in the region and is the same as the local B-field it produces.^ Example 1: The magnetic dipole moment of an atom .

^ Infer the direction of the magnetic field.

^ A changing electric field can produce a magnetic field.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

.Magnetization can be thought of as the magnetic equivalent of the polarization density P used for electrical charges.^ In: 1997 Annual Review of Research on Biological Effects of Electric and Magnetic Fields from the Generation, Delivery, and Use of Electricity.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

.In other words, M begins and ends at bound magnetic charges.^ Magnetic forces are forces between moving charges and other moving charges, so a magnetic field can never accelerate a charged particle starting from rest.

^ There is no difference between the “stuff” in one end of the magnet and the other, q .

^ If a charged particle or ion is exposed to a steady magnetic field, it will begin to go into a circular, or orbital motion at right angles to the applied magnetic field.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

.(Unlike B, magnetization must begin and end near the poles; there is no magnetization outside of the material.^ Also, as there is no change to the weight of a magnet as a result of this movement of flux then one may conclude that the actual quantity of that flux may be constant.
  • Rosemary Ainslie | A Magnetic Field Model 13 January 2010 10:13 UTC www.energeticforum.com [Source type: General]

^ There is no difference between the “stuff” in one end of the magnet and the other, q .

^ There is, however consensus that there is an ASSUMPTION of an electric field within the material of the magnet.
  • Rosemary Ainslie | A Magnetic Field Model 13 January 2010 10:13 UTC www.energeticforum.com [Source type: General]

) .In this model, the source of the M-field are bound magnetic charges such that −∇ · μ0M = ρb, where ρb is the bound magnetic charge density.^ Magnetic fields have no sources or sinks.

^ Where is the moving charge responsible for this magnetic field?

^ Milligauss is a unit of flux density , not magnetic field strength, but the difference is not important.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

.For uniform M this bound charge is zero everywhere except near the poles.^ In this frame of reference, every charge has a partner that cancels it, and the net charge everywhere is zero.

^ The horizontal component of the earth's magnetic field varies from zero, at a magnetic pole, to about 10 -4 T near the equator.

.An equivalent, and more physically correct, way to represent magnetization is to add all of the currents of the dipole moments that produce the magnetization.^ Example 1: The magnetic dipole moment of an atom .

^ If the electron is a pointlike particle, then we have an infinite current I through at the moment when it pierces the imaginary surface, and zero current at all other times.

^ This material clearly shows how to build an electric heating device that produces 17 times more heat than the "equivalent" amount of electricity.
  • Rosemary Ainslie | A Magnetic Field Model 13 January 2010 10:13 UTC www.energeticforum.com [Source type: General]

See #Magnetic dipoles below and magnetic poles vs. atomic currents for more information. The resultant current is called bound current and is the source of the magnetic field due to the magnet. Mathematically, the curl of M equals the bound current.

Magnetism

.Most materials produce their own magnetization M and therefore their own B-field in response to an applied B-field.^ Where is the moving charge responsible for this magnetic field?

^ A changing electric field can produce a magnetic field.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ MR ( magnetoresistive ) A technology based on the effect where electrical resistance in a material changes when brought in contact with a magnetic field .
  • Pro Audio Reference M 13 January 2010 10:13 UTC www.rane.com [Source type: FILTERED WITH BAYES]

.Typically, the response is very weak and exists only when the magnetic field is applied.^ Where is the moving charge responsible for this magnetic field?

^ So far, however, we only know how to calculate the magnetic field of a long, straight wire, .

^ If the sample is initially unmagnetized, 1, and a field H is externally applied, the magnetization increases, 2, but eventually becomes saturated, 3, so that higher fields do not result in any further magnetization, 4.

.The term magnetism is used to describe how these materials respond on the microscopic level and is used to categorize the magnetic phase of a material.^ Living organisms have the ability to somehow sense these minute daily cycles in the Earth's magnetic field and to use them to time their biological cycles.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ MDM ( modular digital multitrack ) Generic term used to describe any of the families of digital audio multitrack recorders.
  • Pro Audio Reference M 13 January 2010 10:13 UTC www.rane.com [Source type: FILTERED WITH BAYES]

^ MI ( musical instrument ) A broad term used to describe the musical instrument marketplace in general.
  • Pro Audio Reference M 13 January 2010 10:13 UTC www.rane.com [Source type: FILTERED WITH BAYES]

Materials are divided into groups based upon their magnetic behavior:
.
  • Diamagnetic materials[19] produce a magnetization that opposes the magnetic field.
  • Paramagnetic materials[19] produce a magnetization in the same direction as the applied magnetic field.
  • Ferromagnetic materials and the closely related ferrimagnetic materials and antferromagnetic materials[20][21] can have a magnetization independent of an applied B-field with a complex relationship between the two fields.
  • Superconductors (and ferromagnetic superconductors)[22][23] are materials that are characterized by perfect conductivity below a critical temperature and magnetic field.^ What is the difference between an electric field and a magnetic field?
    • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

    ^ The relationship between the change in the magnetic field, and the electric field it produces.

    ^ A changing electric field can produce a magnetic field.
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    .They also are highly magnetic and can be perfect diamagnets below a lower critical magnetic field.^ Diamagnetic materials have the interesting property that they are repelled from regions of strong magnetic field, and it is therefore possible to levitate a diamagnetic object above a magnet, as in figure h .

    ^ Assume that no other forces are present besides the possible electrical and magnetic ones, and that the fields, if they are present, are uniform.

    ^ Simultaneously, the magnetic field rearranges itself to a state of lower energy.
    • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

    Superconductors often have a broad range of temperatures and magnetic fields (the so named mixed state) for which they exhibit a complex hysteretic dependence of M on B.

H-field and magnetic materials

In the case of paramagnetism, and diamagnetism the magnetization M is often proportional to the applied magnetic field such that:
\mathbf{B} = \mu \mathbf{H},
where .μ is a material dependent parameter called the permeability (see constitutive equations).^ We need to organize our knowledge about the properties that materials can possess, and see whether this knowledge allows us to calculate anything useful with Maxwell's equations.

.In some cases the permeability may be a second rank tensor so that H may not point in the same direction as B.^ Consider the configuration where the small one is inside the big one with their currents circulating in the same direction, and a second configuration in which the currents circulate in opposite directions.

^ Describe how a series of measurements with a magnetic compass could be used to determine the strength and direction of its magnetic field at some point of interest.

These relations between B and H are examples of constitutive equations. .However, superconductors and ferromagnets have a more complex B to H relation, see hysteresis.^ However, having said that there is the chance that, at it's worst - it might entertain a purist to see the bazaar machinations of thought applied by an outsider to the complexity of the forces.
  • Rosemary Ainslie | A Magnetic Field Model 13 January 2010 10:13 UTC www.energeticforum.com [Source type: General]

In all cases, the definition of H given above:
\mathbf{H}\ \equiv \ \frac{\mathbf{B}}{\mu_0}-\mathbf{M},(definition of H in SI units)
(along with its Gaussian counterpart) is still valid.
.The advantage of the H-field is that its bound sources are treated so differently that they can often be isolated from the free sources.^ Magnetic field significantly different from sham at p < 0.01 in vehicle-treated animals.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

^ Magnetic field significantly different from sham at p <0.01 in vehicle-treated animals.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

^ No significant difference between magnetic field and sham in 7NI-treated animals.
  • Magnetic-Field-Induced DNA Strand Breaks in Brain Cells of the Rat 13 January 2010 10:13 UTC ehp03.niehs.nih.gov [Source type: Academic]

.For example, a line integral of the H-field in a closed loop yields the total free current in the loop (not including the bound current).^ The torque on a current loop in a magnetic field.

^ The total current is I = I free + I bound , and we define an altered version of the magnetic field, .

^ The field of any planar current loop can be found by breaking it down into square dipoles.

.Similarly, a surface integral of H over any closed surface picks out the 'magnetic charges' within that closed surface.^ The magnetic flux through any closed surface is zero.

^ But Gauss' law for magnetism merely says that the magnetic flux through a closed surface is zero.

^ Figure c /3 is closely analogous to figure a /3; in the central gray area, the atomic currents cancel out, but the atoms at the outer surface form a sheet of bound current.

Examining the definition of H helps flesh out this statement.
Taking the divergence of this definition results in
\mathbf{
abla}\cdot\mathbf{B}=\mu_0\mathbf{
abla}\cdot\mathbf{H}+\mathbf{
abla}\cdot\mu_0\mathbf{M}= 0,
where the equation has been rearranged so that its parallel to the displacement field is more obvious. .Noting that − · μ0M = ρb the bound magnetic charge density from the definition of M above and that  · B = 0 represents the absence of free magnetic charges this definition of H requires that μ0 · H = ρtot.^ In other words, the total charge, q , appearing in Maxwell's equartions is actualy q = q free - q bound , where q free is the charge that moves freely through wires, and can be detected in an ammeter, while q bound is the charge bound onto the individual molecules, which can't.

^ Just as an electric dipole contains bound charges, a magnetic dipole has bound currents, which come from the motion of the electrons as they orbit the nucleus, c /1.

^ The total current is I = I free + I bound , and we define an altered version of the magnetic field, .

.In other words, as described above, the definition of H requires that its field lines begin at positive magnetic charge (near south pole) and end at a negative magnetic charge (north pole).^ Where is the moving charge responsible for this magnetic field?

^ That is, it is not a simple field with just a north and south pole, like a bar magnet.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ (In this way, they resemble the field lines of an iron bar magnet, which arch from the north to the south poles.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

Taking the curl of the definition of H yields that:
\mathbf{
abla}	imes\mathbf{H}=\frac{1}{\mu_0}\mathbf{
abla}	imes\mathbf{B}-\mathbf{
abla}	imes\mathbf{M}=\mathbf{J}_{tot}-\mathbf{J}_{b} = \mathbf{J}_f
where Jf represents the free current.[24]

Energy stored in magnetic fields

.In asking how much energy is needed to create a specific magnetic field using a particular current it is important to distinguish between free and bound currents.^ What is the difference between an electric field and a magnetic field?
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^ Does the electron experience a magnetic field created by its own current?

^ Magnetic fields curl around currents.

.It is the free current that we directly 'push' on to create the magnetic field.^ Does the electron experience a magnetic field created by its own current?

^ Magnetic fields curl around currents.

^ The torque on a current loop in a magnetic field.

.The bound currents create a magnetic field that the free current has to work against without doing any of the work.^ The current in the first wire creates a magnetic field that acts on the current in the second wire.
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^ A changing magnetic field can create an electric field.
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^ An electric current flowing in a wire or coil produces its own magnetic field.
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.It is not surprising, therefore, that the H-field is important in magnetic energy calculations since it treats the two sources differently.^ Magnetic fields have no sources or sinks.

^ Do we have infinite energy in the resulting magnetic field?

^ What is the difference between an electric field and a magnetic field?
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In general the incremental amount of work per unit volume δW needed to cause a small change of magnetic field δB is:
\delta W = \mathbf{H}\cdot\delta\mathbf{B}.
If there are no magnetic materials around then we can replace H with Bμ0,
 u = \frac{\mathbf{B}\cdot\mathbf{B}}{2\mu_o}.
For linear, nondispersive, materials (such that B = μH where μ is independent frequency), the energy density can be expressed as:
 u = \frac{\mathbf{B}\cdot\mathbf{B}}{2\mu} = \frac{\mu\mathbf{H}\cdot\mathbf{H}}{2}. (Valid only for linear materials with negligible material dispersion)
.Nonlinear materials cannot use the above equation but must return to the first equation which is always valid.^ We need to organize our knowledge about the properties that materials can possess, and see whether this knowledge allows us to calculate anything useful with Maxwell's equations.

^ We then know, for instance, that there cannot be a valid solution to Maxwell's equations in which the same wave pattern moves with double that velocity.

.In particular, the energy density stored in the fields of hysteretic materials such as ferromagnets and superconductors depends on how the magnetic field was created.^ Do we have infinite energy in the resulting magnetic field?

^ A changing magnetic field can create an electric field.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ Energy in the magnetic field .

Electromagnetism: the relationship between magnetic and electric fields

The magnetic field due to a changing electric field

.A changing electric field generates a magnetic field proportional to the time rate of the change of the electric field.^ She observes that a changing magnetic field creates a curly electric field.

^ The relationship between the change in the magnetic field, and the electric field it produces.

^ Geometry of the electric and magnetic fields .

.This fact is known as Maxwell's correction to Ampère's law.^ Verify Ampère's law in the case shown in the figure, assuming the known equation for the field of a wire.

^ We have found one specific example of the general law of nature known as Ampère's law: .

^ Unadorned with the ∂Φ E /∂ t term, Maxwell's equation for Γ B reads as c 2 Γ B = 4π k I through , which is Ampère's law.

Therefore the full Ampère's law is:

abla 	imes \mathbf{B} = \mu_0\mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}} {\partial t},\
where .J is the current density, and partial derivatives indicate spatial location is fixed when the time derivative is taken.^ If the particle is pointlike, then it takes zero time to pass any particular location, and the current is then infinite at that point in space.

The last term is Maxwell's correction. .This equation is valid even when magnetic materials are involved, but in practice it is often easier to use an alternate equation.^ An easy way to approach this is to use the fact that vB has the same units as E , which can be seen by comparing the equations for magnetic and electric forces used above.

^ Modern magnetic therapy is based on traditional ideas, but uses stronger and "out of phase" magnetic materials.
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^ Such an effect is completely inconsistent with the static version of Maxwell's equations; the equations don't even refer to time, so if the magnetic field is changing over time, they will not do anything special.

Electric force due to a changing B-field

.Above is a discussion of how a changing E-field creates a B-field.^ A changing magnetic field can create an electric field.
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^ She observes that a changing magnetic field creates a curly electric field.

^ The relationship Γ E ∝ -∂ B /∂ t tells us that a changing magnetic field creates an electric field in the surrounding region of space, but the phrase “surrounding region of space” is vague, and needs to be made mathematical.

.The inverse process also occurs: a changing magnetic field, such as a magnet moving through a stationary coil, generates an electric field (and therefore tends to drive a current in the coil).^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

^ Where is the moving charge responsible for this magnetic field?

^ Determine the electric and magnetic fields.

.(These two effects bootstrap together to form electromagnetic waves, such as light.^ X-ray photons traveling through such strong fields readily split into two, or merge together; and many other novel physical effects come into play.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ Maxwell convinced himself that light was an electromagnetic wave partly because his equations predicted waves moving at the velocity of light, c .

^ Induction effects like these also lead to the existence of light, which is a wave disturbance in the electric and magnetic fields.

) .This is known as Faraday's law and forms the basis of many electric generators and electrical motors.^ This is the basis of power transformers and electric power generation.
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^ This is known as Faraday's law.

^ We have found one specific example of the general law of nature known as Ampère's law: .

Faraday's law is commonly represented as:
\mathcal{E} = - \frac{d\Phi_m}{dt},
where .\scriptstyle\mathcal{E} is the electromotive force (or EMF, the voltage generated around a closed loop) and Φm is the magnetic flux—the product of the area times the magnetic field normal to that area.^ The torque on a current loop in a magnetic field.

^ Magnetic fields curl around currents.

^ The magnetic flux through any closed surface is zero.

.(This definition of magnetic flux is why engineers often refer to B as "magnetic flux density".) This law includes both flux changes because of the magnetic field generated by a time varying E-field (transformer EMF) and flux changes because of movement through a magnetic field (motional EMF).^ Both of these fields change over time, however.

^ A changing electric field can produce a magnetic field.
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^ As it spins, the nearby magnetic field changes.

A form of Faraday's law of induction that does not include motional EMF is the Maxwell–Faraday equation:

abla 	imes \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t},\
one of Maxwell's equations. .This equation is valid even in the presence of magnetic material.^ Such an effect is completely inconsistent with the static version of Maxwell's equations; the equations don't even refer to time, so if the magnetic field is changing over time, they will not do anything special.

^ A complete statement of Maxwell's equations in the presence of electric and magnetic materials is as follows: .

^ The external field can then be reduced, 5, and even eliminated completely, but the material will retain its magnetization.

[25]

Maxwell's equations

.Like all vector fields the B-field has two important mathematical properties that relates it to its sources.^ We find ourselves in a region where the field is very much as it was before, except that all the field vectors have had one unit worth of added to them.

^ Just as a tiny part of a curve looks straight, a tiny part of this magnetic field looks like the field vectors are just getting shorter by the same amount with each step to the right.

^ The clockwise and counterclockwise fields created by the two wires combine by vector addition, and normally cancel out almost exactly.

.These two properties, along with the two corresponding properties of the electric field, make up Maxwell's Equations.^ The Φ E equation is Gauss' law: charges make diverging electric fields.

^ Maxwell's equations for static fields .

^ Dividing these two equations, we find .

.Maxwell's Equations together with the Lorentz force law form a complete description of classical electrodynamics including both electricity and magnetism.^ A complete statement of Maxwell's equations in the presence of electric and magnetic materials is as follows: .

^ Electric and magnetic forces seem similar in many ways.

^ This buildup of charge would start to quench both currents due to electrical forces, but the current in the right side of the wire, which is driven by the weaker magnetic field, would be the first to stop.

.The first property is the divergence of a vector field A,  · A which represents how A 'flows' outward from a given point.^ By symmetry, the field in this plane cannot have any component in the radial direction (inward toward the dipole, or outward away from it); it is perpendicular to the plane, and in the opposite direction compared to the dipole vector.

^ The magnetic field vectors lead in paths that loop back on themselves, without ever converging or diverging at a point, as in the fields shown in figure r .

^ For a given AC voltage applied across the inductor, how does the magnetic field depend on N ?

.As discussed above a B-field line never starts nor ends at a point but instead forms a complete loop.^ Magnetic forces are forces between moving charges and other moving charges, so a magnetic field can never accelerate a charged particle starting from rest.

^ It undoubtedly seems artificial to you that we have discussed dipoles only in the form of a square loop of current.

^ The currents are in opposite directions, and we can imagine them as being joined together at the ends to form a complete circuit, like a tube made of paper that has been squashed almost flat.

This is mathematically equivalent to saying that the divergence of B is zero. (Such vector fields are called solenoidal vector fields.) .This property is called Gauss's law for magnetism and is equivalent to the statement that there are no magnetic charges or magnetic monopoles.^ No magnetic monopoles .

^ The Φ E equation is Gauss' law: charges make diverging electric fields.

^ Gauss' law in differential form relates , a scalar, to the charge density, another scalar.

.The electric field on the other hand begins and ends at electrical charges so that its divergence is non-zero and proportional to the charge density (See Gauss's law).^ The Φ E equation is Gauss' law: charges make diverging electric fields.

^ This electric field is not created by charges .

^ But Ampère's law for electric fields says the curl of E is supposed to be zero.

.
Diagram showing how the magnetic field is a pseudovector: A loop of wire (black), carrying a current, creates a magnetic field (blue).
^ Any wire that carries an AC electrical current produces magnetic fields.
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^ What is the magnetic field inside a long, straight wire in which the current density is j ?

^ The torque on a current loop in a magnetic field.

.When the wire is reflected in a mirror (dotted line), the magnetic field it generates is not reflected in the mirror: Instead, it is reflected and reversed.^ Non-localized fields due to household wiring are usually highest in the room next to where the power line connects or where there is a circuit breaker panel.
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^ (Of course, magnetic field lines are actually invisible to the eye, but we draw them here so you can see what's happening.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ Any wire that carries an AC electrical current produces magnetic fields.
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The position of the wire and its current are (polar) vectors, so they reflect normally. The magnetic field is a pseudovector, so it changes sign when reflected.
.The second mathematical property is called the curl, such that  × A represents how A curls or 'circulates' around a given point.^ Such circulation is called "convection."
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ The increasing magnetic field causes electrons to circulate (current) around the second coil in such a way as to oppose the increasing magnetic field that the first coil is trying to establish.
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^ Because the field is twisted, there is a component of B pointed around the green loop, yielding a non-zero circulation.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

The result of the curl is called a 'circulation source' The curl of B and of E are given above and are called the Ampère–Maxwell equation and Faraday's law respectively.
The complete set of Maxwell's equations then are:

abla \cdot \mathbf{B} = 0,

abla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0},

abla 	imes \mathbf{B} = \mu_0\mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}} {\partial t},

abla 	imes \mathbf{E} = - \frac{\partial \mathbf{B}} {\partial t},
where .J = complete microscopic current density and ρ is the charge density.^ Let's model the current in wire 2 by pretending that there is a line charge inside it, possessing density per unit length λ 2 and moving at velocity v 2 .

.Technically, B is a pseudovector (also called an axial vector) due to being defined by a vector cross product.^ This is equivalent to the vector cross product .

^ Momentum, however, is a vector, and there is only one physically meaningful way of multiplying two vectors to get a vector result, which is the cross product (see page 854).

^ As proved on page 854, however, there is only one physically useful way of defining such a multiplication, which is the cross product.

.Because of the right-hand rule, if a current-carrying loop were viewed in a mirror, the resulting B vector would be both mirror imaged and flipped in orientation, whereas an ordinary vector (e.g., velocity) would be mirror-imaged only.^ This agrees with the right-hand rule.

^ This is in agreement with the right-hand rule.

^ Momentum, however, is a vector, and there is only one physically meaningful way of multiplying two vectors to get a vector result, which is the cross product (see page 854).

(See diagram to right.)
.As discussed above, materials respond to an applied electric E field and an applied magnetic B field by producing their own internal 'bound' charge and current distributions that contribute to E and B but are difficult to calculate.^ Shielding magnetic fields is more difficult than shielding electric fields.
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^ This electric field is not created by charges .

^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

To circumvent this problem the auxiliary H and D fields are defined so that Maxwell's equations can be re-factored in terms of the free current density Jf and free charge density ρf:

abla \cdot \mathbf{B} = 0,

abla \cdot \mathbf{D} = \rho_f,

abla 	imes \mathbf{H} = \mathbf{J}_f + \frac{\partial \mathbf{D}} {\partial t},

abla 	imes \mathbf{E} = - \frac{\partial \mathbf{B}} {\partial t}.
.These equations are not any more general then the original equations (if the 'bound' charges and currents in the material are known').^ These charged particles readily carry currents.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ These crustal motions generally drive currents outside the star, and generate X-rays.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

.They also need to be supplemented by the relationship between B and H as well as that between E and D.^ (To do this problem, you need to know the relativistic relationship between the energy and momentum of a beam of light.

.On the other hand, for simple relationships between these quantities this form of Maxwell's equations can circumvent the need to calculate the bound charges and currents.^ At all other times (when charges are stable), no current flows.
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^ Now this is very subtle, because Maxwell's equations treat these charges on an equal basis, but in terms of practical measurements, they are completely different.

^ The proportionality to current makes sense, since magnetic forces are interactions between moving charges, and current is a measure of the motion of charge.

Electric and magnetic fields: different aspects of the same phenomenon

.According to special relativity, the partition of the electromagnetic force into separate electric and magnetic components is not fundamental, but varies with the observational frame of reference; an electric force perceived by one observer is perceived by another (in a different frame of reference) as a mixture of electric and magnetic forces.^ In her frame of reference, it's the bar magnet that is moving.

^ Or an example where the fields are purely electric in one frame, but purely magnetic in another?

^ But observers in different frames of reference do not agree on simultaneity.

.(Also, a magnetic force in one reference frame is perceived as a mixture of electric and magnetic forces in another.^ In her frame of reference, it's the bar magnet that is moving.

^ Or an example where the fields are purely electric in one frame, but purely magnetic in another?

^ Observers in the two frames agree on how much force there is, so in the loop's frame, we have an electric field .

)
.More specifically, special relativity combines the electric and magnetic fields into a rank-2 tensor, called the electromagnetic tensor.^ Shielding magnetic fields is more difficult than shielding electric fields.
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^ Geometry of the electric and magnetic fields .

^ Prove that in an electromagnetic wave, half the energy is in the electric field and half in the magnetic field.

Changing reference frames mixes these components. .This is analogous to the way that special relativity mixes space and time into spacetime, and mass, momentum and energy into four-momentum.^ In this way, the energy of a magnetic twist outside a magnetar is gradually dissipated into X-rays.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

Magnetic vector potential

.In advanced topics such as quantum mechanics and relativity it is often easier to work with a potential formulation of electrodynamics rather than in terms of the electric and magnetic fields.^ Shielding magnetic fields is more difficult than shielding electric fields.
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^ What is the difference between an electric field and a magnetic field?
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^ Magnetic fields are much more common in the home than are electric fields.
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In this representation, the vector potential, A, and the scalar potential, φ, are defined such that:
\mathbf{B} = 
abla 	imes \mathbf{A},
\mathbf{E} = - 
abla \phi - \frac { \partial \mathbf{A} } { \partial t }.
.The vector potential A may be interpreted as a generalized potential momentum per unit charge[26] just as φ is interpreted as a generalized potential energy per unit charge.^ Let ±λ be the charge per unit length of each line charge without relativistic contraction, i.e., in the frame moving with that line charge.

^ A line charge, with charge per unit length λ, moves at velocity v along its own length.

^ We haven't yet found the proportionality factor that goes in front of the B 2 , but that doesn't matter, because the energy per unit length turns out to be infinite!

.Maxwell's equations when expressed in terms of the potentials can be cast into a form that agrees with special relativity with little effort.^ Now this is very subtle, because Maxwell's equations treat these charges on an equal basis, but in terms of practical measurements, they are completely different.

^ With the addition of the ∂Φ E /∂ t term, Maxwell's equations are capable of describing electromagnetic waves.

^ Such an effect is completely inconsistent with the static version of Maxwell's equations; the equations don't even refer to time, so if the magnetic field is changing over time, they will not do anything special.

[27] .In relativity A together with φ forms the four-potential analogous to the four-momentum which combines the momentum and energy of a particle.^ If there wasn't this kind of consistency between the momentum and the energy, then we could violate conservation of momentum by combining light beams or splitting them up.

.Using the four potential instead of the electromagnetic tensor has the advantage of being much simpler; further it can be easily modified to work with quantum mechanics.^ Also, the use of a power-conditioning outlet strip (specifying reduced electromagnetic interference) is recommended to avoid radio waves being picked up from the power line by the computer.
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^ Even the water bed heater, being farther away from the body, because it is used for several hours at a time, the total administered dose is much higher.
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^ This configuration has the advantage of being fairly open, so that other apparatus can be easily placed inside and subjected to the field while remaining visible from the outside.

Quantum electrodynamics

.In modern physics, the electromagnetic field is understood to be not a classical field, but rather a quantum field; it is represented not as a vector of three numbers at each point, but as a vector of three quantum operators at each point.^ Many fascinating physical effects occur in magnetic fields with strength exceeding the "quantum electrodynamic field strength" of B Q = 4.4 X 10 13 Gauss.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ The magnetic field vectors lead in paths that loop back on themselves, without ever converging or diverging at a point, as in the fields shown in figure r .

^ A piezoelectric effect is the creation of an electromagnetic field pulse when a crystalline structure is physically stressed or pushed out of its normal shape.
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.These theories explain that the electromagnetic field is derived from the photon field; indeed, all electromagnetic interactions are mediated by this field.^ The significant increase in these systems and their interactions with other energy fields in our homes, cars and work places will in fact be significantly increasing health risks.
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^ All electromagnetic fields are force fields, carrying energy and capable of producing an action at a distance.
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^ All of the possible frequencies of electromagnetic waves or fields can be put onto an electromagnetic spectrum, starting with the slowest frequencies and going to the highest.
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The most accurate modern description of the electromagnetic interaction (and much else) is Quantum electrodynamics (QED),[28] which is incorporated into a more complete theory known as the "Standard Model of particle physics".
.QED describes the electromagnetic interaction between charged particles (and their antiparticles) as due to the exchange of virtual photons.^ Magnetic forces are forces between moving charges and other moving charges, so a magnetic field can never accelerate a charged particle starting from rest.

^ Particle-antiparticle pairs are spontaneously created from photons whenever sufficient energy is present.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ The proportionality to current makes sense, since magnetic forces are interactions between moving charges, and current is a measure of the motion of charge.

The magnitude of these interactions is computed using perturbation theory; these rather complex formulas have a remarkable pictorial representation as Feynman diagrams.
Predictions of QED agree with experiments to an extremely high degree of accuracy: currently about 10−12 (and limited by experimental errors); for details see precision tests of QED. .This makes QED one of the most accurate physical theories constructed thus far.^ That wouldn't make sense, because there is no physical reason why one part of the wire would behave differently than any other.

All equations in this article are in the classical approximation, which is less accurate than the quantum description as mentioned above. However, under most everyday circumstances, the difference between the two theories is negligible.

Measuring the B-field

.Devices used to measure the local magnetic field are called magnetometers.^ The magnetite crystals "tell" the pigeon's brain the exact direction of the Earth's magnetic field, and the pigeon uses this information to navigate with its amazing precision.
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^ With the advent of such devices as walkie-talkies and mobile phones, it has become apparent that few studies address the consequences of localized exposures to RF fields to the head.
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^ The flow of the electrical currents in the brain produce a magnetic field that can be measured and analyzed several feet away from the head.
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Important classes of magnetometers include using a rotating coil, Hall effect magnetometers, NMR magnetometer, SQUID magnetometer, and a fluxgate magnetometer. .The magnetic fields of distant astronomical objects can be determined by noting their effects on local charged particles.^ Thus the magnetic field acts like a "bottle," holding charged particles.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ If a charged particle or ion is exposed to a steady magnetic field, it will begin to go into a circular, or orbital motion at right angles to the applied magnetic field.
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^ As the instability grows, the changing, shearing, twisting field drives strong dissipative currents above the star, energizing particles trapped in the exterior magnetic field.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

.For instance, electrons spiraling around a field line produce synchotron radiation which is detectable in radio waves.^ Occasionally a nearby power line will produce this type of field.
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^ The increasing magnetic field causes electrons to circulate (current) around the second coil in such a way as to oppose the increasing magnetic field that the first coil is trying to establish.
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^ Also, the use of a power-conditioning outlet strip (specifying reduced electromagnetic interference) is recommended to avoid radio waves being picked up from the power line by the computer.
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.The smallest magnetic field measured[29] is on the order of attoteslas (10−18 tesla); the largest magnetic field produced in a laboratory is 2,800 T (VNIIEF in Sarov, Russia, 1998)[30] The magnetic field of some astronomical objects such as magnetars are much higher; magnetars range from 0.1 to 100 GT (108 to 1011 T).^ The spatial variation of the magnetic field is on the order of (10 9 T/10 4 m)=10 5 T/m.

^ A changing electric field can produce a magnetic field.
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^ As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

[31] .See orders of magnitude (magnetic field).^ (Of course, magnetic field lines are actually invisible to the eye, but we draw them here so you can see what's happening.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ For more information, see my review article, Physics in Ultra-strong Magnetic Fields .
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ In order to act as a "magnet," these atoms must be lined up in the same direction so that the individual magnetic fields combine to produce one big field.
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History

One of the first drawings of a magnetic field, by René Descartes, 1644. It illustrated his theory that magnetism was caused by the circulation of tiny helical particles, "threaded parts", through threaded pores in magnets.
.Perhaps the earliest description of a magnetic field was performed by the French scholar Petrus Peregrinus and published in his Epistola Petri Peregrini de Maricourt ad Sygerum de Foucaucourt Militem de Magnete and is dated 1269 A.D. Petrus Peregrinus mapped out the magnetic field on the surface of a spherical magnet.^ The arrows map the magnetic field B .

^ Now perhaps we can use reasoning with the same flavor to show that changing magnetic fields produce curly electric fields.

^ We, and all other living things, are surrounded by a magnetic field extending out into space from our bodies, and the fields from the brain reflect what is happening in the brain.
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.Noting that the resulting field lines crossed at two points he named those points 'poles' in analogy to Earth's poles.^ Momentum, however, is a vector, and there is only one physically meaningful way of multiplying two vectors to get a vector result, which is the cross product (see page 854).

^ All matter on Earth assists in creating this field and so becomes charged with this magnetic resonance, displaying different results, dependant on the substance.
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^ The core will reach saturation more quickly when the coil's field is in the same direction as the Earth's, but will not saturate as early in the next half-cycle, when the two fields are in opposite directions.

.Almost three centuries later, near the end of the sixteenth century, William Gilbert of Colchester replicated Petrus Peregrinus' work and was the first to state explicitly that Earth itself was a magnet.^ Simultaneously, the magnetic field rearranges itself to a state of lower energy.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ Near a neutron star, magnetic field lines are anchored at both ends on the stellar surface, describing arches outside the star.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ Occasionally, the magnetic field becomes unstable on much larger scales, and rapidly rearranges itself to a state of lower energy.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

William Gilbert's great work De Magnete was published in 1600 A.D. and helped to establish the study of magnetism as a science.
.The modern understanding that the B-field is the more fundamental field with the H-field being an auxiliary field was not easy to arrive at.^ But with the advantage of modern hindsight, we can understand in fundamental terms the facts that Faraday had to take simply as mysterious experimental observations.

^ For these reasons, let's look at an alternative method of defining the magnetic field which, although not as fundamental or mathematically simple, may be more appealing.

.Indeed, largely because of mathematical similarities to the electric field, the H-field was developed first and was thought at first to be the more fundamental of the two.^ Observers in the two frames agree on how much force there is, so in the loop's frame, we have an electric field .

^ Since the electric field is curly, an electron can keep gaining more and more energy by circling through it again and again.

^ The core will reach saturation more quickly when the coil's field is in the same direction as the Earth's, but will not saturate as early in the next half-cycle, when the two fields are in opposite directions.

.The modern distinction between the B- and H- fields was not needed until Siméon-Denis Poisson (1781–1840) developed one of the first mathematical theories of magnetism.^ What is the difference between an electric field and a magnetic field?
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^ Find the induced magnetic field at a point between the plates, at a distance R from the axis.

^ As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

.Poisson's model, developed in 1824, assumed that magnetism was due to magnetic charges.^ A charged particle of mass m and charge q moves in a circle due to a uniform magnetic field of magnitude B , which points perpendicular to the plane of the circle.

^ The magnetic force on the lone charge q due to the current I is .

^ One solution to this problem relies on the fact that the force experienced by a charged particle in an electric field, F E =q E , is independent of its velocity, but the force due to a magnetic field, F B =q v × B , isn't.

.In analogy to electric charges, magnetic charges produce an H-field.^ This electric field is not created by charges .

^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

^ Where is the moving charge responsible for this magnetic field?

.In modern notation, Poisson's model is exactly analogous to electrostatics with the H-field replacing the electric field E-field and the B-field replacing the auxiliary D-field.^ This is the same as the field of a magnetic dipole in its midplane, except that the electric coupling constant k replaces the magnetic version k / c 2 , and the electric dipole moment D is substituted for the magnetic dipole moment m .

^ The conventional notation is to incorporate this fudge factor into Gauss's law by defining an altered version of the electric field, .

^ Since some of the fields referred to in Maxwell's equations are the electric and magnetic fields E and B , while others are the auxiliary fields D and H , some of the constraints deal with E and B , others with D and H .

Poisson's model was, unfortunately, incorrect. .Magnetism is not due to magnetic charges.^ A charged particle of mass m and charge q moves in a circle due to a uniform magnetic field of magnitude B , which points perpendicular to the plane of the circle.

^ The magnetic force on the lone charge q due to the current I is .

^ One solution to this problem relies on the fact that the force experienced by a charged particle in an electric field, F E =q E , is independent of its velocity, but the force due to a magnetic field, F B =q v × B , isn't.

.Nor is magnetism created by the H-field polarizing magnetic charge in a material.^ This electric field is not created by charges .

^ Where is the moving charge responsible for this magnetic field?

^ Modify the calculation on page 617 to determine the component of the magnetic field of a sheet of charge that is perpendicular to the sheet.

The model, however, was remarkably successful for being fundamentally wrong. .It predicts the correct relationship between the H-field and the B-field, even though it wrongly places H as the fundamental field with B as the auxiliary field.^ As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

^ The relationship between the change in the magnetic field, and the electric field it produces.

^ Although the relationship E ≤ftrightarrow q between electric fields and their sources is unalterably locked in by Gauss's law, that's not what we see in practical measurements.

.It predicts the correct forces between magnets.^ As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

^ Magnetic forces are forces between moving charges and other moving charges, so a magnetic field can never accelerate a charged particle starting from rest.

^ The proportionality to current makes sense, since magnetic forces are interactions between moving charges, and current is a measure of the motion of charge.

.It even predicts the correct energy stored in the magnetic fields.^ Do we have infinite energy in the resulting magnetic field?

^ Energy in the magnetic field .

^ As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

.By the definition of magnetization, in this model, and in analogy to the physics of springs, the work done per unit volume, in stretching and twisting the bonds between magnetic charge to increment the magnetization by μ0δM is W = H · μ0δM.^ No charge will actually flow through the air gap between them, yet a magnetic field will be created in that gap as if the charge were flowing.
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^ Magnetic forces are forces between moving charges and other moving charges, so a magnetic field can never accelerate a charged particle starting from rest.

^ The proportionality to current makes sense, since magnetic forces are interactions between moving charges, and current is a measure of the motion of charge.

.In this model, B = μ0 (H + M ) is an effective magnetization which includes the H-field term to account for the energy of setting up the magnetic field in a vacuum.^ Do we have infinite energy in the resulting magnetic field?

^ Find the increase in the magnetic-field energy, in terms of η, v , and the unknown constant a .

^ Energy in the magnetic field .

.Therefore the total energy density increment needed to increment the magnetic field is W = H · δB.^ Do we have infinite energy in the resulting magnetic field?

^ Energy in the magnetic field .

^ We therefore know that the momentum density of a light beam must depend on a field multiplied by a field.

This is the correct result, but it is derived from an incorrect model.
.In retrospect the success of this model is due largely to the remarkable coincidence that from the 'outside' the field of an electric dipole has the exact same form as that of a magnetic dipole.^ Geometry of the electric and magnetic fields .

^ What about the field of a magnetic dipole outside of the dipole's midplane?

^ Sunlight, as well as the light from electric lights, is the same thing as the magnetic field.
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.It is therefore only for the physics of magnetism 'inside' of magnetic material where the simpler model of magnetic charges fails.^ Diamagnetic materials have the interesting property that they are repelled from regions of strong magnetic field, and it is therefore possible to levitate a diamagnetic object above a magnet, as in figure h .

^ Therefore the bound currents in a material inserted inside a solenoid tend to reinforce the free currents, and the result is to strengthen the field.

^ E 1 = 0 In frame 1, any force experienced by the lone charge must therefore be attributed solely to magnetism.

.It is also important to note that this model is still useful in many situations dealing with magnetic material.^ Because so many people use cellular telephones, it is important to learn whether RF radiation affects human health, and to provide reassurance if it does not.
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^ Modern magnetic therapy is based on traditional ideas, but uses stronger and "out of phase" magnetic materials.
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^ But even when the model is physically unrealistic, it still gives the right answers when you use it to compute magnetic effects.

.One example of its utility is the concept of magnetic circuits.^ Or an example where the fields are purely electric in one frame, but purely magnetic in another?

^ (We could also construct an example like the one in figure c on page 602, in which the field was purely magnetic.

^ We have already seen one example of this on page 554, where we inferred that an inductor's time-varying magnetic field creates an electric field --- an electric field which is not created by any charges anywhere.

.The formation of the correct theory of magnetism begins with a series of revolutionary discoveries in 1820, four years before Poisson's model was developed.^ Because cancer takes decades to develop, it will be another 10 or 20 years before "mobiles" manifest a bonanza in brain tumors.
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.(The first clue that something was amiss, though, was that unlike electrical charges magnetic poles cannot be separated from each other or form magnetic currents.^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

^ In one case the sources are charges and the field is electric; in the other case we have currents and magnetic fields.

^ If the current is a DC (direct current), the magnetic field is steady, like that form a permanent magnet.
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) .The revolution began when Hans Christian Oersted discovered that an electrical current generates a magnetic field that encircles the wire.^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

^ Any wire that carries an AC electrical current produces magnetic fields.
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^ What is the magnetic field inside a long, straight wire in which the current density is j ?

.In a quick succession that discovery was followed by André-Marie Ampère showing that parallel wires having currents in the same direction attract, and by Jean-Baptiste Biot and Felix Savart developing the correct equation, the Biot–Savart law, for the magnetic field of a current carrying wire.^ Any wire that carries an AC electrical current produces magnetic fields.
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^ Besides being influenced by a magnetic field, a wire that is carrying a current also produces a magnetic field.
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^ The current in the first wire creates a magnetic field that acts on the current in the second wire.
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.In 1825, Ampère extended this revolution by publishing his Ampère's law which provided a more mathematically subtle and correct description of the magnetic field generated by a current than the Biot–Savart law.^ Shielding magnetic fields is more difficult than shielding electric fields.
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^ Magnetic fields are much more common in the home than are electric fields.
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^ Magnetic fields curl around currents.

.Subsequent development in the nineteenth century interlinked magnetic and electric phenomena even tighter, until the concept of magnetic charge was not needed.^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

^ From arguments about relative motion, we concluded that moving electric charges create magnetic fields.

^ The charge by itself up above the wire is like a test charge, being used to determine the magnetic and electric fields created by the wire.

.Magnetism became an electric phenomenon with even the magnetism of permanent magnets being due to small loops of current in their interior.^ The torque on a current loop in a magnetic field.

^ An electric current flowing in a wire or coil produces its own magnetic field.
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^ An electric motorized clock, plugged into a wall socket, produces an amazingly high magnetic field because of the small electric motor that runs it.
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.This development was aided greatly by Michael Faraday, who in 1831 showed that a changing magnetic field generates an encircling electric field.^ She observes that a changing magnetic field creates a curly electric field.

^ The relationship between the change in the magnetic field, and the electric field it produces.

^ Geometry of the electric and magnetic fields .

.In 1861, James Clerk Maxwell wrote a paper entitled On Physical Lines of Force in which he attempted to explain Faraday's magnetic lines of force in terms of a sea of tiny molecular vortices.^ James Clerk Maxwell (1831-1879) .

^ This observer also predicts that the particles will collide, but explains their motion in terms of both an electric field, E , and a magnetic field, B .

^ This whole line of reasoning was not available to Faraday and his contemporaries, since they thought the relative nature of motion only applied to matter, not to electric and magnetic fields.

.These molecular vortices occupied all space and they were aligned in a solenoidal fashion such that their rotation axes traced out the magnetic lines of force.^ A diffuse flux of such particles rains down on the Earth all the time, from the depths of space.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ When the magnetic forces get strong enough, they can also yield to the magnetic stress and move "plastically," truly changing the crust's structure.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ Moreover, if magnetic twists (and currents) extend out far from the star, to regions where outgoing magnetic waves are generated due to the stellar rotation, then they will affect the rate at which the star spins down.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

.When two like magnetic poles repel each other, the magnetic lines of force spread outwards from each other in the space between the two poles.^ As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

^ Magnetic forces are forces between moving charges and other moving charges, so a magnetic field can never accelerate a charged particle starting from rest.

^ The proportionality to current makes sense, since magnetic forces are interactions between moving charges, and current is a measure of the motion of charge.

.Maxwell considered that magnetic repulsion was the consequence of a lateral pressure between adjacent lines of force, due to centrifugal force in the equatorial plane of the molecular vortices.^ If the velocity vector is initially perpendicular to the field, then the curve of its motion will remain in the plane perpendicular to the field, so the magnitude of the magnetic force on it will stay the same.

^ Magnetic forces are forces between moving charges and other moving charges, so a magnetic field can never accelerate a charged particle starting from rest.

^ The proportionality to current makes sense, since magnetic forces are interactions between moving charges, and current is a measure of the motion of charge.

.When deriving the equation for magnetic force in part I of his 1861 paper, Maxwell used a quantity which was closely related to the circumferential speed of the vortices.^ To satisfy Maxwell's equations, the time derivatives of the fields must also be twice as large for the blue light.

^ The fluxgate compass is a type of magnetic compass without moving parts, commonly used on ships and aircraft.

^ We need to organize our knowledge about the properties that materials can possess, and see whether this knowledge allows us to calculate anything useful with Maxwell's equations.

This quantity was therefore a measure of the vorticity in the magnetic lines of force, and Maxwell referred to it as the intensity of the magnetic force. .In the 1861 paper, the magnetic intensity which we denote as v, was always multiplied by the term μ as a weighting for the cross sectional density of the lines of force.^ If the dimensions of the cross-sectional square (height and front-to-back) are b , find the magnetic field (magnitude and direction) along the long central axis.

^ With electricity, it turned out to be useful to define an electric field rather than always working in terms of electric forces.

^ In section 10.4 , I've already argued that the energy density of the magnetic field must be proportional to .

.The quantity v corresponds reasonably closely to the modern magnetic field vector H, and the product μv corresponds very closely to the modern magnetic flux density B, where μ is referred to as the magnetic permeability.^ We can also anticipate that the magnetic field will be a vector.

^ As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

^ Now perhaps we can use reasoning with the same flavor to show that changing magnetic fields produce curly electric fields.

.Although the classical theory of electrodynamics was essentially complete with Maxwell's equations, the twentieth century saw a number of improvements and extensions to the theory.^ Now this is very subtle, because Maxwell's equations treat these charges on an equal basis, but in terms of practical measurements, they are completely different.

^ Such an effect is completely inconsistent with the static version of Maxwell's equations; the equations don't even refer to time, so if the magnetic field is changing over time, they will not do anything special.

^ A complete statement of Maxwell's equations in the presence of electric and magnetic materials is as follows: .

.Albert Einstein, in his great paper of 1905 that established relativity, showed that both the electric and magnetic fields were part of the same phenomena viewed from different reference frames.^ In her frame of reference, it's the bar magnet that is moving.

^ Or an example where the fields are purely electric in one frame, but purely magnetic in another?

^ Geometry of the electric and magnetic fields .

Finally, the emergent field of quantum mechanics was merged with electrodynamics to form quantum electrodynamics or QED.
.In the late nineteenth century the moving magnet and conductor problem developed as an important thought experiment that eventually helped Albert Einstein to develop special relativity.^ From arguments about relative motion, we concluded that moving electric charges create magnetic fields.

^ In the frame of reference where the loop is moving, a charge q moving along with the loop at velocity v will experience a magnetic force .

^ The protons and electrons in the coil are moving through a magnetic field, so they experience forces.

This thought experiment revolves around the interpretation of Faraday's law, as explained next:
.Imagine a conducting loop moving relative to a magnet as seen by two different observers: one on the magnet the other on the loop.^ One loop is in the y - z plane, the other in the x - y plane.

^ A different observer, a /2, says the particles are moving.

^ Observers in the two frames agree on how much force there is, so in the loop's frame, we have an electric field .

.Both observers see the identical EMF generated in the coil using the flux form of Faraday's law, but explain the result using two different reasons.^ Momentum, however, is a vector, and there is only one physically meaningful way of multiplying two vectors to get a vector result, which is the cross product (see page 854).

^ The two processes are supposed to use completely different waves of energy and at different intensities.
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^ Two separate physical reasons for a proportionality to length result in an overall proportionality to length squared, which is the same as the area of the loop.

.The observer on the magnet sees the magnet as stationary with an unchanging magnetic field, while the conducting loop moves.^ Where is the moving charge responsible for this magnetic field?

^ The torque on a current loop in a magnetic field.

^ A permanent magnetic field is stationary or still, unless you are moving the magnet.
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.All of the charges within the loop move with the loop, and due to the B-field experience a sideways Lorentz force, which generates the EMF. On the other hand, an observer on the loop sees a changing magnetic field due to a moving magnet (relative to the loop's reference frame) and no Lorentz force (charges in the loop are not moving).^ Magnetic fields have no sources or sinks.

^ In this frame of reference, the earth is moving, and therefore the local magnetic field is changing in strength by 10 -9 T/s.

^ Where is the moving charge responsible for this magnetic field?

.This changing magnetic field means ∂B / ∂t ≠ 0, which creates an electric field that generates the current.^ Any wire that carries an AC electrical current produces magnetic fields.
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^ An AC electric field will also create a current in the body.
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^ The magnetic field, in turn, creates an electric field, which reinforces the existing electric field.
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.Prior to special relativity, it was customary to draw a sharp distinction between these two cases; a stationary magnet and a moving loop only produces motional EMF due to the Lorentz force from the B-field, while a moving magnet through a stationary loop produces only transformer EMF due to the electric field E generated by a changing B.^ What is the difference between an electric field and a magnetic field?
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^ Where is the moving charge responsible for this magnetic field?

^ From arguments about relative motion, we concluded that moving electric charges create magnetic fields.

See Faraday's law as two different phenomena. Einstein, on the other hand, proposed the equivalence of these two scenarios[32] in the first postulate of relativity that the physics depends on only relative motion. .Motional EMF and transformer EMF, therefore are the same phenomenon as seen in different reference frames.^ A charged particle and a current, seen in two different frames of reference.

^ The pair of charged particles, as seen in two different frames of reference.

^ In this frame of reference, the earth is moving, and therefore the local magnetic field is changing in strength by 10 -9 T/s.

Likewise, the same is true of E and B, which are not separate, but are aspects of the same electromagnetic tensor.

Important uses and examples of magnetic field

Magnetic circuits

.An important use of H is in magnetic circuits where inside a linear material B = μ H.^ If a current of 1.0 A is used, find the magnetic field inside the solenoid if the core is air, and if the core is made of iron with μ/μ o =4,000.

.Here, μ is the magnetic permeability of the material.^ Here are the magnetic permeabilities of some substances: .

^ The result is that when a magnetic field enters a high-permeability material, it tends to twist abruptly to one side, and the pattern of the field tends to be channeled through the material like water through a funnel.

^ A magnetically permeable material is placed at the center of a solenoid.

.This result is similar in form to Ohm's law J = σ E, where J is the current density, σ is the conductance and E is the electric field.^ The Φ E equation is Gauss' law: charges make diverging electric fields.

^ The small arrows show the result of the Biot-Savart law at various positions relative to the current segment .

^ Gauss' law in differential form relates , a scalar, to the charge density, another scalar.

Extending this analogy we derive the counterpart to the macroscopic Ohm's law ( I = V ⁄ R ) as:
\Phi = \frac F R_m,
where \Phi = \int \mathbf{B}\cdot d\mathbf{A} is the magnetic flux in the circuit, F = \int \mathbf{H}\cdot d\mathbf{l} is the magnetomotive force applied to the circuit, and Rm is the reluctance of the circuit. Here the reluctance Rm is a quantity similar in nature to resistance for the flux.
.Using this analogy it is straight-forward to calculate the magnetic flux of complicated magnetic field geometries, by using all the available techniques of circuit theory.^ Geometry of the electric and magnetic fields .

^ The magnetic field of a long, straight wire.

^ Modify the calculation on page 617 to determine the component of the magnetic field of a sheet of charge that is perpendicular to the sheet.

Hall effect

.The charge carriers of a current carrying conductor placed in a transverse magnetic field experience a sideways Lorentz force; this results in a charge separation in a direction perpendicular to the current and to the magnetic field.^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

^ Where is the moving charge responsible for this magnetic field?

^ Any wire that carries an AC electrical current produces magnetic fields.
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.The resultant voltage in that direction is proportional to the applied magnetic field.^ Infer the direction of the magnetic field.

^ Do we have infinite energy in the resulting magnetic field?

^ The current is at right angles to the direction of the changing magnetic field, and is strongest near the extremities of a person.
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This is known as the Hall effect.
.The Hall effect is often used to measure the magnitude of a magnetic field.^ When a field is curly, we can measure its curliness using a circulation.

^ Effects like magnetic photon splitting cannot be measured in terrestrial laboratories, but may be detected in emissions from these unique cosmic laboratores.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ Now perhaps we can use reasoning with the same flavor to show that changing magnetic fields produce curly electric fields.

.It is used as well to find the sign of the dominant charge carriers in materials such as semiconductors (negative electrons or positive holes).^ Positive and negative signs in Ampère's law.

^ Positive and negative signs .

^ These lodestones have been charged by the Earth, and thus are harmoniously in tune with the human bodies' frequencies as well, they have for thousands of years been successfully used in the healing arts.
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Magnetic field shape descriptions

.
Schematic quadrupole magnet ("four-pole") magnetic field.
^ That is, it is not a simple field with just a north and south pole, like a bar magnet.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ (In this way, they resemble the field lines of an iron bar magnet, which arch from the north to the south poles.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

.There are four steel pole tips, two opposing magnetic north poles and two opposing magnetic south poles.
  • An azimuthal magnetic field is one that runs east-west.
  • A meridional magnetic field is one that runs north-south.^ That is, it is not a simple field with just a north and south pole, like a bar magnet.
    • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

    ^ Roughly speaking, it looks like the field of one big dipole, especially farther away from the magnet.

    ^ As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

    .In the solar dynamo model of the Sun, differential rotation of the solar plasma causes the meridional magnetic field to stretch into an azimuthal magnetic field, a process called the omega-effect.^ Dynamos operate in the interior of the Earth and the Sun, giving them their magnetic fields.
    • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

    ^ An electric motorized clock, plugged into a wall socket, produces an amazingly high magnetic field because of the small electric motor that runs it.
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    ^ The changing magnetic field creates an electric field directly in the wire, which causes electrons in the wire to move.
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    The reverse process is called the alpha-effect.[33]
  • .
  • A quadrupole magnetic field is one seen, for example, between the poles of four bar magnets.^ Where is the moving charge responsible for this magnetic field?

    ^ Or an example where the fields are purely electric in one frame, but purely magnetic in another?

    ^ A charged particle is in a region of space in which there is a uniform magnetic field .

    .The field strength grows linearly with the radial distance from its longitudinal axis.
  • A solenoidal magnetic field is similar to a dipole magnetic field, except that a solid bar magnet is replaced by a hollow electromagnetic coil magnet.
  • A toroidal magnetic field occurs in a doughnut-shaped coil, the electric current spiraling around the tube-like surface, and is found, for example, in a tokamak.
  • A poloidal magnetic field is generated by a current flowing in a ring, and is found, for example, in a tokamak.
  • A radial magnetic field is one in which the field lines are directed from the center outwards, similar to the spokes in a bicycle wheel.^ If the current is a DC (direct current), the magnetic field is steady, like that form a permanent magnet.
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    ^ Or an example where the fields are purely electric in one frame, but purely magnetic in another?

    ^ Example 1: The magnetic dipole moment of an atom .

    An example can be found in a loudspeaker transducers (driver).[34]
  • .
  • A helical magnetic field is corkscrew-shaped, and sometimes seen in space plasmas such as the Orion Molecular Cloud.^ Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.
    • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

    ^ A charged particle is in a region of space in which there is a uniform magnetic field .

    ^ Such a substance, subjected to a magnetic field, tends to align itself, c /2, so that a sheet of current circulates around the externally applied field.

    [35]

Magnetic dipoles

Magnetic field lines around a ”magnetostatic dipole” pointing to the right.
.The magnetic field of a magnetic dipole is depicted on the right.^ Roughly speaking, it looks like the field of one big dipole, especially farther away from the magnet.

^ The current is at right angles to the direction of the changing magnetic field, and is strongest near the extremities of a person.
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^ The magnetic field pattern around a bar magnet is created by the superposition of the dipole fields of the individual iron atoms.

.From outside, the ideal magnetic dipole is identical to that of an ideal electric dipole of the same strength.^ Now perhaps we can use reasoning with the same flavor to show that changing magnetic fields produce curly electric fields.

^ This is the same as the field of a magnetic dipole in its midplane, except that the electric coupling constant k replaces the magnetic version k / c 2 , and the electric dipole moment D is substituted for the magnetic dipole moment m .

^ An easy way to approach this is to use the fact that vB has the same units as E , which can be seen by comparing the equations for magnetic and electric forces used above.

.Unlike the electric dipole, a magnetic dipole is properly modeled as a current loop having a current I and an area a.^ The torque on a current loop in a magnetic field.

^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

^ An electric dipole, unlike a magnetic one, can be built out of two opposite monopoles, i.e., charges, separated by a certain distance, and it is then straightforward to show by vector addition that the field of an electric dipole is .

Such a current loop has a magnetic moment of:
m=Ia, \,
where the direction of .m is perpendicular to the area of the loop and depends on the direction of the current using the right hand rule.^ This is in agreement with the right-hand rule.

^ Verify the direction of the force using right-hand rules.

^ This agrees with the right-hand rule.

.An ideal magnetic dipole is modeled as a real magnetic dipole whose area a has been reduced to zero and its current I increased to infinity such that the product m = Ia is finite.^ Such a substance, subjected to a magnetic field, tends to align itself, c /2, so that a sheet of current circulates around the externally applied field.

^ Apparently, nearly all the atoms in such a magnet are oriented randomly, and do not contribute to the magnet's dipole moment.

^ The increasing magnetic field causes electrons to circulate (current) around the second coil in such a way as to oppose the increasing magnetic field that the first coil is trying to establish.
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.In this model it is easy to see the connection between angular momentum and magnetic moment which is the basis of the Einstein-de Haas effect "rotation by magnetization" and its inverse, the Barnett effect or "magnetization by rotation".[36] Rotating the loop faster (in the same direction) increases the current and therefore the magnetic moment, for example.^ Example 1: The magnetic dipole moment of an atom .

^ The s state, for example, has zero angular momentum.

^ Suppose the currents are in the same direction.

.It is sometimes useful to model the magnetic dipole similar to the electric dipole with two equal but opposite magnetic charges (one south the other north) separated by distance d.^ An electric dipole, unlike a magnetic one, can be built out of two opposite monopoles, i.e., charges, separated by a certain distance, and it is then straightforward to show by vector addition that the field of an electric dipole is .

^ In one case the sources are charges and the field is electric; in the other case we have currents and magnetic fields.

^ Roughly speaking, it looks like the field of one big dipole, especially farther away from the magnet.

This model produces an H-field not a B-field. .Such a model is deficient, though, both in that there are no magnetic charges and in that it obscures the link between electricity and magnetism.^ What is the difference between an electric field and a magnetic field?
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^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

^ No charge will actually flow through the air gap between them, yet a magnetic field will be created in that gap as if the charge were flowing.
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.Further, as discussed above it fails to explain the inherent connection between angular momentum and magnetism.^ If the braking was due to magnetic waves carrying away energy and angular momentum, as seemed plausible, then the field strength was 8 X 10 14 Gauss.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ Magnetism, as we discussed previously, is an interaction between a moving charge and another moving charge, as opposed to electric forces, which act between any pair of charges, regardless of their motion.

Earth's magnetic field

.
A sketch of Earth's magnetic field representing the source of Earth's magnetic field as a magnet.
^ Magnetic fields have no sources or sinks.

^ Living organisms have the ability to somehow sense these minute daily cycles in the Earth's magnetic field and to use them to time their biological cycles.
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^ The magnetite crystals "tell" the pigeon's brain the exact direction of the Earth's magnetic field, and the pigeon uses this information to navigate with its amazing precision.
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.The north pole of earth is near the top of the diagram, the south pole near the bottom.^ Since the distance from the equator to a pole is about 10 7 m, we can estimate, very roughly, that the horizontal component of the earth's magnetic field typically varies by about 10 -11 T/m as you go north or south.

^ That is, it is not a simple field with just a north and south pole, like a bar magnet.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ (In this way, they resemble the field lines of an iron bar magnet, which arch from the north to the south poles.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

.Notice that the south pole of that magnet is deep in Earth's interior below Earth's North Magnetic Pole.^ Since the distance from the equator to a pole is about 10 7 m, we can estimate, very roughly, that the horizontal component of the earth's magnetic field typically varies by about 10 -11 T/m as you go north or south.

^ That is, it is not a simple field with just a north and south pole, like a bar magnet.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ For example, magnetic field lines continually drift through the star's liquid interior, stressing the crust from below.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

Earth's magnetic field is produced in the outer liquid part of its core due to a dynamo that produce electrical currents there.
.Because of Earth's magnetic field, a compass placed anywhere on Earth turns so that the "north pole" of the magnet inside the compass points roughly north, toward Earth's north magnetic pole in northern Canada.^ The Earths magnetic field, which deflects compass needles .
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ The electric field at point P is , and the magnetic field is .

^ Upon detecting a GRB, Swift swiftly (within 20-70 seconds) turns and points both an X-ray telescope and an optical-UV telescope toward it.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

.This is the traditional definition of the "north pole" of a magnet, although other equivalent definitions are also possible.^ You manage to learn quite a bit of each other's languages, but you're stumped when you try to establish the definitions of left and right (or, equivalently, clockwise and counterclockwise).

^ Assume that no other forces are present besides the possible electrical and magnetic ones, and that the fields, if they are present, are uniform.

^ That is, it is not a simple field with just a north and south pole, like a bar magnet.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

.One confusion that arises from this definition is that if Earth itself is considered as a magnet, the south pole of that magnet would be the one nearer the north magnetic pole, and vice-versa.^ Suppose, for example, that the axis of the coil is aligned with the magnetic north-south.

^ The compasses in the chain are stable when aligned with one another, because each one's north end is attracted to its neighbor's south end.

^ The aliens might have reversed their definition of the magnetic field, in which case their drawings of field patterns would look like mirror images of ours, as in the left panel of figure t .

[37] .(Opposite poles attract, so the north pole of the compass magnet is attracted to the south pole of Earth's interior magnet.^ Suppose, for example, that the axis of the coil is aligned with the magnetic north-south.

^ The compasses in the chain are stable when aligned with one another, because each one's north end is attracted to its neighbor's south end.

^ The horizontal component of the earth's magnetic field varies from zero, at a magnetic pole, to about 10 -4 T near the equator.

) .The north magnetic pole is so named not because of the polarity of the field there but because of its geographical location.^ Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ This is because the current in the coil sets up its own magnetic field, and that field exerts a torque on the magnet.

^ A charged particle is in a region of space in which there is a uniform magnetic field .

.The figure to the right is a sketch of Earth's magnetic field represented by field lines.^ The current is at right angles to the direction of the changing magnetic field, and is strongest near the extremities of a person.
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^ The magnetite crystals "tell" the pigeon's brain the exact direction of the Earth's magnetic field, and the pigeon uses this information to navigate with its amazing precision.
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^ In this frame of reference, the earth is moving, and therefore the local magnetic field is changing in strength by 10 -9 T/s.

.For most locations, the magnetic field has a significant up/down component in addition to the North/South component.^ Suppose, for example, that the axis of the coil is aligned with the magnetic north-south.

^ Modify the calculation on page 617 to determine the component of the magnetic field of a sheet of charge that is perpendicular to the sheet.

^ Their magnetic fields could sweep up diffuse gas from interstellar space, helping to make dead magnetars glow.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

.(There is also an East/West component; Earth's magnetic poles do not coincide exactly with Earth's geological pole.^ Since the distance from the equator to a pole is about 10 7 m, we can estimate, very roughly, that the horizontal component of the earth's magnetic field typically varies by about 10 -11 T/m as you go north or south.

^ The horizontal component of the earth's magnetic field varies from zero, at a magnetic pole, to about 10 -4 T near the equator.

) .The magnetic field is as if there were a magnet deep in Earth's interior.^ Dynamos operate in the interior of the Earth and the Sun, giving them their magnetic fields.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ A current will not flow through a resistor unless there is some electric field pushing the electrons, so we conclude that the changing magnetic field has produced an electric field in the surrounding space.

^ There are three types of energy involved: the increase in the magnetic field energy, the increase in the energy of the outside world, and the decrease in energy as the battery is drained.

.Earth's magnetic field is probably due to a dynamo that produces electric currents in the outer liquid part of its core.^ The electric field of a sheet of charge, and the magnetic field of a sheet of current.

^ The relationship between the change in the magnetic field, and the electric field it produces.

^ Any wire that carries an AC electrical current produces magnetic fields.
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.Earth's magnetic field is not constant: Its strength and the location of its poles vary.^ The strength of the Earth's magnetic field averages about half a gauss.
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^ (This field-strength given by a combination of fundamental constants: B Q = m e 2 c 3 / h e , where m e is the mass of the electron, c is the speed of light, h is Planck's constant divided by 2 π, and e is the charge on an electron.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

The poles even periodically reverse direction, in a process called geomagnetic reversal.

Rotating magnetic fields

.The rotating magnetic field is a key principle in the operation of alternating-current motors.^ Magnetic fields curl around currents.

^ The torque on a current loop in a magnetic field.

^ An electric current flowing in a wire or coil produces its own magnetic field.
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.A permanent magnet in such a field rotates so as to maintain its alignment with the external field.^ As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

^ Because the hysteresis curve is highly nonlinear, the addition of an external field such as the Earth's alters the core's behavior.

^ If the current is a DC (direct current), the magnetic field is steady, like that form a permanent magnet.
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.This effect was conceptualized by Nikola Tesla, and later utilized in his, and others', early AC (alternating-current) electric motors.^ Any wire that carries an AC electrical current produces magnetic fields.
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^ An AC electric field will also create a current in the body.
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^ Electric current in your home is supposed to flow out of one side of the outlet, through an appliance, and back into the wall through the other side of the outlet.

.A rotating magnetic field can be constructed using two orthogonal coils with 90 degrees phase difference in their AC currents.^ What is the difference between an electric field and a magnetic field?
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^ Any wire that carries an AC electrical current produces magnetic fields.
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^ Magnetic fields curl around currents.

.However, in practice such a system would be supplied through a three-wire arrangement with unequal currents.^ A large current flows through the wire.

^ Four long wires are arranged, as shown, so that their cross-section forms a square, with connections at the ends so that current flows through all four before exiting.

^ A wire carrying current I passes perpendicularly through the center of the rectangular Ampèrian surface.

.This inequality would cause serious problems in standardization of the conductor size and so, in order to overcome it, three-phase systems are used where the three currents are equal in magnitude and have 120 degrees phase difference.^ Relate λ 2 and v 2 to the current I 2 , using the result of problem 5 a.

^ The magnitude of this force equals (homework problem 6 ), and using the definition of force, d p /d t , we find for the magnitude of the momentum transferred: .

^ For a given emf applied by an external radio wave, the current induced in the circuit has been attenuated by an order of magnitude, relative to its value without the ferrite bead.

.Three similar coils having mutual geometrical angles of 120 degrees create the rotating magnetic field in this case.^ The coil on the input side creates a magnetic field.

^ A changing magnetic field can create an electric field.
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^ An electric current flowing in a wire or coil produces its own magnetic field.
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.The ability of the three-phase system to create a rotating field, utilized in electric motors, is one of the main reasons why three-phase systems dominate the world's electrical power supply systems.^ This electric field is not created by charges .

^ A changing magnetic field can create an electric field.
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^ In reception, both conductors are bathed in the same electric and magnetic fields, so an emf that adds current on one side subtracts current from the other side, resulting in cancellation.

.Because magnets degrade with time, synchronous motors and induction motors use short-circuited rotors (instead of a magnet) following the rotating magnetic field of a multicoiled stator.^ Now perhaps we can use reasoning with the same flavor to show that changing magnetic fields produce curly electric fields.

^ Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ This is because the current in the coil sets up its own magnetic field, and that field exerts a torque on the magnet.

.The short-circuited turns of the rotor develop eddy currents in the rotating field of the stator, and these currents in turn move the rotor by the Lorentz force.^ Magnetic fields are produced by moving electrical currents, and the field of a bar magnet is produced by the spinning electrons around the atomic nuclei in the iron material of the magnet itself.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

^ Since the magnetic field lines were anchored to the rotating neutron star, the zones of glowing gas also turned every 8 seconds.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ For these currents induced by magnetic fields, the current per area increases proportional to the linear size of the organism.
  • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

.In 1882, Nikola Tesla identified the concept of the rotating magnetic field.^ A radio pulsar's magnetic field is essentially stable; its main role is to passively facilitate the loss of rotational energy.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

^ The unit of magnetic field, the tesla, is named after Serbian-American inventor Nikola Tesla.

^ Since the magnetic field lines were anchored to the rotating neutron star, the zones of glowing gas also turned every 8 seconds.
  • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

In 1885, Galileo Ferraris independently researched the concept. In 1888, Tesla gained U.S. Patent 381,968 for his work. Also in 1888, Ferraris published his research in a paper to the Royal Academy of Sciences in Turin.

See also

General
Mathematics
  • Ampère's law – law describing how currents act as circulation sources for magnetic fields.
  • Biot–Savart law – the magnetic field set up by a steadily flowing line current.
  • Magnetic helicity – extent to which a magnetic field "wraps around itself".
  • Maxwell's equations – four equations describing the behavior of electric and magnetic fields and their interaction with matter.
Applications
  • Dynamo theory – a proposed mechanism for the creation of the Earth's magnetic field.
  • Earth's magnetic field – a discussion of the magnetic field of the Earth.
  • Electric motor – AC motors used magnetic fields.
  • Helmholtz coil – a device for producing a region of nearly uniform magnetic field.
  • Magnetic field viewing film – Film used to view the magnetic field of an area.
  • Maxwell coil – a device for producing a large volume of an almost constant magnetic field.
  • Stellar magnetic field – a discussion of the magnetic field of stars.
  • Teltron Tube – device used to display an electron beam and demonstrates effect of electric and magnetic fields on moving charges.

Notes and references

  1. ^ Technically, magnetic field is a pseudo vector; pseudo-vectors, which also include torque and rotational velocity, are similar to vectors except that they remain unchanged when the coordinates are inverted.
  2. ^ The standard graduate textbook by J. D. Jackson "Classical Electrodynamics" specifically follows the historical tradition, specifically, "In the presence of magnetic materials the dipole tends to align itself in a certain direction. That direction is by definition the direction of the magnetic flux density, denoted by B, provided the dipole is sufficiently small and weak that it does not perturb the existing field". Similarly, in Section 5 of Jackson, H is referred to as the magnetic field. Hence, Edward Purcell, in Electricity and Magnetism, McGraw-Hill, 1963, writes, Even some modern writers who treat B as the primary field feel obliged to call it the magnetic induction because the name magnetic field was historically preempted by H. This seems clumsy and pedantic. If you go into the laboratory and ask a physicist what causes the pion trajectories in his bubble chamber to curve, he'll probably answer "magnetic field", not "magnetic induction." You will seldom hear a geophysicist refer to the Earth's magnetic induction, or an astrophysicist talk about the magnetic induction of the galaxy. We propose to keep on calling B the magnetic field. As for H, although other names have been invented for it, we shall call it "the field H" or even "the magnetic field H." In a similar vein, M Gerloch (1983). Magnetism and Ligand-field Analysis. Cambridge University Press. p. 110. ISBN 0521249392. http://books.google.com/books?id=Ovo8AAAAIAAJ&pg=PA110.  says: “So we may think of both B and H as magnetic fields, but drop the word 'magnetic' from H so as to maintain the distinction … As Purcell points out, 'it is only the names that give trouble, not the symbols'.”
  3. ^ R. Nave (2005). "Magnetic Field Strength H". HyperPhysics. Georgia State University, Deptartement of Physics and Astronomy. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfield.html. 
  4. ^ Magnetic Field Strength Converter, UnitConversion.org.
  5. ^ H. P. Myers (1997). Introductory solid state physics (2nd ed.). Taylor & Francis. p. 366. ISBN 074840659X. http://books.google.com/books?id=QhqyWH7DDQ0C&pg=PA366. 
  6. ^ Yuval Ne ̕eman, Y. Kirsh (1996). The Particle Hunters (2 ed.). Cambridge University Press. p. 56. ISBN 0521476860. http://books.google.com/books?id=K4jcfCguj8YC&pg=PA56. 
  7. ^ John S Townsend (2000). "Stern–Gerlach experiments". A Modern Approach to Quantum Mechanics (2 ed.). University Science Books. pp. 1–23. ISBN 1891389130. http://books.google.com/books?id=3_7uriPX028C&pg=PA3. 
  8. ^ See Eq. 11.42 in E. Richard Cohen, David R. Lide, George L. Trigg (2003). AIP physics desk reference (3 ed.). Birkhäuser. p. 381. ISBN 0387989730. http://books.google.com/books?id=JStYf6WlXpgC&pg=PA381. 
  9. ^ Griffiths, David J. (1999). .Introduction to Electrodynamics (3rd ed.^ Introduction to Electrodynamics (3rd ed.
    • Magnetic Field K-12 Experiments for Lesson Plans & Science Fair Projects 13 January 2010 10:13 UTC www.juliantrubin.com [Source type: Academic]
    • PowerPedia:Magnetic field - PESWiki 13 January 2010 10:13 UTC peswiki.com [Source type: Academic]

    ^ Classical Electrodynamics (3rd ed.
    • Magnetic Field K-12 Experiments for Lesson Plans & Science Fair Projects 13 January 2010 10:13 UTC www.juliantrubin.com [Source type: Academic]
    • PowerPedia:Magnetic field - PESWiki 13 January 2010 10:13 UTC peswiki.com [Source type: Academic]

    )
    . Prentice Hall. pp. 255–8. ISBN 0-13-805326-X. OCLC 40251748.
     
  10. ^ The use of iron filings to display a field presents something of an exception to this picture; the filing alter the magnetic field so that it is much larger along the "lines" of iron, due to the large permeability of iron relative to air.
  11. ^ To see that this must be true imagine placing a compass inside a magnet. There, the north pole of the compass will point toward the north pole of the magnet since magnets stacked on each other point in the same direction.
  12. ^ Two experiments produced candidate events that were initially interpreted as monopoles, but these are now regarded to be inconclusive. For details and references, see magnetic monopole.
  13. ^ In special relativity this means that electric and magnetic fields are two parts of the same phenomenon, for a moving charge produces both an electric and a magnetic field. But in a reference frame where the particle is not moving, there is only an electric field. However, the same physics applies to all reference systems. In this reference system, the electric field changes as well to produces the same force as the original reference frame. It is probably a mistake, however, to say that the electric field causes the magnetic field when relativity is taken into account, since relativity favors no particular reference frame. (One could just as easily say that the magnetic field caused an electric field.) More importantly, it is not always possible to move into a coordinate system in which all of the charges are stationary. See classical electromagnetism and special relativity.[citation needed]
  14. ^ Griffiths, David J. (1999). Introduction to Electrodynamics (3rd ed.). Prentice Hall. p. 438. ISBN 0-13-805326-X. OCLC 40251748. 
  15. ^ In practice the Biot–Savart law and other laws of magnetostatics can often be used even when the charge is changing in time as long as it is not changing too quickly. This situation is known as being quasistatic.[citation needed]
  16. ^ Griffiths, David J. (1999). Introduction to Electrodynamics (3rd ed.). Prentice Hall. pp. 222–225. ISBN 0-13-805326-X. OCLC 40251748. 
  17. ^ The Biot–Savart law contains the additional restriction (boundary condition) that the B-field must go to zero fast enough at infinity. It also depends on the divergence of B being zero, which is always valid. (There are no magnetic charges.)
  18. ^ Deissler, R.J. (2008). "Dipole in a magnetic field, work, and quantum spin". Physical Review E 77 (3, pt 2): 036609. doi:10.1103/PhysRevE.77.036609. PMID 18517545. http://academic.csuohio.edu/deissler/PhysRevE_77_036609.pdf. 
  19. ^ a b RJD Tilley (2004). Understanding Solids. Wiley. p. 368. ISBN 0470852755. http://books.google.com/books?id=ZVgOLCXNoMoC&pg=PA368. 
  20. ^ Sōshin Chikazumi, Chad D. Graham (1997). Physics of ferromagnetism (2 ed.). Oxford University Press. p. 118. ISBN 0198517769. http://books.google.com/books?id=AZVfuxXF2GsC&printsec=frontcover. 
  21. ^ Amikam Aharoni (2000). Introduction to the theory of ferromagnetism (2 ed.). Oxford University Press. p. 27. ISBN 0198508085. http://books.google.com/books?id=9RvNuIDh0qMC&pg=PA27. 
  22. ^ M Brian Maple et al. (2008). "Unconventional superconductivity in novel materials". in K. H. Bennemann, John B. Ketterson. Superconductivity. Springer. p. 640. ISBN 3540732527. http://books.google.com/books?id=PguAgEQTiQwC&pg=PA640. 
  23. ^ Naoum Karchev (2003). "Itinerant ferromagnetism and superconductivity". in Paul S. Lewis, D. Di (CON) Castro. Superconductivity research at the leading edge. Nova Publishers. p. 169. ISBN 1590338618. http://books.google.com/books?id=3AFo_yxBkD0C&pg=PA169. 
  24. ^ John Clarke Slater, Nathaniel Herman Frank (1969). Electromagnetism (first published in 1947 ed.). Courier Dover Publications. p. 69. ISBN 0486622630. http://books.google.com/books?id=GYsphnFwUuUC&pg=PA69. 
  25. ^ A complete expression for Faraday's law of induction in terms of the electric E and magnetic fields can be written as: 	extstyle\mathcal{E} = - \frac{d\Phi_m}{dt} 	extstyle= \oint_{\partial \Sigma (t)}\left( \mathbf{E}( \mathbf{r},\ t) +\mathbf{ v 	imes B}(\mathbf{r},\ t)\right) \cdot d\boldsymbol{\ell}\ 	extstyle=-\frac {d} {dt} \iint_{\Sigma (t)} d \boldsymbol {A} \cdot \mathbf {B}(\mathbf{r},\ t), where ∂Σ(t) is the moving closed path bounding the moving surface Σ(t), and dA is an element of surface area of Σ(t). The first integral calculates the work done moving a charge a distance d based upon the Lorentz force law. In the case where the bounding surface is stationary, the Kelvin–Stokes theorem can be used to show this equation is equivalent to the Maxwell–Faraday equation.
  26. ^ E. J. Konopinski (1978). "What the electromagnetic vector potential describes". Am. J. Phys. 46 (5): 499–502. doi:10.1119/1.11298. 
  27. ^ Griffiths, David J. (1999). .Introduction to Electrodynamics (3rd ed.^ Introduction to Electrodynamics (3rd ed.
    • Magnetic Field K-12 Experiments for Lesson Plans & Science Fair Projects 13 January 2010 10:13 UTC www.juliantrubin.com [Source type: Academic]
    • PowerPedia:Magnetic field - PESWiki 13 January 2010 10:13 UTC peswiki.com [Source type: Academic]

    ^ Classical Electrodynamics (3rd ed.
    • Magnetic Field K-12 Experiments for Lesson Plans & Science Fair Projects 13 January 2010 10:13 UTC www.juliantrubin.com [Source type: Academic]
    • PowerPedia:Magnetic field - PESWiki 13 January 2010 10:13 UTC peswiki.com [Source type: Academic]

    )
    . Prentice Hall. p. 422. ISBN 0-13-805326-X. OCLC 40251748.
     
  28. ^ For a good qualitative introduction see: Feynman, Richard (2006). QED: the strange theory of light and matter. Princeton University Press. ISBN 0-691-12575-9. 
  29. ^ [1] Gravity Probe B
  30. ^ "With record magnetic fields to the 21st Century". IEEE Xplore. http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=823621. 
  31. ^ Kouveliotou, C.; Duncan, R. C.; Thompson, C. (February 2003). "Magnetars". Scientific American; Page 36.
  32. ^ Einstein, Albert (1905). "Zur Elektrodynamik bewegter Körper (On the Electrodynamics of Moving Bodies)". Annalen der Physik (17): 891–921. http://www.fourmilab.ch/etexts/einstein/specrel/www/. Retrieved 2009-06-18. "They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.1 We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”).". 
  33. ^ The Solar Dynamo, retrieved Sep 15, 2007.
  34. ^ I. S. Falconer and M. I. Large (edited by I. M. Sefton), "Magnetism: Fields and Forces" Lecture E6, The University of Sydney, retrieved 3 Oct 2008
  35. ^ Robert Sanders, "Astronomers find magnetic Slinky in Orion", 12 January 2006 at UC Berkeley. Retrieved 3 Oct 2008
  36. ^ (See magnetic moment for further information.) B. D. Cullity, C. D. Graham (2008). Introduction to Magnetic Materials (2 ed.). Wiley-IEEE. p. 103. ISBN 0471477419. http://books.google.com/books?id=ixAe4qIGEmwC&pg=PA103. 
  37. ^ College Physics, Volume 10, by Serway, Vuille, and Faughn, page 628 weblink. "the geographic North Pole of Earth corresponds to a magnetic south pole, and the geographic South Pole of Earth corresponds to a magnetic north pole".

Further reading

Web
  • Nave, R.. ."Magnetic Field Strength H".^ Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.
    • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

    ^ In this frame of reference, the earth is moving, and therefore the local magnetic field is changing in strength by 10 -9 T/s.

    ^ Compute and , and compare with the strengths of static fields you experience in everyday life: E ∼ 10 6 V/m in a thunderstorm, and B ∼ 10 -3 T for the Earth's magnetic field.

    http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfield.html
    . Retrieved 2007-06-04.
     
  • Oppelt, Arnulf (2006-11-02). ."magnetic field strength".^ Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.
    • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

    ^ In this frame of reference, the earth is moving, and therefore the local magnetic field is changing in strength by 10 -9 T/s.

    ^ Compute and , and compare with the strengths of static fields you experience in everyday life: E ∼ 10 6 V/m in a thunderstorm, and B ∼ 10 -3 T for the Earth's magnetic field.

    http://searchsmb.techtarget.com/sDefinition/0,290660,sid44_gci763586,00.html
    . .Retrieved 2007-06-04. 
  • "magnetic field strength converter".^ Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.
    • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

    ^ In this frame of reference, the earth is moving, and therefore the local magnetic field is changing in strength by 10 -9 T/s.

    ^ Compute and , and compare with the strengths of static fields you experience in everyday life: E ∼ 10 6 V/m in a thunderstorm, and B ∼ 10 -3 T for the Earth's magnetic field.

    .http://www.unitconversion.org/unit_converter/magnetic-field-strength.html.^ Physicists have not made steady fields stronger than 4.5 x 10 5 Gauss in the lab because the magnetic stresses of such fields exceed the tensile strength of terrestrial materials.
    • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

    ^ In this frame of reference, the earth is moving, and therefore the local magnetic field is changing in strength by 10 -9 T/s.

    ^ Compute and , and compare with the strengths of static fields you experience in everyday life: E ∼ 10 6 V/m in a thunderstorm, and B ∼ 10 -3 T for the Earth's magnetic field.

    Retrieved 2007-06-04
    . 
Books
  • Durney, Carl H. and Johnson, Curtis C. (1969). Introduction to modern electromagnetics. McGraw-Hill. ISBN 0-07-018388-0. 
  • Griffiths, David J. (1999). .Introduction to Electrodynamics (3rd ed.^ Introduction to Electrodynamics (3rd ed.
    • Magnetic Field K-12 Experiments for Lesson Plans & Science Fair Projects 13 January 2010 10:13 UTC www.juliantrubin.com [Source type: Academic]
    • PowerPedia:Magnetic field - PESWiki 13 January 2010 10:13 UTC peswiki.com [Source type: Academic]

    ^ Classical Electrodynamics (3rd ed.
    • Magnetic Field K-12 Experiments for Lesson Plans & Science Fair Projects 13 January 2010 10:13 UTC www.juliantrubin.com [Source type: Academic]
    • PowerPedia:Magnetic field - PESWiki 13 January 2010 10:13 UTC peswiki.com [Source type: Academic]

    )
    . Prentice Hall. ISBN 0-13-805326-X. OCLC 40251748.
     
  • Jackson, John D. (1999). .Classical Electrodynamics (3rd ed.^ Introduction to Electrodynamics (3rd ed.
    • Magnetic Field K-12 Experiments for Lesson Plans & Science Fair Projects 13 January 2010 10:13 UTC www.juliantrubin.com [Source type: Academic]

    ^ Classical Electrodynamics (3rd ed.
    • Magnetic Field K-12 Experiments for Lesson Plans & Science Fair Projects 13 January 2010 10:13 UTC www.juliantrubin.com [Source type: Academic]

    )
    . Wiley. ISBN 0-471-30932-X. OCLC 224523909.
     
  • Tipler, Paul (2004). .Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.^ Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.
    • Magnetic Field K-12 Experiments for Lesson Plans & Science Fair Projects 13 January 2010 10:13 UTC www.juliantrubin.com [Source type: Academic]
    • PowerPedia:Magnetic field - PESWiki 13 January 2010 10:13 UTC peswiki.com [Source type: Academic]

    ^ Magnetic field lines shown by iron filings In physics , the magnetic field is a field that permeates space and which exerts a magnetic force on moving electric charges and magnetic dipoles .
    • Magnetic Field K-12 Experiments for Lesson Plans & Science Fair Projects 13 January 2010 10:13 UTC www.juliantrubin.com [Source type: Academic]

    ^ Ordinary incandescent light bulbs (and electric blankets made since 1992) produce very little magnetic field.
    • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

    )
    . W. H. Freeman. ISBN 0-7167-0810-8. OCLC 51095685.
     
  • Furlani, Edward P. (2001). Permanent Magnet and Electromechanical Devices: Materials, Analysis and Applications. Academic Press Series in Electromagnetism. ISBN 0-12-269951-3. OCLC 162129430. 

External links

Information
.
  • "Magnetism", The Magnetic Field.^ Electromagnetic waves are supposed to have their electric and magnetic fields perpendicular to each other.

    ^ However, the electromagnetic wave also has a magnetic field, and a magnetic field transfers momentum to (exerts a force on) a current.

    ^ In terms of transmission, the magnetic field created by the outgoing current is almost exactly canceled by the field from the return current, so electromagnetic waves are only weakly induced.

    theory.uwinnipeg.ca.
Field density
  • Jiles, David (1994). Introduction to Electronic Properties of Materials (1st ed.). Springer. ISBN 0-412-49580-5.
Rotating magnetic fields
.
  • "Introduction to Generators and Motors", rotating magnetic field.^ An electric motorized clock, plugged into a wall socket, produces an amazingly high magnetic field because of the small electric motor that runs it.
    • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

    ^ A radio pulsar's magnetic field is essentially stable; its main role is to passively facilitate the loss of rotational energy.
    • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

    ^ A basic generator, f , consists of a permanent magnet that rotates within a coil of wire.

    Integrated Publishing.
Diagrams
.
  • McCulloch, Malcolm,"A2: Electrical Power and Machines", Rotating magnetic field.^ Geometry of the electric and magnetic fields .

    ^ A changing magnetic field can create an electric field.
    • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

    ^ What is the difference between an electric field and a magnetic field?
    • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

    eng.ox.ac.uk.
  • .
  • "AC Motor Theory" Figure 2 Rotating Magnetic Field.^ An electric motorized clock, plugged into a wall socket, produces an amazingly high magnetic field because of the small electric motor that runs it.
    • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

    ^ However, the magnetic field patterns shown in figure s seems to violate this principle.

    ^ A radio pulsar's magnetic field is essentially stable; its main role is to passively facilitate the loss of rotational energy.
    • `MAGNETARS', SOFT GAMMA REPEATERS & VERY STRONG MAGNETIC FIELDS Robert C. Duncan, University of Texas at Austin 13 January 2010 10:13 UTC solomon.as.utexas.edu [Source type: General]

    Integrated Publishing.
Journal Articles
.
  • Yaakov Kraftmakher, "Two experiments with rotating magnetic field". 2001 Eur.^ As we'll see shortly, the magnetic field is required in order to maintain consistency between the predictions made in the two frames of reference.

    ^ Does the electron experience a magnetic field from the proton?

    ^ Compute and , and compare with the strengths of static fields you experience in everyday life: E ∼ 10 6 V/m in a thunderstorm, and B ∼ 10 -3 T for the Earth's magnetic field.

    J. Phys. .22 477-482.
  • Sonia Melle, Miguel A. Rubio and Gerald G. Fuller "Structure and dynamics of magnetorheological fluids in rotating magnetic fields". Phys.^ Does the electron experience a magnetic field from the proton?

    ^ This field is created by electrons orbiting atoms inside the magnet.

    ^ The increasing magnetic field causes electrons to circulate (current) around the second coil in such a way as to oppose the increasing magnetic field that the first coil is trying to establish.
    • Electromagnetic Fields 13 January 2010 10:13 UTC www.tuberose.com [Source type: FILTERED WITH BAYES]

    Rev. E 61, 4111 – 4117 (2000).

Simple English

The Magnetic field is the area around a magnet in which a magnetic force is exerted. Moving electric charges produce magnetic fields. Magnetic fields are usually shown by magnetic flux lines. At all times the direction of the magnetic field is shown by the direction of the magnetic flux lines. The strength of a magnet has to do with the spaces between magnetic flux lines. The closer the flux lines are to each other, the stronger the magnet. The farther apart they are, the weaker the magnet. The flux lines can be seen by placing iron filings over a magnet. Magnetic fields give power to other particles that come in contact with the magnetic field. In physics, the magnetic field is a field that permeates space and which exerts a magnetic force on moving electric charges and magnetic dipoles. Magnetic fields surround electric currents, magnetic dipoles, and changing electric fields.

When placed in a magnetic field, magnetic dipoles align their axes to be parallel with the field lines, as can be seen when iron filings are in the presence of a magnet. Magnetic fields also have their own energy and momentum, with an energy density proportional to the square of the field intensity. The magnetic field is measured in the units of teslas (SI units) or gauss (cgs units).

There are some notable specific forms of the magnetic field. For the physics of magnetic materials, see magnetism and magnet, and more specifically ferromagnetism, paramagnetism, and diamagnetism. For constant magnetic fields, such as are generated by stationary dipoles and steady currents, see magnetostatics. For magnetic fields created by changing electric fields, see electromagnetism.

The electric field and the magnetic field are components of the electromagnetic field.



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