Coulomb's law is a law of physics describing the electrostatic interaction between electrically charged particles. It was studied and first published in 1783 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism. Nevertheless, the dependence of the electric force with distance (inverse square law) had been proposed previously by Joseph Priestley^{[1]} and the dependence with both distance and charge had been discovered, but not published, by Henry Cavendish, prior to Coulomb's works.
Coulomb's law may be stated in scalar form as follows:
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The scalar form of Coulomb's law will only describe the magnitude of the electrostatic force between two electric charges. If direction is required, then the vector form is required as well. The magnitude of the electrostatic force (F) on a charge (q_{1}) due to the presence of a second charge (q_{2}), is given by
where r is the distance between the two charges and k_{e} a proportionality constant. A positive force implies a repulsive interaction, while a negative force implies an attractive interaction.^{[2]}
The proportionality constant k_{e}, called the Coulomb constant (sometimes called the Coulomb force constant), is related to defined properties of space and can be calculated exactly:^{[3]}
By definition in SI units, the speed of light in vacuum, denoted c,^{[4]} is 299,792,458 m·s^{−1},^{[5]} and the magnetic constant (μ_{0}), is defined as 4π × 10^{−7} H·m^{−1},^{[6]} leading to the consequential defined value for the electric constant (ε_{0}) as ε_{0} = 1/(μ_{0}c^{2}) ≈ 8.854187817×10^{−12} F·m^{−1}.^{[7]} In cgs units, the unit charge, esu of charge or statcoulomb, is defined so that this Coulomb constant is 1 and dimensionless.
This formula says that the magnitude of the force is directly proportional to the magnitude of the charges of each object and inversely proportional to the square of the distance between them. The exponent in Coulomb's Law has been found to be equal to −2 with precision of at least 2.7±3.1×10^{−16}.^{[8]}
Coulomb's law can also be interpreted in terms of atomic units with the force expressed in Hartrees per Bohr radius, the charge in terms of the elementary charge, and the distances in terms of the Bohr radius.
It follows from the Lorentz Force Law that the magnitude of the electric field (E) created by a single point charge (q) at a certain distance (r) is given by:
For a positive charge, the direction of the electric field points along lines directed radially away from the location of the point charge, while the direction is the opposite for a negative charge. The SI units of electric field are volts per meter or newtons per coulomb.
In order to obtain both the magnitude and direction of the force on a charge, q_{1} at position , experiencing a field due to the presence of another charge, q_{2} at position , the full vector form of Coulomb's law is required.
where r is the separation of the two charges. This is simply the scalar definition of Coulomb's law with the direction given by the unit vector, , parallel with the line from charge q_{2} to charge q_{1}.^{[9]}
If both charges have the same sign (like charges) then the product q_{1}q_{2} is positive and the direction of the force on q_{1} is given by ; the charges repel each other. If the charges have opposite signs then the product q_{1}q_{2} is negative and the direction of the force on q_{1} is given by ; the charges attract each other.
The principle of linear superposition may be used to calculate the force on a small test charge, q, due to a system of N discrete charges:
where q_{i} and are the magnitude and position respectively of the i^{th} charge, is a unit vector in the direction of (a vector pointing from charge q_{i} to charge q), and R_{i} is the magnitude of (the separation between charges q_{i} and q).^{[9]}
For a charge distribution an integral over the region containing the charge is equivalent to an infinite summation, treating each infinitesimal element of space as a point charge dq.
For a linear charge distribution (a good approximation for charge in a wire) where gives the charge per unit length at position , and is an infinitesimal element of length,
For a surface charge distribution (a good approximation for charge on a plate in a parallel plate capacitor) where gives the charge per unit area at position , and is an infinitesimal element of area,
For a volume charge distribution (such as charge within a bulk metal) where gives the charge per unit volume at position , and is an infinitesimal element of volume,
The force on a small test charge at position is given by
Below is a graphical representation of Coulomb's law, when q_{1}q_{2} > 0. The vector is the force experienced by q_{1}. The vector is the force experienced by q_{2}. Their magnitudes will always be equal. The vector is the displacement vector between two charges (q_{1} and q_{2}).
In either formulation, Coulomb’s law is fully accurate only when the objects are stationary, and remains approximately correct only for slow movement. These conditions are collectively known as the electrostatic approximation. When movement takes place, magnetic fields are produced which alter the force on the two objects. The magnetic interaction between moving charges may be thought of as a manifestation of the force from the electrostatic field but with Einstein’s theory of relativity taken into consideration.
Particle property  Relationship  Field property  
Vector quantity 



Relationship  
Scalar quantity 


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[[File:thumb220pxrightCharles Augustin de Coulomb]]
Coulomb's law is a function developed in the 1780s by physicist Charles Augustin de Coulomb. It explains how strong the force will be between two electrostatic charges. Electrostatic means electric charges without any motion.
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Let's think two electric charges exist in an empty space. If two charges are opposite, (+) and () charges for example, they will attract each other. And if two charges are both the same, both (+) or both () for example, they will push each other. This is similar to how magnetics act, as N and S attract each other, and as N and N, S and S push each other.
This is because electric charges make an electric field, such as magnetics make a magnetic field. When both electric charges make their own field, as two field will exist in one space at the same time, and they will make force to each other. The force they make to each other is called Coulomb's force or Electrostatic force. Coulomb's law explains how big the force will be.
Coulomb's law explains the scale between two electric charges. The scale of electrostatic force follows the function below.
Coulomb's law explains that the force scale F is relative to ratio of $q\_1,q\_2$,$\backslash frac\{1\}\{r^2\}$.
$q\_1$ and $q\_2$ are scale of each electric charges. $r$ is distance between two electric charges. And $K\_c$ has a certain value. It does not change relative to $q\_1$ , $q\_2$ or $r$. While $\{K\_c\}$ remains constant, when multiples of $q\_1$ and $q\_2$ become bigger, the electrostatic force will also get bigger. When the distance $r$ become bigger, the electrostatic force will become smaller to ratio of $\backslash frac\{1\}\{r^2\}$.
The exact size of $K\_c$ is
$\backslash begin\{align\}\; k\_c\; \&=\; 8.987\backslash \; 551\backslash \; 787\backslash \; \backslash times\; 10^9\; \backslash \backslash \; \backslash end\{align\}$
$\backslash approx\; 9\; \backslash times\; 10^9$N m^{2} C^{−2} (or m F^{−1}). This constant is called as Coulomb's Force Constant or Electrostatic Force Constant.
The relation between the force F and the distance $r$ follows the Inversesquare Law. Inversesquare law means means that when the distance $r$ grow bigger, electrostatic force will become smaller to ratio of $\backslash frac\{1\}\{r^2\}$. Gravitation, Electromagnetic radiation, Sound Intensity also follows this law.
