# Electric flux: Wikis

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# Encyclopedia

Electromagnetism
Electricity · Magnetism
Electrostatics
Electric flux · Polarization density

In electromagnetism, electric flux is the flux of the electric field. Electric flux is proportional to the number of electric field lines going through a virtual surface. The electric flux $d\Phi_E\,$ through a small area $d\mathbf{A}$ is given by

$d\Phi_E = \mathbf{E} \cdot d\mathbf{A}$

(the electric field, E, multiplied by the component of area perpendicular to the field). The electric flux over a surface S is therefore given by the surface integral:

$\Phi_E = \int_S \mathbf{E} \cdot d\mathbf{A}$

where E is the electric field and dA is a differential area on the closed surface S with an outward facing surface normal defining its direction.

For a closed Gaussian surface, electric flux is given by:

$\Phi_E = \oint_S \mathbf{E} \cdot d\mathbf{A} = \frac{Q_S}{\epsilon_0}$

where QS is the charge enclosed by the surface (including both free and bound charge), and ε0 is the electric constant. This relation is known as Gauss' law for electric field in its integral form and it is one of the four Maxwell's equations.

Electrical flux has SI units of volt metres (V m), or, equivalently, newton metres squared per coulomb (N m2 C−1). The SI base units of the electric flux are kg•m3•s-3•A-1.