# Electric flux

In electromagnetism, **electric flux** is the measure of flow of the electric field through a given area.^{[1]}

Generally speaking flux is a flow, such as the flow of charge, or current. The electric field E is analogous to a force, since qE is a force. The electric field is proportional to the gradient of the voltage. The electric field drives charge. The ratio of the force over the flow is an impedance.

## Overview[edit]

An electric "charge," such as a single electron in space, has an electric field surrounding it. In pictorial form, this electric field is shown as a dot, the charge, radiating "lines of flux." These are called Gauss lines.^{[2]} Electric Flux Density is the amount of electric flux, the number of "lines," passing through a given area. Units are Gauss/square meter.^{[3]} Electric flux is proportional to the number of electric field lines going through a normally perpendicular surface. If the electric field is uniform, the electric flux passing through a surface of vector area **S** is

where **E** is the electric field (having units of V/m), *E* is its magnitude, *S* is the area of the surface, and *θ* is the angle between the electric field lines and the normal (perpendicular) to *S*.

For a non-uniform electric field, the electric flux *d*Φ_{E} through a small surface area *d***S** is given by

(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:

where **E** is the electric field and *d***S** 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:

where

**E**is the electric field,*S*is any closed surface,*Q*is the total electric charge inside the surface*S*,*ε*_{0}is the electric constant (a universal constant, also called the "permittivity of free space") (ε_{0}≈ 8.854 187 817... x 10^{−12}farads per meter (F·m^{−1})).

This relation is known as Gauss' law for electric field in its integral form and it is one of the four Maxwell's equations.

While the electric flux is not affected by charges that are not within the closed surface, the net electric field, **E**, in the Gauss' Law equation, can be affected by charges that lie outside the closed surface. While Gauss' Law holds for all situations, it is only useful for "by hand" calculations when high degrees of symmetry exist in the electric field. Examples include spherical and cylindrical symmetry.

Electrical flux has SI units of volt meters (*V m*), or, equivalently, newton meters squared per coulomb (*N m*^{2} *C*^{−1}). Thus, the SI base units of electric flux are *kg·m*^{3}*·s*^{−3}*·A*^{−1}.

Its dimensional formula is [L^{3}MT^{−3}I^{−1}].

## See also[edit]

## Notes[edit]

- Purcell, Edward, Morin, David; Electricity and Magnetism, 3rd Edition; Cambridge University Press, New York. 2013 ISBN 9781107014022.
- Browne, Michael, PhD; Physics for Engineering and Science, 2nd Edition; McGraw Hill/Schaum, New York; 2010. ISBN 0071613994