Electric flux


In electromagnetism, electric flux is the measure of the electric field through a given surface, although an electric field in itself cannot flow. It is a way of describing the electric field strength at any distance from the charge causing the field.
The electric field E can exert a force on an electric charge at any point in space. The electric field is proportional to the gradient of the voltage.

Overview

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. The density of these lines corresponds to the electric field strength, which could also be called the electric flux density: the number of "lines" per unit area. Electric flux is proportional to the total number of electric field lines going through a surface. For simplicity in calculations, it is often convenient to consider a surface perpendicular to the flux lines. If the electric field is uniform, the electric flux passing through a surface of vector area is
where is the electric field, is its magnitude, is the area of the surface, and is the angle between the electric field lines and the normal to.
For a non-uniform electric field, the electric flux through a small surface area is given by
. The electric flux over a surface is therefore given by the surface integral:
where is the electric field and is a differential area on the closed surface with an outward facing surface normal defining its direction.
For a closed Gaussian surface, electric flux is given by:
where
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,, 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 most 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, or, equivalently, newton meters squared per coulomb. Thus, the SI base units of electric flux are. Its dimensional formula is.