Electric flux

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. In other words the number of electric lines of force passing through the given surface area which is held perpendicular to the direction of electric lines of force is called electric flux. 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 Q_S is the net 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.

It is important to note that 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 metres (V m), or, equivalently, newton metres squared per coulomb (N m² C⁻¹). Thus, the SI base units of electric flux are kg•m³•s⁻³•A⁻¹. Dimensional formula is L³M¹T^-1I^-1.

See also

• Magnetic flux

External links

• Electric flux — HyperPhysics