What is the Meaning of Electric Flux – How is it defined ?

Electric Flux – Definition :

Electric flux gives the measure of flow of the electric field through a given area. We may define electric flux as-

 Electric flux is proportional to the number of electric field lines passing normally through a  surface.

If the electric field is uniform, the electric flux passing through a surface of vector area S is calculated by following formula –

Φ_E = E.S= E S cosθ

where – E is the electric field (measured in 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.

Now if we are dealing with a non-uniform electric field, then electric flux dΦ_E through an infinitesimally small surface area dS is calculated by following formula-

dΦ_E = E.dS

The scalar product of electric field and area vector (Oh! off course area is not a vector, however in some case treating it as vector simplifies our situation without affecting the result. For more detail on this read my article Area Vector ). The total electric flux over a surface S is therefore given by the surface integral –

${\mathbf{\varphi }}_{\mathbf{E}}\mathbf{ }\mathbf{=}{\mathbf{\iint }}_{\mathbf{S}}\mathbf{ }\mathit{E}\mathbf{.}\mathit{d}\mathit{S}$

where E is the electric field and dS is a differential element of the surface S, with an outward facing surface normal defining its direction.

Now for a closed surface, electric flux is given by –

${\mathbf{\varphi }}_{\mathbf{E}}\mathbf{ }\mathbf{=}{\mathbf{\oint }}_{\mathbf{s}}\mathit{E}\mathbf{.}\mathit{d}\mathit{S}$

where

E is the electric field,

S is any closed surface,

Unit of Electric Flux

Electrical flux has SI units of volt meters (V m), or, equivalently, newton meters squared per coulomb (N m²C^-1). Thus, the SI base units of electric flux are kg-m³-s^-3-A^-1 .

Its dimensional formula is [ L³MT^-3I^-1 ].