In electromagnetism, electric flux is the measure of flow of the electric field through a given area. 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
\Phi_E = \mathbf{E} \cdot \mathbf{S} = ES \cos \theta,
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 dΦE through a small surface area dS is given by
d\Phi_E = \mathbf{E} \cdot d\mathbf{S}
(the electric field, E, multiplied by the component of area parallel to the field). The electric flux over a surface S is therefore given by the surface integral:
\Phi_E = \iint_S \mathbf{E} \cdot d\mathbf{S}
where E is the electric field and dS is a differential area on the closed surface S with an outward facing surface normal defining its direction.