Mathematically, electric flux (`phi`) through an area element `ΔS` is defined by

`phi = vecE.vec(ΔS) = EΔS costheta`

Geometrically, flux gives the number of electric field line crossing a unit area of a surface, the surface held normally to the field lines.

If a surface S is large, then it is divided into a large number of infinitesimal area element such that

`phi_text(total) = int_s vecE.vec(dS)` = surface integral of electric field over the surface. For a closed surfaced S.