Flux of the Electric Field

Consider a closed surface S immersed in nonuniform electric field. Divide the surface into small squares of area dS. We represent each such elements of area by vector dS, whose magnitude is the area dS. The direction of ds is defined to be that of the outward-drawn normal to the surface. Since the squares are very small, the electric field E for all points in the square is constant. The vectors E and dS make an angle θ with each other.

The electric flux dФ through the area dS is defined as
     dФ = E. dS = E dS cos θ

dФ is <> 0 depending on whether θ is <> π/2 respectively.

The total flux through the closed surface S is obtained by integrating the above equation over the surface. Thus
    Ф = Ф     d Ф = Ф E. dS

This circle on the integral sign indicates that the integration is to be taken over the entire (closed) surface. The flux of the electric field is a scalar. Its unit is Nm²C^-1 or Vm.