The electric flux is defined as the total number of electric lines of force, crossing through the given area.
Consider a closed surface S in a non−uniform electric field (Fig.).
Consider a very small area ds on this surface. The direction of ds is drawn normal to the surface outward. The electric field over ds is supposed to be a constant E. E and ds make an angle θ with each other.
The electric flux dφ through the area ds is, dφ = E*ds (read as E dot ds) = E ds cosθ
The total flux through the closed surface S is obtained by integrating the above equation over the surface.
φ = ∮ dφ =∮ E * ds
The circle on the integral indicates that, the integration is to be taken over the closed surface. The electric flux is a scalar quantity.
It's unit is N m^2 C^−1
