The electric flux (ϕ) is defined as total number of electric lines of force passing normally through a surface in the electric field ϕ is a scalar quantity. For a closed surface, placed in electric field, the flux is negative when the lines of force enter into the surface and positive when they leave the surface. In order to find the total flux linked with a surface, the surface is divided into infinitesimal small parts and sum of electric flux through all such small elements is find out.
The flux linked with an element of surface area dS is equal to the product of the
component of electric field E normal to the surface and area of the element, i.e.,
dϕ = E cosθdS = E.Ds
Therefore, the total electric flux linked through the entire surface S is then given by
ϕ=ʃ s E cos θ ds = ʃ s E .ds