Shown below is a distribution of charges. The flux of electric field due to these charges through the surface S is

According to Gauss's theorem, the electric flux through any closed surface is equal to 1/ε0 times the net charge q enclosed by the surface, that isϕE=∮E→·dA→=qε0Since total charge enclosed by surface is zero,∴Total electric flux,ϕ = 0