Question

Why two eqipotential surfaces never intersect each other ?

Answer 1

The surfaces which have same electric potential throughout is called equipotential surface. Now, corresponding to every equipotential surface there exist an electric potential and corresponding to every electric potential there exist an electric field. Thus, as we know two vectors cannot have different directions at a given point, so, if two equipotential surface intersect it would mean that at that very point the electric field will have two different directions which is not possible.