Question

Justify why two equipotential surfaces cannot intersect

Answer 1

they cannot intersect each other because two different equipotential surface have different electric potential, so if they intersect then the point of intersection will have two different potentials at the same point which is not possible.

Answer 2

Because electric field lines can't point to two directions at the same point.

1) An equipotential surface is one which has same electric potential throughout the whole surface.

2) This means, that the electric field of an equipotential surface points i one direction only.

3) But if two equipotential surfaces intersect at a point, it means electric field has two directions at that point which is not possible.