Question

Why can't equipotential surfaces with different values intersect?

Walter Lewin says "violation of conservation of energy."

Can someone explain further?

Answer 1

if two equipotential surfaces intersects, at the point of intersection/intersections there will be two potentials and at a single point there never be two different potentials(by the definition of potential)

Answer 2

An equipotential surface is a kind of field, a field has only a single value at any one point.
I think what Prof. Lewin means is that energy would have to come from nowhere (violating conservation) in order for another field to be created in the same place.
Or something like that. :">