Why can't equipotentials intersect?

Question

I know that it is impossible for equipotentials to intersect. I am having a hard time trying to explain it and relate it to the equation E=∆V/d. Can anyone put it into words for me? Thanks.

Answer 1

They would not be equipotentials!

If one is a constant 50 volts and another a constant 100 volts they cannot intersect because that means they would have the same voltage at that point which is impossible.

Answer 2

this is because the tangent at electrical field lines give the direction of magnetic field due to the line at that point , if two equipotential surface intersect than there will be two directions of magnetic field at the same point , which is not possible and hence equipotential surface never intersect ...........

Answer 3

It is toatally posiible for equipotentials to intersect at sadle points.

Answer 4

if they intersect, then at the point of intersection, the function will have two values, which is impossible in this context.