Question

7. If the electric field at any point is zero, will it mean
that the potential will also be zero at that point?
Explain.

Answer 1

we know that electric field is in reverse sense of the directional gradient of electric potential, so if V is constant, E should be zero. So, for E to be zero, either V has to be zero, or constant, or the 3 directional derivative components of V must cancel out each other in space. So we cant claim that V always has to be zero, if E is zero in a region, since E is a vector & V is a scalar quantity. But if V is zero, then surely E has to be zero; the reverse case is not true always.