Assume that the electric field e is equal to zero at a given point. does it mean that the electric potential v must also be equal to zero at this point? if not, then provide an example to prove your answer. if you think that the answer is "yes", justify it.

Explanation:

In electrostatics, the electric field is related to the gradient of the electric potential V with :

This means that for constant electric potential the electric field must be zero:

This is not the only case in which we would find an zero electric field, as, any scalar field with gradient zero will give an zero electric field. For example:

give an electric field of zero at point (0,0,0)

would be false hope this out