Question

The electric field and the electric potential at a point are E and V respectively. Then, the incorrect statements are :

Answer 1

The electric field is $E=-\frac{dV}{dx}$
If $V=0$, we can not say $E$ must be zero, we say only $E$ may be zero.
If $V\ne 0$, $E$ must be zero when $V$ is max i.e, $\frac{dV}{dx}=0$ For example, inside the conductor $E=0,$ but $V\ne 0$
If $E\ne 0$ , $V$ may be zero when two equal and opposite charges separated by a distance and at the midpoint in between the charges field is non-zero but potential is zero.