Chapter 17, Problem 6Q

To determine

If $V=0$ at a point in space, must $\overrightarrow{E}=0$ ? If $\overrightarrow{E}=0$ at some point, must $V=0$ at that point?

Answer to Problem 6Q

Solution:

The answer for the question is explained in the explanation part.

Explanation of Solution

We have electric field, $E\text{=}\frac{1}{4\pi {\epsilon }_0}\frac{Q}{r^2}$ and $V\text{=}\frac{1}{4\pi {\epsilon }_0}\frac{Q}{r}$

Consider two positive charges of same value separated by a distance r. At the centre of line joining between them $\overrightarrow{E}=0$ but $V\ne 0$. This is also same in case of two negative charges.

Consider one positive charge and one negative charge of same value separated by a distance r. At the centre of line joining between them $\overrightarrow{E}\ne 0$ but $V=0$.