Chapter 25, Problem 1OQ

To determine

The electric potential in a certain region of space.

Answer to Problem 1OQ

The correct conclusion is option (b) It does not vary with position.

Explanation of Solution

Write the expression for electric field in terms of potential difference.

    $E=-\frac{dV}{dr}$

Here, $dr$ is the distance from the charge to the field point and $dV$ is the potential difference.

Conclusion:

Substitute $0$ for $E$ in the above equation.

    $\begin{array}{c}0=-\frac{dV}{dr}\\ \frac{dV}{dr}=0\end{array}$

When the value of electric potential after differentiation is equal to $0$, then it is said to be constant which means that the electric potential is constant when the value of electric field is $0$ and it does not vary with the position.

Therefore, option (b) It does not vary with position; is the correct conclusion.