Question

The electric field at the origin is along the positive X-axis. A small circle is drawn with the centre at the origin cutting the axes at points A, B, C and D having coordinates $(a,0),(0,a),(-a,0),(0,-a)$ respectively. Out of the given points on the periphery of the circle, the potential is minimum at :

• A. A
• B. B
• C. C
• D. D

Answer 1

The correct option is A A

The relation between electric field and potential is given by $\overrightarrow{E}=-\frac{\partial V}{\partial x}\hat{i}-\frac{\partial V}{\partial y}\hat{j}$

Given that, at origin, electric field is along positive x-axis.

Thus, $\frac{\partial V}{\partial x}<0$ and $\frac{\partial V}{\partial y}=0$

Thus, $V$ decreases in the positive x-direction and remains constant in y-direction.

Hence, minimum $V$ occurs at $(a,0)$ i.e., $A$