Question

An electric charge $10^{-6} \, \mu C$ is placed at the origin (0, 0) of an X-Y coordinate system. Two points P and Q are situated at $(\sqrt{3}, \sqrt{3}) \, \text{mm}$ and $(\sqrt{6}, 0) \, \text{mm}$ respectively. The potential difference between the points P and Q will be:

• A. 0 V
• B. $\sqrt{6}$ V
• C. $\sqrt{3}$ V
• D. 3 V

Answer 1

Answer: (A)

0 V

Answer 2

The potential difference between two points P and Q due to a point charge Q is given by:

$\Delta V = KQ \left( \frac{1}{r_1} - \frac{1}{r_2} \right)$

where

$r_1 = \sqrt{(\sqrt{3})^2 + (\sqrt{3})^2} = \sqrt{6} \quad \text{and} \quad r_2 = \sqrt{(\sqrt{6})^2 + 0^2} = \sqrt{6}$

Since $r_1 = r_2$, the potential difference is zero:

$\Delta V = 0$