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

The Correct Option is A

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:

\[ \Delta V = 0 \]