Question

An electric charge $10^{-3}\, \mu C$ is placed at the origin of the x-y plane. The potential difference between points A and B located at $(\sqrt{2}\, m, \sqrt{2}\, m)$ and $(2m, 0m)$ respectively is

• A. 4.5 V
• B. 9 V
• C. 0 V
• D. 2 V

Hint:

Potential depends only on distance from point charge; points equidistant from charge have same potential.

Answer 1

The Correct Option is C

Potential \(V\) due to a point charge at a distance \(r\) is: \[ V = \frac{kQ}{r} \] Where \(k\) is Coulomb's constant, \(Q\) is charge, and \(r\) is distance from charge. Calculate distances of points A and B from origin: \[ r_A = \sqrt{(\sqrt{2})^2 + (\sqrt{2})^2} = \sqrt{2 + 2} = \sqrt{4} = 2\, m \] \[ r_B = \sqrt{(2)^2 + 0^2} = 2\, m \] Since both points are at the same distance from charge, potentials at A and B are equal. Therefore, potential difference: \[ V_A - V_B = 0\, V \]