Question

Four equal charges \( Q \) each are placed at four corners of a square of side \( a \). Work done in carrying a charge \( -q \) from its centre to infinity is

• A. zero
• B. \( \frac{\sqrt{2} q}{\pi \epsilon_0 a} \)
• C. \( \frac{q^2}{2 \pi \epsilon_0 a} \)
• D. \( \frac{q^2}{\pi \epsilon_0 a} \)

Hint:

Work done in moving a charge in an electric field is given by the product of charge and potential difference.

Answer 1

The Correct Option is D

Step 1: Electric potential due to point charges.
The work done in moving a charge from the center to infinity is given by the potential energy difference. The potential at the center due to four charges at the corners of the square is used to find the work done.

Step 2: Conclusion.
The work done in moving the charge from the center to infinity is \( \frac{q^2}{\pi \epsilon_0 a} \), which corresponds to option (4).