Question

Two point charges of charge $+q$ each are placed a distance $2d$ apart. A grounded solid conducting sphere of radius $a$ is placed midway between them. Assume $a^2 \ll d^2$. Which of the following statements is/are true?

• A. If $a > \frac{d}{8}$, the net force acting on the charges is directed towards each other.
• B. The potential at the surface of the sphere is zero
• C. Total induced charge on the sphere is ($-\frac{2aq}{d}$)
• D. The potential at the center of the sphere is non-zero

Answer 1

Answer: (A), (B), (C)

If $a > \frac{d}{8}$, the net force acting on the charges is directed towards each other.

Answer 2

The correct Answers are (A): If $a > \frac{d}{8}$, the net force acting on the charges is directed towards each other,
(B): The potential at the surface of the sphere is zero,
(C): Total induced charge on the sphere is ($-\frac{2aq}{d}$)