Question

Two point charge, each of magnitude +Q is placed at a distance d from the centre of an uncharged conducting sphere of radius R at the positions making an angle ${30}^0$ (at the centre) with each other. Then the potential of the sphere is (d > R) :

• A. $\frac{1}{4\pi {ϵ}_0}\frac{Q}{(d-R)}$
• B. $\frac{1}{4\pi {ϵ}_0}\frac{Q}{d}$
• C. $\frac{1}{4\pi {ϵ}_0}\frac{Q}{R}$
• D. $\frac{1}{2\pi {ϵ}_0}\frac{Q}{d}$

Answer 1

The correct option is D $\frac{1}{2\pi {ϵ}_0}\frac{Q}{d}$

Since the body is a conductor, it is an equipotential body and the potential on its surface equals the potential at its center. The potential due to the induced charges is zero at the center ( the conductor is initially neutral).
Therefore, the potential at its center $=kQ/d+kQ/d=2kQ/d=\frac{2}{4\pi {ϵ}_0}\times \frac{Q}{d}$ potential on its surface.