A point charge $q$ is placed at a distance $a$ from the center of an uncharged conducting sphere of radius $R$ ($a>R$). What is the potential at the center of the sphere?

Solution

1. The potential at any point inside a conductor is constant and equal to the potential on its surface.
2. The potential on the surface of the sphere is the sum of the potential due to the point charge $q$ and the potential due to the induced charges on the sphere.
3. Since the sphere is uncharged, the net potential due to induced charges at the center is zero.
4. Thus, the potential at the center is solely due to the point charge $q$ at distance $a$, which is $V=\frac{q}{4\pi {ϵ}_{0}a}$.
5. Hence the answer is (A).