An uncharged solid conducting sphere of radius R has an off-center spherical cavity. A point charge +q is placed inside the cavity at a distance x from the center of the solid sphere. What is the electric potential of the solid conductor? (Assume the potential at infinity is zero, and k = 1 4 ₀ )

Step-by-step solution

The electric potential of a conductor in electrostatic equilibrium is constant throughout its volume and on its surface. When a point charge +q is placed inside the cavity, it induces a charge -q on the inner surface of the cavity and a charge +q on the outer surface of the sphere. By the principle of electrostatic shielding, the electric field produced by the point charge +q and the induced charge -q on the inner surface is completely confined within the cavity. Their combined contribution to the electric potentia