In summary, a solid conducting sphere with charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. The potential difference between the surface of the sphere and the outer surface of the shell is V. If the shell is given a charge of -3Q, the new potential difference between the same two surfaces is also V. The radius of the outer surface of the shell is R, the inner surface is r, and the radius of the sphere is X. The formula for potential at a point is Q/4πε. The potential at the outer surface of the shell is Q/4πεR, and the potential at the surface of the sphere due to charge inside is Q/4πεX. The net potential
