Suppose that we have a hollow sphere (spherical shell) whose surface is held at some constant potential V0. What is the potential inside the sphere? I had an argument with my physics professor over this. He claims that the potential inside depends on how far you are from the center and becomes zero at the center ("so that it doesn't blow up"). Wouldn't the potential at ANY point inside the sphere just be V0? Would the answer matter depending on whether the surface is a conductor on insulator, even?