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?
Best Answer
If there is no charge inside the sphere, the potential must be the solution of the equation $$ \nabla^2 \phi =0 $$ with boundary condition $\phi=\phi_0$ on the surface. The function $\phi=\phi_0$ inside the sphere is a solution, and it is unique. If there are charges inside the sphere the potential is different, and can be constructed, for example, using the image charges method. As you are explicitly assigning the potential on the boundary, this is independent from the fact that the surface is conducting or not.