Question

A charge is located at the center of sphere a (radius ra=0.0010 m), which is in the center of sphere b (radius rb=0.0012 m ). spheres a and b are both equipotential surfaces. what is the ratio va/vb of the potentials of these surfaces?

Answer 1

Va = K Qa / ra

Vb = = K Qb / rb

Va / Vb = .0012 / .0010 = 1.2

Note that Qa and Qb are the same because Gauss Law says that the enclosed charge will act as if it were replaced by a charge at the center of the sphere. (the charge density of the surfaces are different)

One can picture the situation where a metallic spherical shell has an inner radius of R1 and an outer radius of R2 - a charge +Q will induce a charge of -Q on the inner surface of the sphere leaving a net charge of Q on the outer surface of the sphere. Be careful because there can be no net field lines in the shell otherwise a current would flow. (Also there would be no potential difference between the two surfaces of the sphere)