A solid conducting sphere of radius \(R\) and carrying charge \(+q\) is embedded in an electrically neutral nonconducting spherical shell of inner radius \(R\) and outer radius \(2 R\). The material of which the shell is made has a dielectric constant of 4.0.

(a) Relative to a potential of zero at infinity, what is the potential at the center of the conducting sphere?

(b) If the dielectric constant of the shell doubles, what happens to the potential at the center of the sphere?