A spherical capacitor consists of two concentric conducting spherical shells of radii \(R\) and \(2 R\).

(a) How long would a coaxial cylindrical capacitor made of two concentric cylindrical conductors of radii \(R\) and \(2 R\) have to be in order to have the same capacitance as the spherical capacitor?

(b) What plate separation distance would be required for a parallel-plate capacitor made of two circular conductors each of radius \(R\) in order to have the same capacitance as the spherical capacitor?