A capacitor is constructed of two concentric cylinders of radii a and b (b > a) having a length L >> b. A charge of +Q is on the inner cylinder and a charge of –Q is on the outer cylinder. The region between the two cylinders is filled with a dielectric having a dielectric constant k.

(a) Find the potential difference between the cylinders.

(b) Find the density of the free charge σf on the inner cylinder and the outer cylinder.

(c) Find the bound charge density σb on the inner cylindrical surface of the dielectric and the outer surface.

(d) Find the total stored electrostatic energy.

(e) If the dielectric will move without friction, how much mechanical work is required to remove the dielectric cylindrical shell?