A cylindrical capacitor of a length L consists of a conductive wire of radius a at the centre, surrounded by a concentric thin conductive shell of radius b. The space between the conductive wire and the thin shell is filled with a dielectric material of permitivity . (a) If the charge carried by the capacitor is Q, neglecting the edge effects (fringing field), find the electric field as a function of radial distance r.

(b) Find the capacitance of this capacitor.

(c) Suppose this capacitor is connected to a battery of potential U, when the dielectric material is partially pulled out of the capacitor with a length of Z outside the capacitor, neglecting the edge effects, find the magnitude and direction of the force that needs to apply in order to move the dielectric material to this position.