A parallel-plate capacitor of plate area A and plate separation d is connected to a 200V battery until it is fully charged. The battery is then disconnected, after which the plates are carefully pulled apart until the separation becomes 3d.
(a) Show that the new potential difference between the plates is three times its initial value.
(b) Derive an expression for the ratio of the final electrostatic energy stored in the capacitor to the initial energy.
(c) Calculate the work done by the external agent in increasing the plate separation and state whether this work is positive or negative, explaining your reasoning.