A parallel-plate capacitor has plates of area \(A\) separated by a distance \(d\). The magnitude of the charge on each plate is \(q\).

(a) Determine the magnitude of the force exerted by the positively charged plate on the negatively charged one.

(b) Suppose you increase the separation between the plates by an amount \(\Delta x\). How much work do you need to do on the capacitor to achieve this increase?

(c) What is the change in the electric potential energy of the capacitor?

(d) Moving the plate adds additional space with electric field between the plates. Show that the energy stored in the electric field in this additional space is equal to the work done on the capacitor.