Electrodes of area A are spaced distance d apart to form a parallel-plate capacitor. The electrodes are charged to ±q.
a. What is the infinitesimal increase in electric potential energy dU if an infinitesimal amount of charge dq is moved from the negative electrode to the positive electrode?
b. An uncharged capacitor can be charged to ±Q by transferring charge dq over and over and over. Use your answer to part a to show that the potential energy of a capacitor charged to ±Q is U_cap = 1/2Q ΔV_C.