The square region defined by−a ≤ x ≤ a and−a ≤ y ≤ a in the z = 0 plane is a conductor held at potential φ = V . The rest of the z = 0 plane is a conductor held at potential φ = 0. The plane z = d is also a conductor held at zero potential.

(a) Find the potential for 0 ≤ z ≤ d in the form of a Fourier integral.

(b) Find the total charge induced on the upper surface of the lower (z = 0) plate. The answer is very simple. Do not leave it in the form of an unevaluated integral or infinite series.

(c) Sketch field lines of E(r) between the plates.

d V 2a 2a All