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.

Transcribed Image Text:

d V 2a 2a All