A hollow cube has conducting walls defined by six planes x=0, y=0, z=0, and x=a, y=a, z=a. The walls z=0 and z=a are held at a constant potential V. The other four sides are at zero potential.
(a) Find the potential Φ(x,y,z) at any point inside the cube.
(b) Evaluate the potential at the center of the cube numerically, accurate to three significant figures. How many terms in the series is it necessary to keep in order to attain this accuracy? Compare your numerical result with the average value of the potential on the walls. See Problem 2.28.
(c) Find the surface-charge density on the surface z=a.