1. A metal cylinder of radius a and length L has both ends held at a zero potential, and the sides are at constant potential Vo. (a) Find the potential Þ(p, o, z) everywhere in the interior of the cylinder. Assume the cylinder is aligned with the z axis and that and that the ends are located at z = 0 and z = L. I suggest choosing a functional form that vanishes explicitly for z = L and z = L. (b) Now consider the same question, but with some shifts applied: Þ'(p, o, z') = Þ(p, o, z + L/2) - Vo, i.e., such that the center of the cylinder is now at the origin, the potential

1. A metal cylinder of radius a and length L has both ends held at a zero potential, and the sides are at constant potential Vo. (a) Find the potential Þ(p, o, z) everywhere in the interior of the cylinder. Assume the cylinder is aligned with the z axis and that and that the ends are located at z = 0 and z = L. I suggest choosing a functional form that vanishes explicitly for z = L and z = L. (b) Now consider the same question, but with some shifts applied: Þ'(p, o, z') = Þ(p, o, z + L/2) - Vo, i.e., such that the center of the cylinder is now at the origin, the potential