A permanent magnet in the shape of a right circular cylinder of length L and radius R is oriented so that its symmetry axis coincides with the z-axis. The origin of coordinates is at the center of the magnet. If the cylinder has uniform axial magnetization M, a.) determine U^* (z) at points on the symmetry axis, both inside and outside the magnet, and b.) use the results of part a.) to find the magnetic induction B_z at points on the symmetry axis, both inside and outside the magnet.