Answer Happy

• Problem 13.4. A uniformly-magnetized cylinder An cylinder of radius R and length is magnetized with magnetization M R2 = Mo 2+R² ż that is parallel to the cylinder axis, which is chosen to be in the direction ĉ and to coincide with the z axis. The origin is assumed to be at the center of the cylinder. a) Draw a large clear picture of a cross-section of the cylinder of length 1 in the x-z plane that shows the axes and the direction of the magnetization M. On this picture, also show unit vectors ân that are outward normal vectors to the cylin- der's surfaces. Put the origin at the center of the cylinder. b) Use cylindrical coordinates to find the volume magnetization current JM = V x M throughout the cylinder. c) Use cylindrical coordinates to find the surface magnetization current jm = M x în on all surfaces of the cylinder. d) Suppose you could make a solenoid by wrapping wire around a cardboard tube to produce the same length and radius and the same magnetic induction field at the center of the cylinder as in this magnetized cylinder. What would the free current distribution have to be to accomplish this? (Ignore end effects.) =