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4321_HW12FA08 - Physics 4321 Homework Set 12 Due December 1...

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Physics 4321 Homework Set 12 November 24, 2008 Due: December 1, 2008 1. If J f = 0 everywhere, curl H = 0 everywhere, and then we can express H as H = -grad W, where W is a scalar potential. Use Eq. (6.23) to show that 2 W = (div M ). Note that this is a Poisson-like equation with div M as the source. Therefore, if div M = 0, we recover Laplace’s equation and all the machinery we developed earlier with the electric potential. 2. A coaxial cable consist of two very thin, concentric conducting tubes, with the inner tube carrying current into the page and the outer tube out of the page. In each tube, the current is uniformly distributed over the surface. The region between the tubes is filled with a material whose susceptibility is χ m . Calculate B , H , M , J b , and K b between the tubes. The radius of the inner tube is a and that of the outer tube is b . 3. A current I exists in a long, straight wire having radius a . The wire is made from a linear magnetic material whose susceptibility is χ m . The current is distributed uniformly throughout the wire.
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