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emhw10 - Electromagnetic Theory I Problem Set 10 Due 7...

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Electromagnetic Theory I Problem Set 10 Due: 7 November 2011 37. A point magnetic dipole with moment m = m ˆ z is placed at the center of a spherical shell with uniform magnetic permeability μ , and with inner and outer radii a, b respectively. a) Set up the boundary equations that determine the magnetic field in the three regions 0 < r < a , a < r < b , r > b . b) Solve the equations of part a) to find the B and H fields in all three regions. c) Discuss the two extreme limits μ → ∞ and μ 0. Determine the limiting B and H fields in each region, and discuss the qualitative differences of the two limits. d) Calculate the difference Δ U = U μ =0 - U μ = of the total magnetic field energy stored in the two limiting situations. Handle the divergence when r 0 by excluding the region 0 < r δ a in the energy integral. The divergence cancels in Δ U , and you can then take δ 0. Can you understand the sign in terms of the qualitative behavior of the fields?
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