Electromagnetic Theory IProblem Set 10Due: 7 November 201137. A point magnetic dipole with momentm=mˆzis placed at the center of a sphericalshell with uniform magnetic permeabilityμ, and with inner and outer radiia, brespectively.a) Set up the boundary equations that determine the magnetic field in the three regions0< r < a,a < r < b,r > b.b) Solve the equations of part a) to find theBandHfields in all three regions.c) Discuss the two extreme limitsμ→ ∞andμ→0. Determine the limitingBandHfields in each region, and discuss the qualitative differences of the two limits.d) Calculate the difference ΔU=Uμ=0-Uμ=∞of the total magnetic field energy stored inthe two limiting situations. Handle the divergence whenr→0 by excluding the region0< r≤δain the energy integral. The divergence cancels in ΔU, and you canthen takeδ→0. Can you understand the sign in terms of the qualitative behavior ofthe fields?
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