HW09sol - Classical Electrodynamics I PHY 505 Fall 2010...

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1 C:\User\Teaching\505-506\F10\HW09sol.doc PHY 505 Classical Electrodynamics I Fall 2010 Homework 9 with solutions Problem 9.1 (to be graded of 20 points). A straight thin wire with dc current I runs in the plane separating two semi-spaces filled with different uniform, soft magnetic materials, with different values ( 1 and 2 ) of the magnetic permeability. Find the spatial distribution of fields B and H , and magnetization M . Solution : Solution : In class, we have calculated the magnetic field induced by a straight wire in free space – see Eq. (5.20). From Sec. 5.7 we know that if the free space is replaced by a uniform material with 0 , the field increases proportionally to , so that for the straight wire n B 2 I , where { , , z } are the standard cylindrical coordinates with vector n z along the direction of the current, and the origin placed at some point of the wire. Let us try to look for the solution of our problem (see Fig. on the right showing its cross-section) in the similar form, but with some effective permeability ef :    2 , ef I B B n r B , so that      r n r n r H  ef 2 I B , where ( r ) is the local permeability, equal to either 1
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HW09sol - Classical Electrodynamics I PHY 505 Fall 2010...

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