HW07 - ef of a medium with many empty spherical cavities of...

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1 C:\User\Teaching\505-506\F10\HW07.doc PHY 505 Classical Electrodynamics I Fall 2010 Homework 7 (due Friday Nov. 5) Problem 7.1 (to be graded of 15 points). Calculate resistance between two large conductors separated with a very thin, plane, insulating partition, with a circular hole of radius R in it – see Fig. on the right. Hint : You may like to use the degenerate ellipsoidal coordinates which have been used in class to find the self-capacitance of a round disk in vacuum – see Sec. 2.3 of the lecture notes Problem 7.2 (15 points). Calculate the effective (average) conductivity
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Unformatted text preview: ef of a medium with many empty spherical cavities of radius R , carved at random points in a uniform Ohmic conductor (see Fig. on the right), in the limit of small sphere concentration, n << R-3 . Hint : Try to use the analogy with a dielectric media. Problem 7.3 (15 points). Find voltage drop V between two corners of a square cut from a uniform sheet with Ohmic conductivity, induced by dc current I which is passed between its two other corners (see Fig. on the right). Hint : Try to use the dc current analog of the charge image method. R I ? V t R 2...
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