hw3_p5406_s04

# hw3_p5406_s04 - a(a). The larger has inner(outer) radii...

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HW 3 Phys5406 S04 due 2/24/04 1) A solid conducting sphere of radius R is cut into hemispheres and then glued together with a thin layer of insulating glue. The hemisphere at positive z has potential V 1 and that at negative z has potential V 2 . Find the potential for r R. For your own education you should show that the solution via Green’s function is the same as that from LaPlace’s equation. Show that the leading terms are Φ = α/r + βz/r 3 + ... If the V 1 hemisphere was at positive x and the V 2 hemisphere at negative x, the problem no longer has azimuthal symmetry. Use the spherical harmonics to obtain the solution and show the leading terms are (as you would expect), Φ = α/r + βx/r 3 + ...What are α, β ? 2) Consider two concentric conducting spherical shells. The smaller has inner(outer) radii
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Unformatted text preview: a(a). The larger has inner(outer) radii b(b). With this geometry do JDJ 3-1. You need not write out the rst four terms. You can leave your solution in terms of integrals (suitably simplied). However obtain the solution in each of the following regions: r a, r b, and a r b. 3) Suppose for the geometry of question 2 the entire inner sphere was at potential V in and the entire outer sphere was at potential V out . Further suppose there was a concentric ring with charge per unit length and radius c, where a < c < b. Once again, nd the potential in the regions: r a, r b, and a r b. 1...
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## This note was uploaded on 12/24/2011 for the course PHYS 5406 taught by Professor Blecher during the Spring '10 term at Virginia Tech.

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