F10hw03

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Unformatted text preview: Problem 2.7 gonsider — potenti—l pro˜lem in the h—lfEsp—™e dened ˜y z ! HD with hiri™hlet ˜ound—ry ™onditions on the pl—ne z a H @—nd —t innityAF 2.7.a. Write down the appropriate Green function GD @~ ; ~ H A xx ap I @x xH A C @x xH A C @x xH A 1 1 2 2 2 2 3 2 3 G@~ ; ~ A. xx 0 I p @x xH A C @x xH A C @x C xH A 1 1 2 2 2 2 3 3 2 where x D x D —nd x denote the xD y D —nd z ™oordin—tesD respe™tivelyF 1 2 3 2.7.b. sf the potenti—l on the pl—ne z a H is spe™ied to ˜e ¨ a V inside — ™ir™le of r—dius a ™entered —t the originD —nd ¨ a H outside th—t ™ir™leD nd —n integr—l expression for the potenti—l —t the point P spe™ied in terms of ™ylindri™—l ™oordin—tes @; '; z AF ‡e9re going to use equ—tion IFRR from t—™ksonX I s ¨@~ HA @GD daH x @IA ¨@~ A a R x @nH S xote th—t ¨@~ HA a V inside the ™ir™le of r—dius a ™entered —t the originF x vet9s ™onvert GD @~ ; ~ HA to ™ylindri™—l ™oordin—tesX xx I GD @~ ; ~ H A a p xx @ ™os ' H ™os 'HA C @ sin ' H sin 'HA C @z z HA I p @ ™os ' H ™os 'HA C @ sin ' H sin 'HA C @z C z HA I as  C H H @™os ' ™os 'H C sin ' sin 'H A C @z z H A | {z } 2 2 2 2 2 2 2 2 cos(' s 2 C H2 'H ) I [email protected] ' ™os 'H {z sin ' sin '}HA C @z C zHA C | 2 cos(' ap 2 2 C H2 'H ) I I p H ™os@' 'HA C @z zHA  C H H ™os@' 'H A C @z C z H A 2 I 2 2 2 ‡e need to nd the n...
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This note was uploaded on 12/08/2011 for the course PHYSICS 505 taught by Professor Liu during the Winter '08 term at University of Michigan.

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