hw2_p5406_s06 - HW 2 Phys5406 S02 due 2/2/06 IA e right...

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Unformatted text preview: HW 2 Phys5406 S02 due 2/2/06 IA e right ™ir™ul—r ™ylinder of r—dius ‚ —nd length v h—s ™onst—nt m—gnetiz—tion M dire™ted —long its —xisF ‡h—t is the m—gneti™ eld —t rD f—r from the origin —t the ™ylinder ™enterc PA ell sp—™e is lled with two ™ondu™ting m—gneti™ m—teri—lsF i—™h ™—rries the s—me uniform ™urrent density te F „he m—teri—ls h—ve perme—˜ilities ¦ —nd ll the sp—™e where x > H —nd x < HD respe™tivelyF pind the elds B, H, MF sn ™l—ss we ™onsidered ™on™entri™D innitely long right ™ir™ul—rD ™ylindri™—l ™ondu™torsF yne h—d r—dius — —nd the other w—s — shell with inner r—dius ˜F „he inner ™ondu™tor w—s —t potenti—l † —nd the outer —t †9F ‡e found the Id qreen9s fun™tion ˜etween the ™ylinders to ˜eD z g1 ln a R ln b=b=a  ln > < =a ; @IA where  is the lesserD gre—ter of  or HF QA vet —aHFS m —nd ˜ a HFT m —nd gr—ph g1 versus H —t  a H:SS m to get —n ide— of wh—t g1 looks likeF g—l™ul—te r2 g1 —nd rH2 g1 when  Ta H F g—l™ul—te @g1 =@ —t  a H ¦ =PF …se these to show th—t in the limit  3 H you get the expe™ted result for r2g1 everywhereF RA ƒuppose — uniform ™h—rge per unit —re—D D w—s distri˜uted —t —ll z —nd  —t H a ‚D where — ‚ ˜ —nd none of the other ˜ound—ry ™onditions were ™h—ngedF ‡h—t is the potenti—l ¨ —t  for —<  <˜F sf the ™h—rge density w—s distri˜uted only over H<  < D ™ould g1 ˜e used to solve the pro˜lemD expl—inF SA ƒolve RA only using q—uss9s v—w to get the E —nd verify th—t you get the s—me —nswer for [email protected] „his is —n e—sy pro˜len illustr—ting the nding @in ™l—ssA —nd use of — qreen9s fun™tion for — pro˜lem you ™ould solve with simple methodsF w—ny h—rder pro˜lemsD where you ™—n9t use q—uss9s l—wD will ˜e en™ounteredF <;> I ...
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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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