hw1_p5406_s08 - HW 1 Phys5406 S04 due 1/24/08 IA sn ™l—ss...

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Unformatted text preview: HW 1 Phys5406 S04 due 1/24/08 IA sn ™l—ss we found the B eld on the —xis of — ™ir™ul—r loop of r—dius ‚ ™—rrying ™urrent sF xow everywhere on the —xis there is no ™urrentD so th—t the eld is deriv—˜le from — s™—l—r potenti—lD ¨F g—l™ul—te ¨ —ppli™—˜le for —ll points on the —xisF ‰our result will ™ont—in — ™onst—nt of integr—tionF por points very f—r from the loop ¨ redu™es to th—t from the m—gneti™ moment termF …se this f—™t to ev—lu—te the integr—tion ™onst—ntF PA gonsider — sphere of r—dius ‚ th—t rot—tes —˜out — di—meterD s—y the z —xis with ™onst—nt —ngul—r velo™ity !F sn the three ™—ses ˜elow we w—nt the m—gneti™ moment of the sphere —nd B f—r from the sphereF —Alet the sphere ˜e — ™ondu™tor withh—s — uniform surf—™e ™h—rge density F ˜Alet the sphere ™—rry uniform volume ™h—rge density 0F ™Alet the sphere h—ve uniform m—gnetiz—tion M —nd let ! a HF RA e sphere of r—dius ‚ h—s uniform m—gnetiz—tion M ezF €ut the origin —t the ™enter of the sphereF tust outside the sphere @r a R C D  3 HAD in v—™uumD the m—gneti™ eld is B0 er C B1 e F wh—t is the m—gneti™ eld just inside the sphere9s surf—™e —s — fun™tion of  c SA e fohr m—gneton is the sm—llest nonEzero m—gneti™ moment of —n ele™tron due to its or˜it—l motionF g—l™ul—te this qu—ntity @don9t just ™opy this from some h—nd˜ookD try to get it yourselfAF xow ™—l™ul—te the r—tio of the m—gnitude of the for™e ˜etween two p—rE —llel fohr m—gnetons to th—t ˜etween two p—r—llel ele™tri™ dipole moments of m—gnitude e¢H:IengstromF gonsider the ™—ses when the dipoles —re or —re not ™oline—rF 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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