A2 z 2 1 pa u 2 12 h 0 2 5 uz 2 dh p i pi a a

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Unformatted text preview: hat, along the axis of the circle (   is 3 dH d'H a H), the potential 5 z H =0 …sing the su˜stitution u a H C z —nd du a PHX 2 2 z ¨@~ A a V x P Vz P a  4 2 'H =0  a2 + z 2 1 du 2 u=z 2 2 3=2 d'H u !a2 +z 2 1 @ PA u = 2 12 'H =0  2 5 u=z 2 d'H p I pI a a Cz z 'H ! z I a V  P p I z P a Cz Vz P 2 =0 2 a V I p 2 ! 2 d'H 2 ! z a2 C z 2 2.7.d. ƒhow th—t —t l—rge dist—n™es @ C z ) a A the potenti—l ™—n ˜e exp—nded in — power series in @ C z A D —nd th—t the le—ding terms —reX 2 2 2 2 2 1 ! ¨a P I R @Qa z A C S @Q a C a A C : : : = C V @ C z A @ C z A †erify th—t the results of p—rt ™ —nd d —re ™onsistent with e—™h other in their ™ommon r—nge of v—lidityF V a2 2 2 2 z 232 2 Q 2 2 2 4 22 a  H V z 2 ¨@~ A a P x dH d'H H =0 H =0 @2 C H2 H ™os@' 'H A C z 2 A3=2 '   2  a H2 H ™os@' 'H A  3=2 Vz H 2 C z 2 ¡ 3=2 I C  a P  dH d'H 2 C z 2 'H =0 H =0 …sing the „—ylor exp—nsion @I C xAn a I C nx C n@n IAx C : : : 2 3 H   a H H H H H Vz H I Q   ™os@' ' A C IS   ™os@' ' A C : : : dH d'H a  P  Cz R  Cz P @ C z A = 'H H H   a H H H H H Vz H Q   ™os@' ' A C IS   ™os@' ' A C : : : dH d'H a  P  Cz R  Cz P @ C z A = 'H H   a Q H H ™os@' 'HA Vz H a P  Cz P @ C z A = 'H H H H H H H C IS  C   ™os @' ' A P ™os@' ' A C : : : dHd'H R @ C z A  H  H ™os@' 'H A Vz I H Q  a = P  Cz P @ C z A 'H P IS H C ...
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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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