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final 2004 solutions

# final 2004 solutions - Solution of Final Exam of ECSE 462...

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Solution of Final Exam of ECSE 462 / fall 2004 Prepared by Changling Luo Question 1 (a) ) 2 sin( ϕ α α S S z S B i u K = [ ] [ ] [ ] + = = = = = = = = r S S S S S S S S S z S S z z S u H g B Ri H H H g B Ri B Ri d B Ri Rd u B i u Rd u K dA J l d H ) 0 ( ) 2 cos( 1 2 ) ( ) 0 ( ) ( ) 2 cos( 1 2 1 ) 2 cos( 2 1 ) 2 sin( ) 2 sin( 0 0 0 0 ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ α α α ϕ α ϕ α ϕ α ϕ α By Gauss’s law [ ] [ ] = = = + = = = + = + = = = = ∫ ∫ r S S S S r S S S S S S S S S S S S S L u g B Ri H B u g B Ri g B Ri g B Ri H g B Ri H H g B Ri d H g B Ri d H d H LR dz Rd H a d B ) 2 cos( 2 ) ( ) ( ) 2 cos( 2 2 ) 2 cos( 1 2 ) ( 2 ) 0 ( 0 ) 0 ( 2 ) 2 sin( 2 1 2 2 ) 0 ( ) 2 cos( 1 2 ) ( 0 ) ( ) ( 0 0 2 0 2 0 2 0 2 0 0 0 2 0 0 ϕ μ μ ϕ ϕ ϕ ϕ ϕ π ϕ π ϕ ϕ ϕ ϕ ϕ ϕ μ ϕ ϕ μ α α α α α α α α π α π α π π π (b) ) 2 sin( δ ϕ α α + = R R z R B i u K and ) 90 2 sin( ° + + = δ ϕ α α R R z R B i u K [ ] [ ] [ ] + + = = + = + = + = = = = r R R R R R R R R R z

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