EE_365_200708FA_homework_11_solution

# EE_365_200708FA_homework_11_solution - 1 ⎛ ∂ ⎞ ⎛...

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1 Homework 11 Solution © Jeffrey Mayer 2005-2007. All rights reserved. EE 365 Fall 2007 1. 1 2 11 1 1 2 1 1 2 () [ ( () ) ] [ ) ][ ) ] ( ) [ )] TT e sab s r sab sab sr r rqd rr T T s r s q ds r s r s q d s r s q r r r q d r r rT r T sqd s r s r r T θθ θ −− ⎛⎞ ∂∂ ′′ =− + ⎜⎟ ⎝⎠ + iL i i Ki LKi L i iK L 1 2 ( ( )) ( ) [( ( )) ] ( ) cos(2 ) sin(2 ) c o s ( )s i n ( ) c o s ( i n ( ) sin(2 ) cos(2 ) sin( ) cos( ) sin r T sr s q d s q d s rr r q d r ls A B r B r sqd Br l s A B r r LLL L L + ⎟⎜ ⎠⎝ +− ⎡⎤ ⎢⎥ −+ + ⎣⎦ i K L i i 1 2 ( ) cos( ) cos( ) cos( ) sin( ) sin( ) cos( ) sin( ) sin( ) sin( ) cos( ) cos( ) sin( ) cos( ) cos( ) sin( ) si r sqd mq r mq r md r md r sqd rqd mq r mq r md r md r r sqd LL L L L L + i i i i 2 sin(2 ) 2 cos(2 ) cos( ) sin( ) n( ) cos( ) 2 cos(2 ) 2 sin(2 ) sin( ) cos( ) sin( ) sin( ) cos( ) cos( ) cos( ) sin( ) sin( ) cos( ) B r r r r sqd B r B r mq r mq r md r md r sqd m L L L θθθ + i i 1 2 cos( ) cos( ) sin( ) sin( ) cos( )sin(2 ) sin( )cos(2 ) cos( ) sin( ) cos( 2 sin( ) cos( ) sin( ) cos( ) rqd q r mq r md r md r r r rr r sqd B r r r r L L + i i i n ( ) sin( ) cos( ) 00 sin( ) cos( ) cos( ) sin( ) cos( ) sin( ) sin( ) cos( ) r sqd md md sqd rqd mq mq md md r r T Bs q d sqd sqd rqd mq mq r r L + + = i ii i i 01 10 md md r B sqd sqd sqd rqd mq mq L i i

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