HW6_Solution

HW6_Solution - ECE 201A Homework 6 solution 1. line charge...

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Unformatted text preview: ECE 201A Homework 6 solution 1. line charge q 2 w Dielectric Slab a x Region I Region II Region III (1 k 2 ) , x = 1 , , 4 w k 2 w 2 w (1 k ) k = 1 + 1 k 2 (1 k 2 ) k (1 k 2 ) k (1 k ) k 2 (1 k ) line charge q 2 w Dielectric Slab a x Region I Region II Region III (1 k 2 ) (1 k 2 ) , , x = x = 1 , 1 , , , 4 w 4 w k k 2 w 2 w 2 w 2 w (1 k ) (1 k ) k = 1 + 1 k = 1 + 1 k 2 (1 k 2 ) k 2 (1 k 2 ) k (1 k 2 ) k (1 k 2 ) k (1 k ) k (1 k ) k 2 (1 k ) k 2 (1 k ) Using the reflection diagram for the flux we can find the multiple images of the line charge as shown in the figure above. The equivalent problem as far as region I is concerned is , everywhere x = Line charges (1 k 2 )q k 2 (1 k 2 )q k 4 (1 k 2 )q x 8 w + a 4 w 6 w + a 4 w 2 w + a , everywhere , everywhere x = x = Line charges (1 k 2 )q (1 k 2 )q k 2 (1 k 2 )q k 2 (1 k 2 )q k 4 (1 k 2 )q k 4 (1 k 2 )q x 8 w + a 8 w + a 4 w 4 w 6 w + a 6 w + a 4 w 4 w 2 w + a 2 w + a The equivalent problem as far as region II is concerned is 1 , everywhere Line charges x 8 w + a 4 w 6 w + a 4 w 2 w a 2 w + a (1 k )q k 2 (1 k )q k 4 (1 k )q 4 w k (1 k )q (6 w + a ) 4 w (2 w a ) (2 w + a ) k 3 (1 k )q 1 , everywhere 1 , everywhere Line charges x 8 w + a 8 w + a 4 w 4 w 6 w + a 6 w + a 4 w 4 w 2 w 2 w a 2 w + a...
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HW6_Solution - ECE 201A Homework 6 solution 1. line charge...

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