329fall09hw7sol - ECE 329 Fall 2009 Homework7 Solution Due:...

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Unformatted text preview: ECE 329 Fall 2009 Homework7 Solution Due: Oct. 13, 2009 1. a) Since B = 0 , we have E =- d dt S B d S = 0 . b) Since d B dt = 0 , we have E =- d dt S B d S =- S d B dt d S = 0 . c) From b) we know that if B is time-independent, then C E d l =- d dt S B d S = 0 holds for any closed loop C . Assume that l 12 E d l is path-dependent and l 12 ,A E d l 6 = l 12 ,B E d l . Then we can choose C = A- B and nd C E d l = l 12 ,A E d l- l 12 ,B E d l 6 = 0 , which can not be true according to the discussion above. Therefore, l 12 E d l can not be path-dependent. d) Although B is time-independent, C is changing with time and thus S is changing with time, which means E =- d dt S B d S can be non-zero. 2. a) The closed surface S can be decomposed into 6 surfaces: S = S 1 + S 2 + S 3 + S 4 + S 5 + S 6 , where S 1 : x = 0 S 2 : x = 2 S 3 : y = 0 S 4 : y = 2 S 5 : z = 0 S 6 : z = 2 . 1 ECE 329 Fall 2009 Therefore, S J d S = S 1 + S 2 + S 3 + S 4 + S 5 + S 6 J d S , where S 1 + S 2 J d S =...
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This note was uploaded on 05/05/2010 for the course ECE 329 taught by Professor Franke during the Spring '08 term at University of Illinois at Urbana–Champaign.

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329fall09hw7sol - ECE 329 Fall 2009 Homework7 Solution Due:...

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