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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 timeindependent, then ˛ C E · d l = d dt ˆ S B · d S = 0 holds for any closed loop C . Assume that ´ l 12 E · d l is pathdependent and ˆ l 12 ,A E · d l 6 = ˆ l 12 ,B E · d l . Then we can choose C = A B and nd ˛ C E · d l = ˆ l 12 ,A E · d l ˆ 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 pathdependent. d) Although B is timeindependent, C is changing with time and thus S is changing with time, which means E = d dt ´ S B · d S can be nonzero. 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 = ˆ S 1 + S 2 + S 3 + S 4 + S 5 + S 6 J · d S , where ˆ S 1 + S 2 J · d S =...
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 Spring '08
 FRANKE
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