329sum11hw5sol - ECE 329 Homework 5 Solution Due: July 1,...

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Unformatted text preview: ECE 329 Homework 5 Solution Due: July 1, 2011, 5PM 1. Applying Gauss law S B d S = 0 and considering B = a x + a y- a R L z , we will compute the magnetic flux through the partial cone surface S 1 shown in the next figure. x y z 2 R R S 4 S 2 S 3 S 1 L For this purpose, let us first define the closed surface S composed by the partial cone surface S 1 , the semicircle S 2 with radius R , the semicircle S 3 with radius 2 R , and the trapezoid S 4 with bases 2 R and 4 R and height L . Now, we can rewrite Gauss law as follows S B d S = S 1 B d S 1 + S 2 B d S 2 + S 3 B d S 3 + S 4 B d S 4 = 0 . On the semicircle S 2 , the magnetic flux is S 2 B d S 2 = S 2 a x + a y- a R L z xdS 2 = a Area 2 = a R 2 2 . On the semicircle S 3 , the magnetic flux is S 3 B d S 3 = S 3 a x + a y- a R L z (- x ) dS 3 =- a Area 3 =- a (2 R ) 2 2 =- 2 aR 2 . On the trapezoid S 4 , the magnetic flux is S 4 B d S 4 = S 4 a x + a y- a R L z (- z ) dS 4 = a R L Area 4 = a R L ( 2 R + 4 R 2 L ) = 3 aR...
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This note was uploaded on 11/06/2011 for the course ECE 329 taught by Professor Kim during the Summer '08 term at University of Illinois, Urbana Champaign.

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329sum11hw5sol - ECE 329 Homework 5 Solution Due: July 1,...

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