329fall08hw2sol

# 329fall08hw2sol - ECE-329 Fall 2008 Homework 2 (Solution)...

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Unformatted text preview: ECE-329 Fall 2008 Homework 2 (Solution) September 10, 2008 1. The infinitesimal electric field at position ( x o , , 0) generated by an infinite charge strip along the z-axis with an infinitesimal width dx is found to be d ~ E = ˆ x ρ S 2 π o x o dx, where ρ S is the uniform surface charge density. We can use this result to compute the electric field produced at the same location by a charge strip of finite width W that extends from x = 0 to x = W < x o (see the next figure). dx x z W d ~ E x o x o- x x Since the contribution of an infinitesimal strip that is placed at a distance x from the origin is simply d ~ E = ˆ x ρ S 2 π o ( x o- x ) dx, the total field produced by the strip can be easily obtained by integrating d ~ E from x = 0 to x = W as follows ~ E = ˆ x W ˆ ρ S 2 π o ( x o- x ) dx = ˆ x ρ S 2 π o [- ln( x o- x )] W = ˆ x ρ S 2 π o (- ln( x o- W ) + ln( x o )) = ˆ x ρ S 2 π o ln x o x o- W . 1 ECE-329 Fall 2008 2. We will apply Gauss law ˛ S ~ E · d ~ S = 1 o ˆ V ρdV to compute the electric flux ¸ S ~ E · d ~ S over the surface of a cube of volume V = L 3 that is centered at the origin. L 2 (1 , 1 , 1) L 2 (- 1 , 1 , 1) L 2 (- 1 , 1 ,- 1) L 2 (1 , 1 ,- 1) L 2 (1 ,- 1 ,- 1) L 2 (1 ,- 1 , 1) L 2 (- 1 ,- 1 , 1) L 2 (- 1 ,- 1 ,- 1) x y z d ~ S 2 d ~ S 1 d ~ S 3 (a) If the electric charge density within the cube is ρ = 1 C / m 3 , the total electric flux can be computed as follows ˛ S ~ E · d ~ S = 1 o ˆ V ρdV = 1 o ˆ V dV = 1 o L/ 2 ˆ- L/ 2 dx L/ 2 ˆ- L/ 2 dy L/ 2 ˆ- L/ 2 dz = L 3 o V · m ....
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## This note was uploaded on 04/14/2009 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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329fall08hw2sol - ECE-329 Fall 2008 Homework 2 (Solution)...

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