329fall09hw2sol - ECE 329 Fall 2009 Homework 2 Solution...

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Unformatted text preview: ECE 329 Fall 2009 Homework 2 Solution September 9, 2009 1. a) According to Gauss' Law, S E d S = 1 V dV = 1 V 1 dV = 1 ( V m ) . b) S E d S = 1 V dV = 1 1 / 2 - 1 / 2 1 / 2 - 1 / 2 1 / 2 - 1 / 2 ( x 2 + y 2 + z 2 ) dxdydz By symmetry, S E d S = 3 1 / 2 - 1 / 2 1 / 2 - 1 / 2 1 / 2 - 1 / 2 x 2 dxdydz = 3 1 / 2 - 1 / 2 x 2 dx = 1 4 ( V m ) . c) Since the charge distribution has the same x, y and z dependencies, we know that the electric ux through the 6 surfaces should be equal to each other, namely S i E d S = 1 6 S E d S = 1 24 ( V m ) , i = 1 , 2 , , 6 . 2. According to Example 5 in Lecture 3 online, this problem can be solved by using symmetry. First, we consider Q 1 . By Gauss' Law, S D 1 d S = Q 1 holds for any S enclosing Q 1 . Due to symmetry, half of the ux should go to the- x direction across the y- z plane (while the other half should go to the + x direction across the x = 2 plane), i.e....
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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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329fall09hw2sol - ECE 329 Fall 2009 Homework 2 Solution...

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