329sp10hw1sol - ECE 329 Spring 2010 Homework 1 - Solution...

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Unformatted text preview: ECE 329 Spring 2010 Homework 1 - Solution Due: Jan. 26, 2010 1. a) D = A + B = 4 b x + 2 b y- 3 b z. b) A + B- 4 C = 4 b x + 2 b y- 3 b z- 4( b x- 2 b y + 3 b z ) = 10 b y- 15 b z. c) | A + B- 4 C | = p 10 2 + 15 2 = 18 . 03 . d) A + 2 B- C = (3 b x + b y- 2 b z ) + 2( b x + b y- b z )- ( b x- 2 b y + 3 b z ) = 4 b x + 5 b y- 7 b z, | A + 2B- C | = p 4 2 + 5 2 + 7 2 = 9 . 49 , u = A + 2B- C | A + 2B- C | = 4 b x + 5 b y- 7 b z 9 . 49 = 0 . 42 b x + 0 . 53 b y- . 74 b z. e) A B = (3 b x + b y- 2 b z ) ( b x + b y- b z ) = 3 1 + 1 1 + (- 2) (- 1) = 6 . f) B C = ( b x + b y- b z ) ( b x- 2 b y + 3 b z ) = b x ( b x- 2 b y + 3 b z ) + b y ( b x- 2 b y + 3 b z )- b z ( b x- 2 b y +3 b z ) = (- 2 b z- 3 b y ) + (- b z + 3 b x )- ( b y + 2 b x ) = b x- 4 b y- 3 b z. 2. In the three cases, we have the same E and B at the origin, but di erent v . Thus, we have di erent F . In each case, v and F must satisfy F = q ( E + v B ) . Therefore, we have the following three....
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This note was uploaded on 04/20/2010 for the course ECE ECE 329 taught by Professor Goddart during the Spring '10 term at University of Illinois at Urbana–Champaign.

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329sp10hw1sol - ECE 329 Spring 2010 Homework 1 - Solution...

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