329sum09hw1sol - ECE-329 Summer 2009 Homework 1 —...

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Unformatted text preview: ECE-329 Summer 2009 Homework 1 — Solution June 17, 2009 1. Given vectors A = 3ˆ x + ˆ y- 2ˆ z, B = ˆ x + ˆ y- ˆ z, C = ˆ x- 2ˆ y + 3ˆ z, we can calculate the following. a) The vector D = A + B = 4ˆ x + 2ˆ y- 3ˆ z. b) The vector A + B- 4 C = 10ˆ y- 15ˆ z. c) The vector magnitude | A + B- 4 C | = √ 10 2 + 15 2 = √ 325 . d) The unit vector ˆ u = A +2 B- C | A +2 B- C | = 4ˆ x +5ˆ y- 7ˆ z √ 4 2 +5 2 +7 2 = 4ˆ x +5ˆ y- 7ˆ z √ 90 . e) The dot product A · B = (3ˆ x + ˆ y- 2ˆ z ) · (ˆ x + ˆ y- ˆ z ) = 3 + 1 + 2 = 6 . f) The cross product B × C = ˆ x ˆ y ˆ z 1 1- 1 1- 2 3 = (3- 2)ˆ x- (3 + 1)ˆ y + (- 2- 1)ˆ z = ˆ x- 4ˆ y- 3ˆ z. 2. In a region, with electric field E and magnetic field B , the force experienced by a charged particle is F = q ( E + v × B ) , where q = 1 C . For three different particle velocities we get three different forces, so that 3ˆ z = E + × B ˆ z = E + 1ˆ y × B 3ˆ z + 4ˆ y = E + 2ˆ z × B ....
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This note was uploaded on 09/16/2011 for the course ECE 329 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.

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329sum09hw1sol - ECE-329 Summer 2009 Homework 1 —...

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