329fall08hw8sol

329fall08hw8sol - ECE-329 Fall 2008 Homework 8 Solution...

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Unformatted text preview: ECE-329 Fall 2008 Homework 8 Solution October 20, 2008 1. The electric field of a plane wave propagating in some medium with = 10 o is described by E =- 10 e z cos( t + z ) x V m where 2 m- 1 and = 2 10 7 rad / s . a) Since the wave propagates in the- z direction, the phase velocity vector is v p =- z - 10 7 z m s . b) The propagation constant is = + j 2 (1 + j ) = 2 2 e j 4 m- 1 . c) The complex impedance is = j 20 (1 + j ) = 20 2 e j 4 . d) The associated magnetic field is H = 10 | | e z cos( t + z- ) y = 2 2 e z cos( t + z- 4 ) y A m . e) Since = + j , we find that + j . 1+0 j. This implies that 1 , and in consequence this material is a good conductor. 2. In problem 1, the conductivity of the material is = Re = 0 . 1 S m , The resultant power dissipated per unit volume is P d = J E = | E | 2 = 10 e 2 z cos 2 ( t + z ) W m 3 , where 2 m- 1 and = 2 10 7 rad / s ....
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329fall08hw8sol - ECE-329 Fall 2008 Homework 8 Solution...

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