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Unformatted text preview: ECE329 Fall 2008 Homework 8 — Solution October 20, 2008 1. The electric field of a plane wave propagating in some medium with μ = 10 μ o is described by E = 10 e αz cos( ωt + βz ) ˆ x V m where α ≈ β ≈ 2 π m 1 and ω = 2 π · 10 7 rad / s . a) Since the wave propagates in the z direction, the phase velocity vector is v p = ω β ˆ z ≈  10 7 ˆ z m s . b) The propagation constant is γ = α + jβ ≈ 2 π (1 + j ) = 2 √ 2 π e j π 4 m 1 . c) The complex impedance is η = jωμ γ ≈ 20 π (1 + j ) = 20 √ 2 π e j π 4 Ω . d) The associated magnetic field is H = 10  η  e αz cos( ωt + βz ∠ η ) ˆ y = π 2 √ 2 e αz cos( ωt + βz π 4 ) ˆ y A m . e) Since γ η = σ + jω , we find that σ + jω ≈ . 1+0 j. This implies that σ ω 1 , and in consequence this material is a good conductor. 2. In problem 1, the conductivity of the material is σ = Re γ η = 0 . 1 S m , The resultant power dissipated per unit volume is P d = J · E = σ  E  2 = 10 e 2 αz cos 2 ( ωt + βz ) W m 3 , where α ≈ β ≈ 2 π m 1 and ω = 2 π · 10 7 rad / s ....
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 Fall '08
 FRANKE
 Electromagnet, Gate, Electric charge, Dielectric

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