329fall09hw8sol - ECE 329 Fall 2009 Homework8 Solution Due...

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Unformatted text preview: ECE 329 Fall 2009 Homework8 Solution Due: Oct. 20, 2009 1. a) E ( y,t ) = ˆ zE z ( y,t ) = ˆ zE z ,t + y c = ˆ z 12Δ t + y/c τ ( V/m ) . b) H ( y,t ) = ˆ xH x ( y,t ) =- ˆ x 1 η E z ( y,t ) =- ˆ x 1 η E z ,t + y c =- ˆ x 12 η Δ t + y/c τ ( A/m ) . c) E × H =- ˆ y 144 η Δ 2 t + y/c τ ( W/m 2 ) , max ( | E × H | ) = 144 η · 1 ≈ 144 120 π = 6 5 π ( W/m 2 ) . d) The trajectory function y ( t ) should satisfy t + y ( t ) /c τ = 0 , or y ( t ) =- ct. e) According to a), E z (- 1500 ,t ) = 12Δ t- 1500 /c τ = 12Δ t- 5 μs 4 μs ( V/m ) , which is plotted below. f) According to b), H x ( y, 12 μs ) =- 12 η Δ 12 μs + y/c 4 μs ≈ - 1 10 π Δ 12 μs + y/ 3 × 10 8 4 μs ( V/m ) , which is shown below. 1 ECE 329 Fall 2009 2. a) η = E y H x = 120 π (Ω) . b) v = c 2 = 1 . 5 × 10 8 ( m/s ) . c) η = r μ = r μ r μ r = 120 π r μ r r . Comparing the above with a), we nd that q μ r r = 1 . On the other hand, v = c √ μ r r ....
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329fall09hw8sol - ECE 329 Fall 2009 Homework8 Solution Due...

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