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# 329fall09hw8 - ECE 329 Homework 8 Due 5 PM 1 A z-polarized...

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ECE 329 Homework 8 Due: October 20, 2009, 5 PM 1. A ˆ z -polarized TEM wave is propagating in a vacuum (i.e., v = c 3 × 10 8 m/s and η = η 0 120 π Ω ) in the - ˆ y direction. If the wave field varies with time at y = 0 according to E z (0 , t ) = 12Δ( t τ ) V/m, where τ = 4 μ s and Δ( t τ ) is the unit triangle function with width τ : a) Determine the vector wavefield E ( y, t ) written explicitly in terms of all space and time variables y and t . b) Determine the accompanying wavefield H ( y, t ) in A/m units. c) Determine the maximum value of Poynting vector E × H . d) What trajectory function y = y ( t ) describes the instantaneous locations of peak values of E × H ? e) Plot E z ( y, t ) as a function of t at y = - 1500 m. f) Plot H x ( y, t ) as a function of y at t = 12 μ s. 2. In a homogeneous perfect dielectric with = r 0 and μ = μ r μ 0 , a plane TEM wave with the following components is observed: E = ˆ yu ( t - z c/ 2 ) + ˆ xg ( t - z c/ 2 ) V/m H = ˆ y 10( t - z c/ 2 ) - ˆ x 1 120 π u ( t - z c/ 2 ) V/m where u ( t ) denotes the unit step function and c is the speed of light in free space. Using the above

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329fall09hw8 - ECE 329 Homework 8 Due 5 PM 1 A z-polarized...

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