329fall10hw7sol

# 329fall10hw7sol - ECE 329 Fall 2010 Homework 7 - Solution...

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Unformatted text preview: ECE 329 Fall 2010 Homework 7 - Solution Due: Oct. 21, 2010 1. a) ˆ P =- ˆ x v = 1 . 5 10- 1 = 15 ( m/s ) = 1 μ v 2 = 3536 ( F/m ) H = 1 η ˆ P × E =- ˆ z q μ sin 2 π · 10 8 t + 10- 1 1 . 5 x ( A/m ) b) ˆ P =- ˆ y v = 2 10- 8 = 2 × 10 8 ( m/s ) = 1 μ v 2 = 1 . 99 × 10- 11 ( F/m ) = 2 . 25 E = η ˆ H × ˆ P =- ˆ z q μ Δ 10 3 t + 10- 8 2 z ( A/m ) c) ˆ P = ˆ z v = ω β = π 10 8 π/ 2 = 2 × 10 8 ( m/s ) = 1 μ v 2 = 1 . 99 × 10- 11 ( F/m ) = 2 . 25 E = η ˆ H × ˆ P = q μ ( ˆ x cos ( π · 10 8 t- π 2 z ) + ˆ y sin ( π · 10 8 t- π 2 z )) ( A/m ) 1 s so ( t τ ) The corresponding electric field is E ( x,t ) = η o 2 J so t ∓ x c ˆ y = η o t ∓ x c rect t ∓ x c τ ˆ y V m for x ≷ and the magnetic field is H ( x,t ) = ± 1 2 J so t ∓ x c ˆ z = ± t ∓ x c rect t ∓ x c τ ˆ z A m for x ≷ , where η o = 120 π Ω is the intrinsic impedance in free-space. a) Plotting E y ( x,t ) and H z ( x,t ) for x = ± 1200 m . Time [ μ s] E y ( x,t )[ μ V m ] 2 4 6 8 10- η o η o x = 1200 m Time [ μ s] H z ( x,t )[ μ A m ] 2 4 6 8 10- 1 1 x = 1200 m Time [ μ s] E y ( x,t )[ μ V m ] 2 4 6 8 10- η o η o x =- 1200 m Time [ μ s] H z ( x,t )[ μ A m ] 2 4 6 8 10- 1 1 x =- 1200 m b) Plotting E y ( x,t ) and H z ( x,t ) for t = 5 μ s . 3 ECE-329 fall 2010 2. On the x = 0 plane, we have a sheet current J ( t ) =- J ( t ) y ˆ =- 2 t rect y ˆ A / m , where τ = 2 μ s . x-axis [km] E y ( x,t )[ μ V m ]- 2- 1 . 5- 1- . 5 . 5 1 1 . 5 2- η o η o t = 5 μ...
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## This note was uploaded on 11/06/2011 for the course ECE 329 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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329fall10hw7sol - ECE 329 Fall 2010 Homework 7 - Solution...

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