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Homework06Materials

# Homework06Materials - ECE 3030 Electromagnetic Fields and...

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Unformatted text preview: ECE 3030: Electromagnetic Fields and Waves Fall 2009 Homework 6 SOLUTIONS for GRADER: Wave Polarization and Media Effects Reminder: Don’t do homework for students; give hints! Date: Wedesday 10/14 Problem 9.4a(iii), b(iii,iv), c(iii): a(iii). Determine the polarization from the electric field, so ~ H( ~ r) = H (ˆx- j ˆy)e jkz = ⇒ E ( ~ r) = η H (ˆy + j ˆx)e jkz Which is left-hand circularly polarized. b(iii). Already done for part (a): ~ H( ~ r) = H (ˆx- j ˆy)e jkz = ⇒ E ( ~ r) = η H (ˆy + j ˆx)e jkz . b(iv). ~ H( ~ r) = ~ ∇ × E ( ~ r)- jωμ = ~ k × ~ E( ~ r) η = ˆ z √ 2 E η e- jk ( x + y ) / √ 2 c(iii). ~ S( ~ r) = ~ E( ~ r) × ~ H * ( ~ r) =- 2 η | H | 2 ˆ z = ⇒ < ~ S( ~ r ,t ) > = 1 2 < n ~ S( ~ r) o =- η | H | 2 ˆ z. Don’t forget to take half of the real part to get the time averaged value. (In this case the phasor Poynting flux was already real.) Problem 9.15 Finding the propagation direction from ~ E and ~ H and the energy....
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