329sp09hw6 - ECE 329 Homework 6 Due: Tue, March 3, 2009,...

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Unformatted text preview: ECE 329 Homework 6 Due: Tue, March 3, 2009, 5PM 1. Verify that vector identity H E- E H = ( E H ) holds for E = 2 xe- z and H = 4 ye- z by expanding both sides of the identity. Treat as a real constant. 2. Consider an infinite surface current density J s =- xJ so cos( t ) flowing on z = 0 surface, where J so > is real-valued amplitude of the monochromatic surface current measured in A/m units. It is found that J s injects field energy into propagating transverse electromagnetic (TEM) waves away from the z = 0 plane at an average rate of 1 W/m 2 that is, the magnitude of the average Poynting vector P is 1 2 W/m 2 for the waves excited by the surface current. a) Denoting the TEM waves excited by J s (above and below the z = 0 plane) as E = xE o cos( t z ) V/m and H = yH o cos( t z ) A/m, where wavenumber = c , determine the numerical values of wave amplitudes E o and H o in V/m and A/m units (assuming wave propagation in free space). Hint: equate the expression for the magnitude of P for each wave to...
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This note was uploaded on 11/16/2009 for the course ECE 329 taught by Professor Franke during the Spring '08 term at University of Illinois at Urbana–Champaign.

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329sp09hw6 - ECE 329 Homework 6 Due: Tue, March 3, 2009,...

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