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Unformatted text preview: ECE 450 Homework 3 Due: Tue, Feb 8, 2011, 5 PM 1. A Hertzian radiation source with the current density J ( r , t ) = xI o x ( x-100 ) ( y ) ( z-100 ) cos( t ) A m 2 , is embedded in free space and its oscillation frequency f = 2 = 300 MHz. Assuming that I o x = 1 A.m, determine the numerical values (in appropriate units) of a) wavelength of the radiation Feld, b) the corresponding wavenumber k , c) retarded vector potential phasor A at r = 200 z , d) the radiation electric Feld phasor E at r = 200 z , e) the radiation magnetic Feld intensity phasor H at r = 200 z , and f) the time-average Poynting vector E H at the same location. Note: the vector quantities in parts (c-f) should be speciFed in terms of unit vectors x , y , z . 2. Three identical Hertzian dipoles I are co-located at the origin aligned with the positive x-, y-, and z-axis, respectively. a) Determine the total retarded vector potential phasor A of the dipoles acting in unison. b) Express the corresponding radiation feld phasor E of the dipoles at (i) ( x, y, z ) = ( d, , 0) , and (ii) ( x, y, z ) = (...
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