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Unformatted text preview: ECE329 Fall 2008 Homework 5 Solution October 23, 2008 1. Let us consider the following four plane waves in free space, E 1 = 2cos( t z ) x V m E 2 = E o (cos( t z ) x sin( t z ) y ) V m H 3 = cos( t + z + 3 ) x + sin( t + z 6 ) y A m H 4 = cos( t x ) z + sin( t x ) y A m . a) The electric and magnetic fields ( E and H ) of uniform plane waves are perpendicular to each other and to the direction of propagation, therefore, it can be verified that such fields satisfy the following relation E = H , where is the unit vector parallel to the propagation direction and is the intrinsic impedance. Using this relation, we can find the expressions for H or E that accompany the waves given above, 1 = z H 1 = 2 o cos( t z ) y A m 2 = z H 2 = E o o (cos( t z ) y + sin( t z ) x ) A m 3 = z E 3 = o ( cos( t + z + 3 ) y sin( t + z 6 ) x ) V m 4 = x E 4 = o (cos( t x ) y sin( t x ) z ) V m . b) The instantaneous power flow density is given by the Poynting vector P = E H . Therefore, the instantaneous power that crosses some surface S is given by P = S P d S . In the case of uniform plane waves, this expression simplifies to...
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This note was uploaded on 11/16/2009 for the course ECE 329 taught by Professor Franke during the Fall '08 term at University of Illinois at Urbana–Champaign.
 Fall '08
 FRANKE
 Electromagnet

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