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Unformatted text preview: EE1 Spring 2008 Homework Solutions #7 (1) The magnetic field in a given dielectric medium is given by: ~ H = y 6 cos 2 z sin (2 10 7 t . 1 x ) where x and z are in meters. Determine: (a) ~ E By inspection, we can see that the given planewave is propagating in the xdirection. We make = 2 10 7 and k = 0 . 1. From Faradays Law (also Maxwells equations): ~ E = ~ B t We know ~ B = ~ H : ~ B = y 6 cos 2 z sin ( t kx ) Calculating the two sides of Faradays Law: ~ E = x ( E z y E y z ) + y ( E x z E z x ) + z ( E y x E x y ) ~ B t = y 6 cos 2 z cos ( t kx ) Equating like terms: ( E x z E z x ) = 6 cos 2 z cos ( t kx ) Since the planewave is traveling in the x direction, there cannot be a field component in the xdirection. Thus, E x must be zero. Then: E z x = 6 cos 2 z cos ( t kx ) Integrating, E z = 6 cos 2 z sin ( t kx ) k 1 The parameter...
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This note was uploaded on 06/18/2008 for the course EE 1 taught by Professor Joshi during the Spring '08 term at UCLA.
 Spring '08
 Joshi

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