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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 plane-wave is propagating in the x-direction. 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 plane-wave is traveling in the x direction, there cannot be a field component in the x-direction. 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