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Unformatted text preview: Phys 2214 Homework #6 Solutions October 26, 2011 1. EM Waves in Vacuum Given Gauss law, ~ E = / , assume = 0, since were in a vacuum. Also, we take the plane wave to be traveling in the + x direction, so ~ E = f ( x ct ) x + g ( x ct ) y + h ( x ct ) z . Note that ~ E can have an xcomponent and still be a plane wave. But, applying Gauss law in vacuum, we get ~ E = 0 = f x + g x + h x = f x + 0 + 0 . So, f/x = 0 and therefore f = constant. But f = E x = constant is not a wave. So, E x = 0. So, there is no component of ~ E in the direction of propagation and the wave must be transverse. 2. Faradays law and EM waves Given Faradays law, ~ E = ~ B/t , with ~ B = B y y ; then B y t y = ~ E = x y z x y z E x E y E z Then B y t = x E z y E y z ! + y E x z E z x ! + z E y x E x y ! . Given ~ E = f ( x ct ) x + g ( x ct ) y + h ( x ct ) z , 1 then E z y = E y z = 0 , E x z = E x y = 0 , and E y x , E z x 6 = 0 ....
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 '11
 DAVIS,J.C.
 Work, Waves And Optics

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