chp38_12 - PHY2061 R D Field Electromagnetic Plane Waves(1...

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PHY2061 R. D. Field Department of Physics chp38_12.doc University of Florida Electromagnetic Plane Waves (1) We have the following two differential equations for E y (x,t) and B z (x,t) : B t E x z y =− (1) and ∂µ ε E t B x y z 1 00 (2) Taking the time derivative of (2) and using (1) gives 2 2 2 2 11 1 E tt B xx B t E x y zz y =− = which implies µε 2 2 2 2 0 E x E t yy −= . Thus E y (x,t) satisfies the wave equation with speed v = 1 / εµ and has a solution in the form of traveling waves as follows: E y (x,t) = E 0 sin(kx- ω t) , where E 0 is the amplitude of the electric field oscillations and where the wave has a unique speed vc k fm s == = = = × ω λ
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This note was uploaded on 05/31/2011 for the course PHY 2061 taught by Professor Fry during the Spring '08 term at University of Florida.

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