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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 0 0 (2) Taking the time derivative of (2) and using (1) gives µ ε µ ε µ ε 2 2 0 0 0 0 0 0 2 2 1 1 1 E t t B x x B t E x y z z y = −  = −  = which implies µ ε 2 2 0 0 2 2 0 E x E t y y = . Thus E y (x,t) satisfies the wave equation with speed v = 1 0 0 / ε µ 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
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