hw9solns - PHYSICS 273 HW#9 SOLUTIONS 9-20 Let the electric...

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PHYSICS 273 HW #9 SOLUTIONS
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9-20 Let the electric field be 0 sin . E kx t Its energy density is 2 2 2 0 0 0 0 1 1 sin with average . 2 4 E kx t E The kinetic energy density of electrons can be found from 2 2 2 2 2 2 2 2 0 0 0 0 2 2 2 1 1 1 1 cos with average 2 2 4 4 p e e ne ne nmv E kx t E E m m (Note that the electron velocity is 0 0 sin cos .) t e e eE eE v kx t dt kx t m m     The magnetic field can be found from 0 0 sin / E B E kx t k    , which yields the magnetic energy density 2 2 2 2 2 0 0 0 1 1 1 1 sin 2 2 2 p B E E kx t   . Its average is therefore 2 2 0 0 1 1 4 p E And the total energy density is then 2 2 2 2 0 0 0 0 2 2 1 1 1 1 (rms) 4 2 p p E E
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