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955_Physics ProblemsTechnical Physics

955_Physics ProblemsTechnical Physics - 296 P34.8...

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296 Electromagnetic Waves P34.8 E E kx t = max cos ω b g = − = − = − = − E x E kx t k E t E kx t E x E kx t k E t E kx t max max max max sin sin cos cos ω ω ω ω ω ω b ga f b ga f b g e j b ga f 2 2 2 2 2 2 We must show: = E x E t 2 0 0 2 2 µ . That is, = − k E kx t E kx t 2 0 0 2 e j b g a f b g max max cos cos ω µ ω ω . But this is true, because k f c 2 2 2 2 0 0 1 1 ω λ µ = F H G I K J = = . The proof for the wave of magnetic field follows precisely the same steps. P34.9 In the fundamental mode, there is a single loop in the standing wave between the plates. Therefore, the distance between the plates is equal to half a wavelength. λ = = = 2 2 2 00 4 00 L . . m m a f Thus, f c = = × = × = λ 3 00 10 4 00 7 50 10 75 0 8 7 . . . . m s m Hz MHz . P34.10 d A to A cm = ± = 6 5% 2 λ λ λ =
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