The figure below shows a plane electromagnetic sinusoidal wave propagating in th

Question

The figure below shows a plane electromagnetic sinusoidal wave propagating in the x direction. Suppose the wavelength is 58.0 m and the electric field vibrates in the xy plane with an amplitude of 24.0 v/m. (a) Calculate the frequency of the wave. MHz (b) Calculate the magnetic field B when the electric field has its maximum value in the negative y direction. magnitude nT direction (c) Write an expression for B with the correct unit vector, with numerical values for B_max, k, and omega, and with its magnitude in the form B = B_max cos (kx - omega t). (Assume B is measured in nT, x is measured in m and t in s.) B = - cos [x - (times 10^7)t]knT

Explanation / Answer

(a)

frequency f = c/lambda

f = 3*10^8/58

f = 5.17 MHz

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(b)

B = E/c = 24/(3*10^8) = 8*10^-8 = 80 nT

direction -z direction

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(c)

k = 2pi/lambda = 2pi/58 = 0.11

w = 2*pi*f = 2*pi*5.17 = 3.25*10^7

B = 80*cos[(0.11x-3.25*10^7*t)]k nT

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