Shows a plane electromagnetic sinusoidal wave propagating in vacuum in the x dir

Question

Shows a plane electromagnetic sinusoidal wave propagating in vacuum in the x direction. Suppose the wavelength is 48.0 m and the electric field vibrates in the xy plane with an amplitude of 22.0 V/m. Calculate the frequency of the wave. MHz Calculate the magnitude and direction of u rightarrow when the electric field has its maximum value in the negative y direction. Write an expression for u rightarrow with the correct unit vector, with numerical values for B_max, k, and omega, and with its magnitude in the form shown below. B = B_max cos(kx - omega t) B = cos(x - t) nT

Explanation / Answer

Frequency = speed of light / wavelenght = 3*10^8 / 48 = 6.25*10^6 Hz

Magnitude of B = E / c = 22 / 3*10^8 = 73.33 nT

Direction will be towards positive x axis

Bmax= 73.33 nT

k = 2*pi / wavelenght = 0.13 m^-1

w = kc = 0.13*3*10^8 = 3.926*10^7 s^-1

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