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 48.0 m and the e field vibrates in the xy plane with an amplitude of 18.0 V/m. (a) Calculate the frequency of the wave. 6.25 MHz (b) Calculate the magnetic field B when the electric field has its maximum value in the negative y direction, magnitude. 0.13 What is the relationship between the amplitudes of the magnetic and electric fields in a wave? nT (c) Write an expression for B with the correct unit vector, with numerical values for B_max k and omega magnitude in the fo B = B_max cos (kx - omega t). (Assume B is measured in nT, x is measured in m and t in s.) What is the amplitude of the magnetic field? cos [0.13 x - (39.27 How is omega related to the frequency? times 10^7)t] k nT

Explanation / Answer

Given
electromagnetic wave propagating in the +ve x direction with wavelength L = 48 m and

elelctric field amplitude = 18 V/m

a)

frequency of the wave is f = c/lambda = 3*10^8 /(48) Hz = 6.25*10^6 Hz = 6.25 MHz

b) magnetic field when the electric field has maximum value in the -ve y direction is

B = Emax/c

= 18/(3*10^8) T = 60*10^-9 T = 60 nT
in the -ve z direction always the electric and magnetic fields are perpendicular to each other

c) B = Bmax cos (kx-wt)

W = 2pif = 2pi*6.25*10^6 rad/s = 39269908.17 rad/s = 3.926990817*10^7 rad/s

   B = -60*10^-9 cos(0.13x -3.926990817*10^7*t) k^ T

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