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 electric field vibrates in the xy plane with an amptitude of 18.0 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 ni (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 - omegat). (Assume B is measured in nT, x is measured in m and t in s.) B = - cos[x - (times 10^7)t) k nT

Explanation / Answer

a) f = c/ = (3 * 108) / 48 = 6.25 * 106 Hz

b) When the electric field is maximum in the negative y direction, magnetic field is maximum in the negative z-direction.

B = E/c = 18 / (3 * 108) = 60 nT (directed towards the -ve z axis)

c) k = 2/ = 2/48 = 0.13 rad/m

= 2f = 2 * 6.25 * 106 = 3.93 * 107 rad/s

So, B = 60cos[0.13x - (3.93 * 107)t] nT

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