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 46.0 m and the electric field vibrates in the xy plane with an amplitude of 24.0 V/m.

magnitude


The figure below shows a plane electromagnetic sinusoidal wave propagating in the x direction. Suppose the wavelength is 46.0 m and the electric field vibrates in the xy plane with an amplitude of 24.0 V/m. Calculate the magnetic field when the electric field has its maximum value in the negative y direction. Write an expression for with the correct unit vector, with numerical values for Bmax, k, and w, and with its magnitude in the form B = Bmax cos (kx ? ?t). (Assume B is measured in nT, x is measured in m and t in s.)

Explanation / Answer

a. as V = Lf

frequency f = V/L = 3*10^8/46 = 6.51 *10^6 Hz = 6.51 MHz

b. electric field and magnetic fioeld are related by E = Bc

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

c. B = 80nT * cos (kx-wt)

k = 2pi/L = 2*3.14/46 = 0.136

w = 2pif = 2*3.14* 6.51*10^6 = 4.088 *10^7

so Bmax = -80nT * cos ( 0.136x- 4.088*10^7 t)

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