A plane electromagnetic wave travels in vacuum with its magn

A plane electromagnetic wave travels in vacuum with its magnetic field given by In what direction is the wave propagating? Calculate the frequency of the wave. (According to Faraday\'s law, the electric and magnetic fields of a plane electromagnetic wave must be in phase and their amplitudes E_0 and B_0 are related by E_0 = cB_0.)

Solution

(a) The wave is propogating in -y direction, and the magnetic field is in + z direction

(b) Wavelenght of wave = 2x3.14/9.72x10⁶

   frequency = speed of light / wavelength = 3x10⁸ / (2x3.14/9.72x10⁶) = 4.64 x 10¹⁴ Hz

(c) E_o = 3x10⁸ B_o =3x10⁸ x 7.8x10^-13= 23.4 x 10^-5

   Since Wave propogates in the directon of EXB so electric filed direction should be in x direction

   E_o (y,t) = 23.4 x 10^-5 sin[(9.72x10⁶ rad/m)y + wt] i