The components of the electric field in an electromagnetic wave traveling in vac

Question

The components of the electric field in an electromagnetic wave traveling in vacuum are described by
Ex = 0, Ey = 0, and
Ez = 5.73 sin(kx - 1.22×108 t) V/m,
where x is measured in meters and t in seconds. Calculate the frequency of the wave.
(in Hz)

Determine the wavelength of the wave.
(in m)

Calculate the amplitude of the magnetic field of the wave.
(in T)

What is the intensity of the wave?
(in W/m^2)

Explanation / Answer

Given Ez = 5.73 sin(kx - 1.22×108 t) V/m

Compare this with Ez = E sin(kx-wt) you get

Maximum electric field E = 5.73 V/m

Angular frequency w =1.22 x10 8 rad/s

Frequency f = w/2(pi) where pi = 22/7

= 19.41 x10 6 Hz

=1.94 x10 7 Hz

wavelength = c/ f

Where c = 3 x10 8 m/s

So, wavelength = 1.54 x10 1 m

Amplitude of magnetic field B= E/c

= 1.91 x10 -8 T

Intensity =(1/2)ce E 2

Where e = permitivity of free space = 8.85 x10 -12 C 2/ Nm 2

Substitute values you get intensity = 4.36 x10 -2

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