Question

Consider a harmonic, electromagnetic plane wave traveling along a line from the origin to the point (2,6,4). It is linearly polarized and its electric field lies in a plane perpendicular to the direction of travel of the wave. The wavelength of the wave is 2.0 mm and it has a frequency of 120 GHz.

a) What is the index of refraction of the medium in which the wave is traveling?

b) Write an expression for E(x,t), that is, the magnitude (i.e. dont worry about the orientation) of the electric field of this plane wave if the amplitude of the electric field is 12 V/m.

c) Compute the irradiance of the wave.

Answer #1

a] The speed of propagation for this wave is:

= 2.4 x 10^{8} m/s

the refractive index for this medium will then be:

n = (3 x 10^{8} / 2.8 x 10^{8}) = 1.25

b]

The electric field will be given by:

=>

=>

c] The irradiance of the wave is given by the average value of the Poynting vector

=>
= 0.191 W/m^{2}.

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