Light, radiant heat (infrared radiation), X rays, and radio waves are all exampl

Question

Light, radiant heat (infrared radiation), X rays, and radio waves are all examples of traveling electromagnetic waves. Electromagnetic waves comprise combinations of electric and magnetic fields that are mutually compatible in the sense that the changes in one generate the other.

The simplest form of a traveling electromagnetic wave is a plane wave. For a wave traveling in the x direction whose electric field is in the y direction, the electric and magnetic fields are given by

This wave is linearly polarized in the y direction.

a) What is the velocity of electromagnetic waves?

b) For an electromagnetic wave with maximum electric field of 1300 , and wavelength of 649 , what is the k (angular wave number) and (angular frequency)?

c) What is the period of the wave described?

d) What is the maximum magnetic field for the wave described?

e) What is the intensity of the wave described?

Explanation / Answer

a)

Velocity of the electromagnetic waves is c

c = 3 * 10^8 m/s

b)

(=649nm)

k = 2/ = 2*3.14/649e-9 = 9676425 9.68 * 10^6 m-1

= c k = 3e8 * 9676425 = 2.9029275e15 = 2.90 * 10^15 rad/s

c)

T = 2/ = 2*3.14/2.9029275e15 = 2.16 * 10^-15 s

d)

B = E/c = 1300/3e8 = 4.33 * 10^-6 T

e)

I = E2/(2c) = (1300*1300)/(2*4*3.14e-7*3e8) = 2.24 * 10^3 W/m2

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