Question

An electromagnetic wave in a vacuum traveling in the +x direction generated by a variable source initially has a wavelength λ of 235 μm and a maximum electric field Emax in the +y direction of 7.70×10−3 V/m . If the period of the wave is then increased by a factor of 2.70, what is the equation of the resulting magnetic field component of the wave?

Answer 1

If the period of the wave is increased by the factor of 2.70, the wavelength of the wave is also increased by a factor of 2.70. So,

`\lambda_2 = 235* 2.70 = 634.5 ~nm`

The magnetic field component can be written as

`\vec{B} = (E_(max))/(c)e^{i(\vec{k}\vec{z}-\omega t)}\^(z)`

The magnetic field is in the z-direction, because the E-field is directed towards +y and the wave is propagating in the +x-direction. The right-hand rule gives us the direction of the B-field.

`\vec{E} * \vec{B} = \vec{S}`

S is the Poynting vector which gives us the propagation of the wave.

We will use the following relationships

`k = 2\pi / \lambda\\f = \omega / 2\pi\\c = \lambda f = \lambda \omega / 2\pi\\\omega = 2\pi c/\lambda`

`\vec{B} = (7.7* 10^(-3))/(3* 10^8)e^{((2\pi)/(3* 10^8)z - (2\pi* 3* 10^8)/(634.5))}\\\vec{B} = 2.56*10^(-11) e^{(2.09*10^(-8)z - 2.96*10^(6)t)}\^(z)`