Question

A plane electromagnetic wave, with wavelength 6 m, travels in vacuum in the positive x direction with its electric vector E, of amplitude 214.6 V/M, directed along y axis. What is the frequency f of the wave? 250 MHz 100 MHz 50 MHz 105 MHz 25 MHz [2 points] (b) A plane electromagnetic wave, with wavelength 6 m, travels in vacuum in the positive x direction with its electric vector E, of amplitude 214.6 V/M, directed along y axis. What is the direction of the magnetic field associated with the wave? (i,j,k are the unit vectors corresponding to x, y and z directions) -j

Answer 1

a) For an EM wave traveling in a vacuum, this equation holds true:

c = fλ

c is the speed of light in a vacuum, f is the frequency, and λ is the wavelength.

Given values:

c = 3×10⁸m/s

λ = 6m

Plug in the values and solve for f:

3×10⁸ = f(6)

f = 50MHz

b) The direction of an EM wave's Poynting vector determines the direction of the wave's propagation.

S = 1/μ₀(E×B)

S is the Poynting vector, μ₀ is the magnetic constant, E is the electric field vector, and B is the magnetic field vector. Note that we are taking the cross product between E and B, not taking the product of two scalar quantities.

Since S depends on the cross product of E and B, you may use the right hand rule in the following way to determine the direction of B:

1. The EM wave travels in the +x direction, therefore S points in the +x direction. Face your palm in the +x direction.
2. E points along the y axis. Let us arbitrarily choose +y. Point your thumb in the +y direction.
3. This will constrain your other fingers to point in the +z direction. If you point your thumb in the -y direction then your fingers will point in the -z direction.

You can conclude that B must point along the z axis, so you can represent B with the k unit vector.