Question

A plane electromagnetic wave travels in vacuum along $z$-direction. What can you say about the directions of its electric and magnetic field vectors? If the frequency of the wave is $30{\text{ }}MHz$, what is its wavelength?

Answer 1

Hint:Here it is given that an electromagnetic wave travels in the $z$ direction of the axis. It is known that the wave does not travel either in the direction of electric field or magnetic field. In the next part of the question we have to find the wavelength of the wave by using the formula of wavelength and its relation with frequency.

Complete step by step answer:
When a wave travels along any direction, then the respective electric field and magnetic field vector lie on the plane which is perpendicular to the direction of propagation of the wave. The magnetic field vector and the electric field vector are also perpendicular to each other.Hence the propagation of waves, the electric field and magnetic field lie mutually perpendicular to each other.

Now, in the given question the propagation of waves is in the $z$-direction. As, the electric, magnetic field vectors and propagation is mutually perpendicular so the magnetic field vectors and electric field vectors lie on the $XY$ plane.The frequency of the wave is given as $f = 30{\text{ }}MHz$. For electromagnetic waves wavelength is,
$\lambda = \dfrac{c}{f}$
where $c$ is the speed of wave in vacuum.
Substituting the values we get,
$\lambda = \dfrac{{3 \times {{10}^8}}}{{30 \times {{10}^6}}} \\
\therefore \lambda= 10{\text{ }}m$

So, the wavelength of the wave is $10{\text{ }}m$.

Note:It must be noted that the speed of an electromagnetic wave is equal to the speed of light in vacuum. The phase difference between the two waves is zero. The energy produced from the wave is equal to both electric field and magnetic field. The electromagnetic wave does not require any material medium for its propagation.