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

Step 1: Find direction of electric and magnetic field vector.
The given electromagnetic wave travels in vacuum along the z - direction. And we know for electromagnetic wave electric field vector, magnetic field vector and direction of wave propagation are mutually perpendicular to each other.
Therefore, electric field vector and magnetic field vector will be in x - y plane and they are mutually perpendicular.
Step 2: Calculate wavelength of the wave.
Formula used: $\lambda =\frac{c}{v}$
Given, Frequency of the wave,
$v=30\text{MHz}=30\times {10}^{6}Hz$
Wavelength of an electromagnetic wave, $\lambda =\frac{C}{v}$ Here, c = speed of light in vacuum $=3\times {10}^{8}m/s,\lambda =\frac{3\times {10}^8}{30\times {10}^6},\lambda =10m$
Final answer: Electric field vector and magnetic field vector will be in x - y plane and they are mutually perpendicular. Wavelength $\lambda =10m$