Question

In electromagnetic waves, the ratio of amplitudes of the electric field and the magnetic field is equal to

Answer 1

Electromagnetic Waves

1. Electromagnetic waves are types of transverse waves since their direction of vibration is perpendicular to their direction of propagation.
2. In an electromagnetic wave, there is a time-varying electric field and magnetic field.
3. The electric field, magnetic field, and direction of propagation are all mutually perpendicular to each other.
4. These electric fields and magnetic fields are mutually generated by both fields according to the principles of electromagnetic induction.
5. Therefore electromagnetic waves do not require a medium and can travel in a vacuum.
6. Light is a form of electromagnetic wave.

Ratio of Amplitudes

The amplitude of electric field is given as $\epsilon$ and the amplitude of magnetic field is given as $\mu$.

We can identify $\epsilon \mu$ as $\frac{1}{v^2}$ where $v$ is the speed of the wave.

$\therefore v=\frac{1}{\sqrt{\epsilon \mu }}$

For free space $\epsilon ={\epsilon }_0=8.854\times {10}^{-12}F/m$ and $\mu ={\mu }_0=4\mathrm{\pi }\times {10}^{-7}\mathrm{H}/\mathrm{m}$.

$\therefore v=c=\frac{1}{\sqrt{{\epsilon }_0{\mu }_0}}$

$\approx 3\times {10}^{8}m/s$

This agrees with the speed of light in free space.

Hence, in electromagnetic waves in free space, the ratio of amplitudes of the electric field and the magnetic field is equal to the speed of light.