Chapter 11

Electromagnetic waves

Electromagnetic wave in vacuum

Spend 10 minutes to prepare for this exercise.

Then, if you run out of ideas for starting, see the supplied index and start searching.

A detailed solution is then proposed.

If you have further questions, feel free to ask them on the forum.

The electromagnetic wave in a vacuum is studied :

Question

Is the corresponding wave plane ? Progressive ? Harmonic ? To justify.

What does it remind you of ?

Hint

Solution

It is not plane, but progressive and harmonic.

It is a wave that may be encountered in a waveguide.

Question

Calculate the magnetic field.

Hint

Solution

We can't use the relationship of structure because the wave is not a plane wave.

We calculate the magnetic field from the Maxwell-Faraday equation :

We find :

Question

Is there any dispersion ?

Hint

Solution

Determining the dispersion relation.

For this, we use the wave equation of the electric field in vacuum (d'Alembert's equation) :

We find :

There is dispersion with a phase velocity that is : (we assume )

Previous
Electromagnetic waves in vacuum
Next
Speed of propagation of energy