Chapter 11

Electromagnetic wave in vacuum

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The electromagnetic wave in a vacuum is studied :

Question

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

What does it remind you of ?

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.

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 ?

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 )

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Electromagnetic waves in vacuum
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Speed of propagation of energy