# Electromagnetic waves

# Reflection on a metal

Take 10 minutes to prepare this exercise.

Then, if you lack ideas to begin, look at the given clue and start searching for the solution.

A detailed solution is then proposed to you.

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

A MPPW is normally sent to a perfectly conductor plane, located in the half-space . The space being vacuum.

The polarization of this wave is circular and the associated electric field can be written in real notation :

## Question

Determining the resultant wave structure in vacuum (for ).

### Hint

### Solution

The total electric field must be zero at the surface (for ), therefore the reflected electric field is :

The structure of the total electric field above metal is :

A standing wave is obtained.

The magnetic field is obtained with Maxwell-Faraday equation :

Where :

We can calculate Poynting vector and verify that its average value is zero : a standing wave does not transport energy.