Electromagnetic waves
To test the understanding of the lesson
Question
A continuous laser emits in a monochromatic light beam of cross section and wavelength .
Find the numerical values of the amplitude of the electric and magnetic fields of the Laser.
Determine the number of photons per unit volume within the beam.
Hint
Solution

Power is the flux of the Poynting vector :
.
We can deduce .
The magnetic field is then given by :

The conservation of energy gives :
Where is the Planck constant and the frequency, which is .
Finally :
Question
Give the definition of a perfect conductor.
Hint
Solution
The conductivity of a perfect conductor is considered infinite.
The electric and magnetic fields are zero inside a perfect conductor.
The skin thickness is assumed to be null.
Question
Give the expression of the d'Alembert equation for a vibratory phenomenon whose wave velocity is .
Hint
Solution
The d'Alembert's equation is, for example for the propagation of an electric field in a vacuum :
With :
Question
For a standing wave, defined nodes and antinodes.
What is the distance between two successive antinodes (two nodes) ?
What is the distance between a successive antinode and a node ?
Hint
Solution

The standing wave (with ) :
The nodes are the points where the amplitude .
The antinodes are the points where the amplitude .
The distance between two successive antinodes (two nodes) equals to , with
The distance between a successive antinode and a node is .
Question
For an electromagnetic MPPW, give the relation of "structure" of the wave, that is to say the vector relationship between the vectors , and (wave vector).
Hint
Solution
The relation of structure for a plane wave :
If the wave propagates in the direction (Oz) at the speed :
Question
What is the speed of propagation of a MPPW in a medium of index ?
Hint
Solution
The velocity of the propagation of a MPPW in a medium of index is :