Chapter 11

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 anti-nodes.

  • What is the distance between two successive anti-nodes (two nodes) ?

  • What is the distance between a successive anti-node and a node ?

Hint

Solution

  • The standing wave (with ) :

    The nodes are the points where the amplitude .

    The anti-nodes are the points where the amplitude .

  • The distance between two successive anti-nodes (two nodes) equals to , with

  • The distance between a successive anti-node 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 :

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