Chapter 34: Electromagnetic Waves
Learning Goals
- Understand the accomplishments of Maxwell and Hertz.
- Be able to state Maxwell's equations.
- Understand the properties of electromagnetic waves.
- Understand Poynting's vector.
- Understand the electromagnetic spectrum.
Electromagnetic Waves
Maxwell’s equations may be manipulated to produce three-dimensional
wave equations for electric and magnetic fields. The solutions to
these equations are called electromagnetic waves. They have
the following properties:
- Electromagnetic waves travel through vacuum with the
speed of light:
- Electromagnetic waves are transverse waves with
E ^
B ^
direction of propagation.
- E and B oscillate in phase, with E/B = c
at all times for which the fields are nonzero.
- Electromagnetic waves carry energy in the direction of
propagation. The Poynting vector S has magnitude
equal to the rate of energy flow through a unit area and
direction equal to the direction of propagation:
- Electromagnetic waves carry momentum and hence
can exert a radiation pressure. If the surface is
perfectly absorbing, P = S/c. Reflective surfaces give
P = 2S/c.
Harmonic Electromagnetic Waves
Harmonic electromagnetic waves have field components given by
where w
is the angular frequency, k is the angular wave number and where
the above wave propagates in the +x direction. The parameters
w and k are related to c by
Intensity
The average value of the Poynting vector is called the
intensity:
