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Chapter 22
LECTURE NOTES
ELECTROMAGNETIC WAVES
Around the time of the American Civil War, Maxwell was able to unify all electric and magnetic
phenomena known at the time in a compact set of four equations. Though expressed in the
language of vector calculus, we will give the essence of the equations below.
Maxwell found his equations predicted that electromagnetic waves would propagate through
space at the speed of light. This led to the identification of light as merely one type of
electromagnetic radiation. Hertz produced and detected EM waves of other frequencies and the
world was on the way to the wonders of radio and television.
Maxwell’s Equations
1.
Gauss’ law for electricity is a generalized version of Coulomb’s law. It relates the electric
flux through any surface to the net charge enclosed by the surface.
2.
Gauss’ law for magnetism states the magnetic flux through any closed surface is zero.
This implies there are no magnetic monopoles (analogs to isolated electric charges).
3.
Faraday’s law states a changing magnetic flux produces an electric field.
4.
Ampere’s law as extended by Maxwell states magnetic fields are produced by electric
currents and changing electric fields.
Electromagnetic (EM) Waves
A changing electric field produces a B that produces E that . . . In this way a wave of
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perpendicular E and B fields propagates through space with velocity v =
which is the
 0 0
same as the speed of light in vacuum (3 x 108 m/s).
B and E are⊥ to each other and the direction of wave travel so an EM wave is a transverse wave.
It is a wave not of matter but of fields that contain energy and carry momentum but are
insubstantial.
ε0
B2
The energy density of an EM wave is u =  0 E =
. The E and B fields each
=
μ0
μ0
2
cB 2 EB
contribute half of the energy density. We define the Poynting vector S =  0 cE =
as
=
μ0
μ0
the rate at which energy is transported by EM waves through a surface in units of W/m2. The
direction of S is the direction of wave travel.
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All EM waves follow the relation v = f λ and since v = the speed of light = c, we have c = f λ.
Visible light has λ = 400 to 750nm. The full range of frequencies for EM waves constitutes the
EM spectrum.
It is difficult to measure a speed as great as 3 x 108 m/s. Michelson made accurate measurements
a century ago and found the speed is constant, regardless of the motion of the source. We return
to this point in chapter 26 on relativity.
Marconi began to send and receive radio waves in the 1890’s. AM radio stations moderate the
amplitude of a carrier radio frequency wave with the audio signal while FM stations modulate
the frequency. Listening to a station like 101.9 on the FM dial means you are receiving waves of
frequency 101.9MHz or 101.9 x 106Hz. Traveling at speed c = 3 x 108 m/s, the wavelength λ =
2.94m for these waves.
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