Page 240 - Electromagnetics

4.6.4 Permittivity and conductivity of a conductor
The free electrons within a conductor may be considered as an electron gas which is
free to move under the influence of an applied field. Since the electrons are not bound to
the atoms of the conductor, there is no restoring force acting on them. However, there
is a damping term associated with electron collisions. We therefore model a conductor
as a plasma, but with a very high collision frequency; in a good metallic conductor ν is
13
typically in the range 10 –10 14 Hz.
We therefore have the conductivity of a conductor from (4.75) as
2
0 ω ν
p
˜ σ(ω) =
2
ω + ν 2
and the permittivity as
2
ω
p
˜ (ω) = 0 1 − .
2
ω + ν 2
Since ν is so large, the conductivity is approximately
0 ω 2 p Nq 2
˜ σ(ω) ≈ = e
ν m e ν
and the permittivity is

˜ (ω) ≈ 0
well past microwave frequencies and into the infrared. Hence the dc conductivity is often
employed by engineers throughout the communications bands. When approaching the
visible spectrum the permittivity and conductivity begin to show a strong frequency
dependence. In the violet and ultraviolet frequency ranges the free-charge conductivity
becomes proportional to 1/ω and is driven toward zero. However, at these frequencies the
resonances of the bound electrons of the metal become important and the permittivity
behaves more like that of a dielectric. At these frequencies the permittivity is best
described using the resonance formula (4.104).

4.6.5 Permeability dyadic of a ferrite
The magnetic properties of materials are complicated and diverse. The formation
of accurate models based on atomic behavior requires an understanding of quantum
mechanics, but simple models may be constructed using classical mechanics along with
very simple quantum-mechanical assumptions, such as the existence of a spin moment.
For an excellent review of the magnetic properties of materials, see Elliott [65].
The magnetic properties of matter ultimately result from atomic currents. In our sim-
ple microscopic view these currents arise from the spin and orbital motion of negatively
charged electrons. These atomic currents potentially give each atom a magnetic moment
m.In diamagnetic materials the orbital and spin moments cancel unless the material is
exposed to an external magnetic field, in which case the orbital electron velocity changes
to produce a net moment opposite the applied field. In paramagnetic materials the spin
moments are greater than the orbital moments, leaving the atoms with a net permanent
magnetic moment. When exposed to an external magnetic field, these moments align in
the same direction as an applied field. In either case, the density of magnetic moments
M is zero in the absence of an applied field.

© 2001 by CRC Press LLC