Propagation of Electromagnetic Waves in a Conducting Medium
In a conducting medium, such that the conductivity
Maxwell's equations become
and
By neglecting resonant or other effects we may use the linear approximations
and
where
and
are independent of time.
Maxwell's equations become
and
Taking the curl of the last of these gives
We have now the wave equation in a conducting medium:
Similarly
The last two equations are called the telegraph equations and incorporate damping terms
and
so electromagnetic waves travelling in a conducting medium experience attenuation proportianal too the conductance.
By assuming
and
are of complex exponential form
the last two of Maxwells equations above become
and
The first telegraph equation then becomes
which has the form of the Helmhotz equation
with
We may use the identity
to demonstrate the that the equations for conducting and non conducting media are the same if the dielectric constant
is replaced by a complex dielectric constant
Since we have replaced
by a complex equivalent, we must obtain a complex equivalent for the refractive index. This is done by writing
where k is a constant called the extinction coefficient.
We replace the propagation constant k by
Assuming that
is parallel to the
– axis, then
This wave is attenuated by the factor
