Near the qualitative behavior depends upon whether or not there is a ``resonance'' there. If there is, then can begin with a complex component that attenuates the propagation of EM energy in a (nearly static) applied electric field. This (as we shall see) accurately describes conduction and resistance. If there isn't, then is nearly all real and the material is a dielectric insulator.
Suppose there are both ``free'' electrons (counted by ) that are
``resonant'' at zero frequency, and ``bound'' electrons (counted by
). Then if we start out with:
We can understand this from
If we assume a harmonic time dependence and a ``normal'' dielectric
constant , we get:
On the other hand, we can instead set the static current to zero
and consider all ``currents'' present to be the result of the
to the field
. In this case:
Equating the two latter terms in the brackets and simplifying, we
obtain the following relation for the conductivity:
We conclude that the distinction between dielectrics and conductors is a matter of perspective away from the purely static case. Away from the static case, ``conductivity'' is simply a feature of resonant amplitudes. It is a matter of taste whether a description is better made in terms of dielectric constants and conductivity or complex dielectric.