Take the tour ×  Is it possible to derive Ohm's law (perhaps in
some appropriate limit) from Maxwell's Equations?  share|improve
this question For a simple theory behind Ohm's law, see e.g. the
Drude model at Wikipedia or this Phys.SE post. –  Qmechanic Oct
16 '12 at 0:09 add comment  2 Answers  up vote 5 down vote
accepted  Ohm's law $\vec\jmath=\sigma\vec{E}$ can be derived
rigorously in the limit of small electric fields using linear
response theory. This leads to Kubo's formula for the electric
conductivity, which relates $\sigma$ to the zero frequency limit
of the retarded current-current correlation function.  $$ \sigma
^{\alpha\beta}(q)=\lim_{\omega\to0}\frac{1}{-
i\omega}\left\{\frac{ne^2}{m}\delta^{\alpha\beta} -
i\langle[j^\alpha(\omega,q),j^\beta(-\omega,-q)]\rangle \right\}
$$  (This derivation, of course, involves more than just
Maxwell's equation. This is properly derived in the context of
non-equilibrium field theory.) The Drude model is a model for
the spectral function of the current-current co