Inertial effects on good conductors: Resistive heating and magnetic diffusion

Inertial effects of charge carriers, on the resistive heating and magnetic diffusion, are explored in good conductors. The influence of inertia is described by introducing a finite relaxation time for the current density, in the framework of an extended Ohm’s law. Due to inertial effects at high frequencies, it is found that the propagation constant vanishes and the attenuation coefficient tends to a finite value, which does not depend on the angular frequency and is fully determined by the relaxation time. Accordingly, it is shown that the total intensity of the resistive heating approaches an asymptotic value. An extension for the diffusion equation is obtained and its general solution is expressed by the introduction of a finite cutoff in the upper limit for the integral of the decaying modes. Such a cutoff precludes the unphysical contribution of modes, decaying faster than the inverse relaxation time, to the computation of the total magnetic field. It is argued that inertial effects on magnetic diffusion should be important at the nano scale.