Trouble with the Drude theory of metallic conduction: Incompatibility with special relativity

TL;DR

This paper demonstrates that the classical Drude model conflicts with special relativity and clarifies the existence of second order electric fields around conductors, aligning experimental observations with Maxwell's theory.

Contribution

It identifies the inconsistency of the Drude model with relativity and explains the origin of second order electric fields near conductors within Maxwell's framework.

Findings

Second order electric fields are produced near current-carrying conductors.

Experimental measurements of electric fields match theoretical predictions.

The Drude model's incompatibility with relativity is highlighted.

Abstract

In this paper, we show that the classical Drude model of electrical conductivity, one of the fundamental models in the theory of electrical conductivity, is inconsistent with the special relativity. Due to this incorrect model, a current carrying closed circuit is thought not to produce second order electric field according to Maxwell's theory of electromagnetism. But, Edwards et al. detected a small second order electric field radially pointing toward a current carrying conductor in a superconducting Nb-Ti coil. Assis et al. claim to show that Maxwell's theory does not predict any second order forces and hence we should take Weber's electrodynamics seriously. But, we show that not only a magnetic field, but also a second order electric field is produced in the vicinity of a current carrying conductor, which is consistent with Maxwell's theory. This electric field points radially toward the current carrying conductor as detected in Edwards' experiments. We also show that the positive field, detected by Sansbury in a U-shaped copper conductor carrying a constant current, should be created as a consequence of our theory. We then estimate the order of the strength of this electric field and show that it is in agreement with the experimental values.