Charges and fields in a current-carrying wire

TL;DR

This paper examines the charge distribution and electromagnetic fields in a current-carrying wire from different reference frames, demonstrating the consistency of classical electromagnetism with Special Relativity and exploring implications of charge neutrality assumptions.

Contribution

It provides a detailed analysis of charge and field configurations in a current-carrying wire considering relativistic effects and the self-induced pinch, highlighting the mutual consistency of electromagnetism and relativity.

Findings

Charge neutrality in the lattice frame leads to specific charge distributions in the electrons frame.

The analysis confirms the compatibility of classical electromagnetism with Special Relativity.

Implications of assuming zero net charge per unit length in the electrons frame are discussed.

Abstract

Charges and fields in a straight, infinite, cylindrical wire carrying a steady current are determined in the rest frames of ions and electrons, starting from the standard assumption that the net charge per unit length is zero in the lattice frame and taking into account a self-induced pinch effect. The analysis presented illustrates the mutual consistency of classical electromagnetism and Special Relativity. Some consequences of the assumption that the net charge per unit length is zero in the electrons frame are also briefly discussed.