On the possibility of a relativistic correction to the E and B fields around a current-carrying wire

TL;DR

This paper explores a potential relativistic correction to the electric and magnetic fields around a current-carrying wire, proposing an alternative approach that predicts a small electric field in the wire's rest frame, which could be experimentally tested.

Contribution

It introduces an alternative theoretical framework for describing fields around a current-carrying wire, predicting a minute charge and electric field in the wire's rest frame.

Findings

An alternative relativistic approach predicts a small electric field in the wire's rest frame.

Experimental sensitivities of cold ions may detect differences between approaches.

The study challenges the standard assumptions about fields in the wire's rest frame.

Abstract

It is well known that electric and magnetic fields may change when they are observed from different frames of reference. For example, the motion of a charged probe particle moving parallel to a current-carrying wire would be described by utilizing different electric or magnetic fields, depending on from which frame of reference the system is observed and described. To describe the situation in all frames by utilizing the theory of relativity, one has to first describe the situation in one particular frame, and this choice in the case of a current-carrying wire is the topic of this paper. In this study I examine an alternative to the standard choice, and consider its theoretical and experimental validity. An outcome of the alternative approach is that in the rest frame of a wire, running a current introduces also an electric field by giving rise to a minute charge. Present day experimental sensitivities, specifically those of cold ions, may be able to differentiate between the observable signatures predicted by the different approaches.