The Electric Force Between Two Straight Parallel Resistive Wires Carrying DC-Currents in the Asymptotic Limit of Infinitely Thin Wires

TL;DR

This paper investigates the electric force between two resistive wires carrying DC currents, revealing that electric forces can dominate magnetic forces in the asymptotic limit of very thin or long wires, which is not accessible by numerical methods.

Contribution

It provides an analytical analysis of electric versus magnetic forces between resistive wires, highlighting the dominance of electric forces in certain asymptotic limits.

Findings

Electric force can dominate magnetic force in very thin or long resistive wires.

The ratio of electric to magnetic forces depends on the ground node choice.

The analysis extends understanding beyond numerical methods in the asymptotic limit.

Abstract

During the years 1948-2019 the ampere was defined via the magnetic force between two long thin parallel wires carrying stationary current. However, if a stationary current flows through a resistive wire, static electric charges appear on the surface of the wire, and this will lead to an additional electric force between the wires. This article discusses the ratio of electric over magnetic forces in the asymptotic limit of infinitely thin wires, which is not accessible by numerical methods. The electric force between the two wires depends also on the choice of the common ground node. For extremely thin or extremely long resistive wires the electric force dominates over the magnetic one.