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

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.