Lorentz contraction and current-carrying wires

Abstract

The force between two parallel current-carrying wires is investigated in the rest frames of the ions and the electrons. A straightforward Lorentz transformation shows that what appears as a purely magnetostatic force in the ion frame appears as a combined magnetostatic and electrostatic force in the electron frame. The derivation makes use of a reasonably well-known problem of a charged particle moving parallel to a current-carrying wire, which is often used to illustrate that what appears as a purely electrostatic force in one frame appears as a purely magnetostatic force in another. This paper, aimed at undergraduate electromagnetism and special relativity courses, serves to dispel the notion that this makes either the electrostatic or the magnetostatic force redundant.