Lorentz Force from a Current-Carrying Wire on a Charge in Motion under the Assumption of Neutrality in the Symmetrical Frame of Reference

Abstract

It is commonly assumed that a wire conducting an electric current is neutralin the laboratory frame of reference (the rest frame of the lattice of positiveions). Some authors consider that the wire is neutral only in a symmetricalframe of reference, in which the velocities of electrons and protons have equalnorm and opposite direction. In this paper, we discuss the Lorentz transfor- mation between different frames of reference in the context of the specialtheory of relativity for a current-carrying conducting wire and a probe chargein motion with respect to the wire. A simple derivation of the Lorentz force inthe laboratory frame of reference for the assumed neutrality in a symmetricalframe of reference is presented. We show that the Lorentz force calculatedassuming neutrality in the symmetrical frame of reference and the one as-suming neutrality in the laboratory frame of reference differ by a term cor-responding to a change in the test charge speed of one half the drift velocityof the electrons. (PDF) Lorentz Force from a Current-Carrying Wire on a Charge in Motion under the Assumption of Neutrality in the Symmetrical Frame of Reference. Available from: https://www.researchgate.net/publication/329908876 _Lorentz_Force_from_a_Current- Carrying_Wire_on_a_Charge_in_Motion_under_the_Assu mption_of_Neutrality_in_the_Symmetrical_Frame_of_R eference [accessed Jan 19 2023].

Antonio Šunjerga

Assistant Professor | Department of Electrical Engineering Fundamentals

Researcher and assistant professor at the Faculty of Electrical Engineering, Mechanical Engineering, and Naval Architecture in Split, with research interests that include lightning physics, lightning protection, and electromagnetic compatibility.