The Relativistic Equations of Motion for a Charged Particle in the Magnetic Field of an Infinite Current-Carrying Wire

Abstract

We show how to produce the closed form solution for the motion of a charged particle in the magnetic field of an infinitely long, current-carrying wire in the relativistic range, thus extending the results produced recently (Asadi-Zeydabadi, M., & Zaidins, C. S., 2019). We outline the areas where the two solutions are similar aa well as where the two solutions are slightly different. We also extend the work in (Asadi-Zeydabadi, M., & Zaidins, C. S., 2019) to the more realistic case where the current generates both a magnetic and an electric field, as is the case in real life. We plan to extend the approach in the future to more complicated cases as the one of the finite length wire. The solution is of great interest for the design of particle accelerators, hence it is interesting for both theoretical physicists and engineers alike.