Magnetism from relativity: the force on a charge moving perpendicularly to a current-carrying wire

Abstract

We deduce the magnetic field produced by an infinite wire on a charge particle q that moves with velocity in a direction perpendicular to that of the wire. The wire carries an electric current I. We calculate the Lorentz force on the particle in the reference frame that travels with the particle; we then go back to the laboratory reference frame and determine the magnetic field.

The Electric Origin of Magnetic Forces Theory: General Framework

“…By adding the cross product of the unit vectors, the final formula for the force affecting the destination element due to the existence of the source element is shown in equation (9).…”

“…For the destination element, the interaction of the positive charge with the crossing discontinuity units is shown in figure (9). At t − i , the positive charge interacts electrically with the discontinuity charges surrounding it.…”

“…Four attempts were found either to tie the laws of magnetism and electricity or to explain the magnetic force as purely electric: (1) Maxwell's equations and the electromagnetic field tensor [3], [35], (2) Lorentz length contraction approach [2], [8], [9], [36], (3) retarded action approach [12], and (4) the electric origin of magnetic force theory [10].…”

“…The Lorentz length contraction approach describes the magnetic force as a natural consequence of special relativity and purely electrostatic forces [2], [8], [9], [36]. This approach considers infinite parallel current-wires only.…”

“…Since then, electricity and magnetism have been treated more and more as different aspects of the same subject [4]- [7]. An early attempt to explore the origin of the magnetic force used relativity and Lorentz contraction to explain the magnetic force as an electric one between long wires carrying currents [2], [8], [9]. This explanation suffers from major problems [10] and the magnetic force is proved to not be a relativistic effect [11].…”