Demystifying the Lorentz Force Equation

Abstract

The Lorentz force equation F = q(E + v × B), which has been used by the engineering community since the early 20th century to control the motion of electrons on free trajectories, in a wide range of technical applications, is a generalized equation that was originally developed by Hendrik Antoon Lorentz at the beginning of the 20th century, and which treats, in a single formulation, two very different aspects of the behavior of free-moving electrons. This article aims to put into perspective the historical context in which the equation was developed, and to clarify how its two different aspects can be clearly separated for practical computational purposes and used in fundamental research in physics, to help reconcile classical/relativistic mechanics and quantum mechanics with electromagnetism, and in particular how its first term can be related to gravitation while its second term can be related to measurable mass from the electromagnetic perspective.