2008/04/29 by F. Rohrlich, Fritz Rohrlich · 2 citations
Physics and Astronomy · #Charge (physics) #Charged particle #Classical mechanics #Coulomb #Coulomb's law #Differential equation #Electron #Equations of motion #Lorentz force #Lorentz transformation #Magnetic field #Particle (ecology) #Physics #Point particle #Quantum Mechanics and Applications #Quantum and Classical Electrodynamics #Quantum electrodynamics #Quantum mechanics #Relativity and Gravitational Theory #physics.class-ph
paper · pdf · doi:10.1103/physreve.77.046609
11 pages
arxiv created 2008/04/29 · openalex publication_date 2008/04/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Using physical arguments, I derive the physically correct equations of motion for a classical charged particle from the Lorentz-Abraham-Dirac equations (LAD) which are well known to be physically incorrect. Since a charged particle can classically not be a point particle because of the Coulomb field divergence, my derivation allows for that by imposing a basic condition on the external force. That condition ensures that the particle's finite size charge distribution appears as a point charge to the external force. Finite radius charge distributions are known not to lead to differential equations of motion. The present work is in agreement with the results by [H. Spohn, Europhys. Lett. 50, 287 (2000)] and by others. An example, uniform acceleration, demonstrates what the above basic condition entails. For clarity of the argument, I discuss the nonrelativistic case before the relativistic one.