Related papers: On the Darwin Lagrangian
We study the dynamics of N charges interacting with the Maxwell field. If their initial velocities are small compared to the velocity of light, c, then in lowest order their motion is governed by the static Coulomb Lagrangian. We…
The Bohr-van Leeuwen theorem is often summarized as saying that there is no classical magnetic susceptibility, in particular no diamagnetism. This is seriously misleading. The theorem assumes position dependent interactions but this is not…
The formulation of a complete theory of classical electromagnetism by Maxwell is one of the milestones of science. The capacity of many-body systems to provide emergent mini-universes with vacua quite distinct from the one we inhabit was…
In the present work foundations of the law of the energy conservation and the introduction of particles in the classical electrodynamics are discussed. We pay attention to a logic error which takes place at an interpretation of the…
A generalization of the classical electrodynamics for systems in absolute motion is presented using a possible alternative to the Lorentz transformation. The main hypothesis assumed in this work are: a) The inertial transformations relate…
In this paper it is proved that, contrary to the results found by A.E. Chubykalo and S.J. Vlaev (Int. J. Mod. Phys. A 14, 3789 (1999)), the retarded electric and magnetic fields for an uniformly accelerated charge exactly satisfy Maxwell…
The manipulation of individual charged particles has been deeply explored in physics's theoretical and experimental domains during the past decades. It is the pillar of several existing devices used for metrology and sensing and is a…
The Lorentz symmetry group entails physical equations whose solutions are retarded. This leads to the concept of a relativistic engine resulting from retardation of electromagnetic fields. We have shown that Newton'n third law cannot…
We considered the electromagnetic field of a charge moving with a constant acceleration along an axis. We found that this field obtained from the Li\'enard-Wiechert potentials does not satisfy Maxwell equations if one considers exclusively…
We report on some recent work of the authors showing the relations between singular (point) perturbation of the Laplacian and the dynamical system describing a charged point particle interacting with the self-generated radiation field (the…
The axiomatic structure of the electromagnetic theory is outlined. We will base classical electrodynamics on (1) electric charge conservation, (2) the Lorentz force, (3) magnetic flux conservation, and (4) on the Maxwell-Lorentz spacetime…
In the present work, we study the classical behavior of an electric dipole in presence of an external uniform magnetic field. We derive equations and constants of motion from the Lagrangian formulation. We obtain an infinitely periodic…
We describe a seemingly unnoticed feature of the text-book Maxwell-Lorentz system of classical electrodynamics which challenges its formulation in terms of an initial value problem. For point-charges, even after appropriate renormalization,…
Starting from delay equations that model field retardation effects, we study the origin of runaway modes that appear in the solutions of the classical equations of motion involving the radiation reaction force. When retardation effects are…
We present equations of motion for charged particles using balanced equations, and without introducing explicitly divergent quantities. This derivation contains as particular cases some well known equations of motion, as the Lorentz-Dirac…
A detailed study is made of the space-time transformation properties of intercharge forces and the associated electric and magnetic force fields, both in classical electrodynamics and in a recently developed relativistic classical…
The Lagrangian and Hamiltonian formulations of electromagnetism are reviewed and the Maxwell equations are obtained from the Hamiltonian for a system of many electric charges. It is shown that three of the equations which were obtained from…
The exact closed equation of motion for microscopic distribution function of classical many-body system with account of interactions retardation between particles is derived. It is shown that interactions retardation leads to irreversible…
It is proposed a Lagrangian for the quasi-rigid extended charged particle, which consists of a bare point particle term plus the standard electromagnetic minimal coupling. The quasi-rigid motion is imposed as a constraint. The extension of…
A thoughtless treatment of Maxwell's equations can lead to the interpretation of the existence of a causal relationship between their different terms and, therefore, that an electric field that varies in time generates a magnetic one and…