Related papers: Introducing Time Dependence into the Static Maxwel…
We argue that the classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the…
We consider for the time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic measurements of the…
We present an introduction to the study of a relativistic particle moving under the influence of its own Frenet-Serret curvatures. With the aim of introducing the notation and conventions used in this paper, we first recall the action of a…
The Displacement Current is a peculiar aspect of Maxwell's equation created by theoretical necessity only to be later validated through experimentation. We analyze the properties of the Displacement Current in the static condition of…
We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo…
Gill and Zachary's proper-time reformulation of Maxwell's equations introduces a source-dependent speed b = sqrt(c^2 + u^2), distinct from standard electrodynamics. This study applies Lie symmetry analysis to the resulting wave equations,…
The structure of electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potential is defined uniquely. Therefore, the approach where Maxwell…
The problem of determining the electromagnetic and gravitational ``self-force'' on a particle in a curved spacetime is investigated using an axiomatic approach. In the electromagnetic case, our key postulate is a ``comparison axiom'', which…
The recoil optical force and torque acting on an electromagnetic dipole are typically derived by computing the imbalance in radiated linear and angular electromagnetic momentum coming from the source, using Maxwell stress tensor…
We provide sufficient conditions for the existence of periodic solutions of the of the Lorentz force equation, which models the motion of a charged particle under the action of an electromagnetic fields. The basic assumptions cover relevant…
By fixing a reference frame in spacetime, it is possible to split the Euler-Lagrange equations associated with a degenerate Lagrangian into purely evolutionary equations and constraints on the allowed Cauchy data with respect to the notion…
The problem of unification of Gravitation and Electromagnetism in four dimensions; some new ideas involving mixtures of commuting and anti-commuting co-ordinates. Maxwell's equations are extracted in terms of the curvature of the…
Using test-particle simulations, we investigate the temporal dependence of the two-point velocity correlation function for charged particles scattering in a time-independent spatially fluctuating magnetic field derived from a…
A mathematical proof is given that Maxwell's equations are an {\it artifact} of Hodge theory together with the laws of Gauss and Amp\`ere, taken as axioms. They are thus geometric in nature, independent of any specific physical mechanisms,…
Although standard quantum mechanics has some non-local features, the probability current of the Schr\"odinger equation is locally conserved, and this allows minimal electromagnetic coupling. For some important extensions of the…
We consider the motion of small bodies in general relativity. The key result captures a sense in which such bodies follow timelike geodesics (or, in the case of charged bodies, Lorentz-force curves). This result clarifies the relationship…
The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic field, force, energy, and momentum, which are intimately tied together by Poynting's theorem and the Lorentz force law. Whereas…
Considerations on the complementary time-dependent coordinate transformations emboding Lorentz transformation (LT) show that the relativistic energy-momentum relationship, implicitly the relativistic mass and energy, do not depend on the…
Formulae relating one and the same force in two inertial frames of reference are derived directly from the Lorentz transformation of space and time coordinates and relativistic equation for the dynamic law of motion in three dimensions. We…
We consider quantum gravitational corrections to Maxwell's equations on flat space background. Although the vacuum polarization is highly gauge dependent, we explicitly show that this gauge dependence is canceled by contributions from the…