Related papers: Obtaining Maxwell's equations heuristically
The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic (EM) field, force, energy, and momentum, which are intimately tied together by Poynting's theorem and by the Lorentz force law.…
The expression for the electromagnetic field of a charge moving along an arbitrary trajectory is obtained in a direct, elegant, and Lorentz invariant manner without resorting to more complicated procedures such as differentiation of the…
We show that there exists a choice of gauge in which the electromagnetic 4-potential may be written as the difference of two 4-velocity vector fields describing the motion of a two-component space-filling relativistic fluid. Maxwell's…
We derive the relativistic velocity addition law, the transformations of electromagnetic fields and space-time intervals by examining the drift velocities in a crossed electromagnetic field configuration. The postulate of the light velocity…
Maxwell equations (Faraday and Ampere-Maxwell laws) can be presented as a three component equation in a way similar to the two component neutrino equation. However, in this case, the electric and magnetic Gauss's laws can not be derived…
Maxwell-Lorenz theory describes only vortex electromagnetic processes. Potential component of the magnetic field is usually excluded by the introduction of mathematical terms: Coulomb and Lorenz gauges. Proposed approach to the construction…
The unified field is a Maxwell-Lorentz field. Maxwell-Lorentz equations for potentials in standard four-dimensional form are satisfied exactly. This is achieved by involving new fundamental field sources, strict definition of which requires…
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…
The purpose of this article is twofold. On one hand, we rigorously derive the Newton--Maxwell equation in the Coulomb gauge from first principles of quantum electrodynamics in agreement with the formal Bohr's correspondence principle of…
Maxwell's equations describe the evolution of electromagnetic fields, together with constraints on the divergence of the magnetic and electric flux densities. These constraints correspond to fundamental physical laws: the nonexistence of…
A fundamental result of classical electromagnetism is that Maxwell's equations imply that electric charge is locally conserved. Here we show the converse: Local charge conservation implies the local existence of fields satisfying Maxwell's…
We present an alternative Eulerian hydrodynamic model for the electromagnetic field in which the discrete vector indices in Maxwell\s equations are replaced by continuous angular freedoms, and develop the corresponding Lagrangian picture in…
A mathematical derivation of Maxwell's equations for gravitation, based on a mathematical proof of Faraday's Law, is presented. The theory provides a linear, relativistic Lagrangian field theory of gravity in a weak field, and paves the way…
By exploiting suitably a fundamental theorem by Hilbert, we show that the equation of motion of the electric charges is a consequence of Maxwell field equations.
We discuss the theory of electromagnetic fields, with an emphasis on aspects relevant to radiofrequency systems in particle accelerators. We begin by reviewing Maxwell's equations and their physical significance. We show that in free space,…
It is shown that the field equations derived from an effective interaction hamiltonian for Maxwell and gravitational fields in the semiclassical approximation of loop quantum gravity using rotational invariant states (such as weave states)…
In accordance with an old suggestion of Asher Peres (1962), we consider the electromagnetic field as fundamental and the metric as a subsidiary field. In following up this thought, we formulate Maxwell's theory in a diffeomorphism invariant…
Maxwell's equations can be obtained in generalized coordinates by considering the electromagnetic field as an external agent. The work here presented shows how to obtain the electrodynamics for a charged particle in generalized coordinates…
We provide for the first time the exact solution of Maxwell's equations for a massless charged particle moving on a generic trajectory at the speed of light. In particular we furnish explicit expressions for the vector potential and the…
The Coulomb force, established in the rest frame of a source-charge $Q$, when transformed to a new frame moving with a velocity $\vec{V}$ has a form $\vec{F}= q\vec{{E}} + q\vec{v} \times \vec{{B}}$, where $\vec{{E}}=\vec{E}'_\parallel +…