Related papers: Obtaining Maxwell's equations heuristically
The classical theory of electrodynamics cannot explain the existence and structure of electric and magnetic dipoles, yet it incorporates such dipoles into its fundamental equations, simply by postulating their existence and properties, just…
This communication is devoted to a brief historical framework and to a comprehensive critical discussion concerning foundational issues of Electrodynamics. Attention is especially focused on the events which, about the end of XIX century,…
After having identified all the possible relationships between the electric field and the magnetic field in a given inertial reference frame we derive the transformation equations for the components of these fields. Special relativity is…
A connection between Maxwell's equations, Newton's laws, and the special theory of relativity is established with a derivation that begins with Newton's verbal enunciation of his first two laws. Derived equations are required to be…
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,…
We combine Maxwell's equations with Eulers's equation, related to a velocity field of an immaterial fluid, where the density of mass is replaced by a charge density. We come out with a differential system able to describe a relevant…
In a brief but brilliant derivation that can be found in Maxwell's Treatise and traced back to his 1861 and 1865 papers, he derives the force on a moving electric charge subject to electromagnetic fields from his mathematical expression of…
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…
Uniqueness results are established for time-independent finite-energy electromagnetic fields which solve the nonlinear Maxwell--Born--Infeld equations in boundary-free space under the condition that either the charge or current density…
Maxwell's four differential equations describing electromagnetism are amongst the most famous equations in science. Feynman said that they provide four of the seven fundamental laws of classical physics. In this paper, we derive Maxwell's…
We show explicitly that the Hertz-form Maxwell's equations and their extensions can be obtained from the non-relativistic expansion of Lorentz transformation of Maxwell's equations. The explicit expression for the parameter $\alpha$ in the…
The concept of electromagnetic field can be neatly formulated by recognizing that the simplest form of the four-force is indeed feasible. We show that Maxwell's equations almost entirely stem from the properties of spacetime, notably from…
By describing the dynamical evolution of a test charged particle in the presence of an electromagnetic field as a succession of infinitesimal Lorentz boosts and rotations it is possible to obtain the Lorentz Force of Electrodynamics. A…
It is now widely accepted that the Maxwell equations of Electrodynamics constitute a self-consistent set of four independent partial differential equations. According to a certain school of thought, however, half of these equations -…
We have derived energy conservation equations from the quaternionic Newton's law that is compatible with Lorentz transformation. This Newton's law yields directly the Euler equation and other equations governing the fluid motion. With this…
In 19th century Maxwell derived Maxwell equations from the knowledge of three experimental physical laws: the Coulomb's law, the Ampere's force law and Faraday's law of induction. However, theoretical basis for Ampere's force law and…
Maxwell's equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero…
Classical Electrodynamics is not a consistent theory because of its field inadequate behaviour in the vicinity of their sources. Its problems with the electron equation of motion and with non-integrable singularity of the electron self…
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…
We show that Maxwell's electromagnetism can be mapped into the Born-Infeld theory in a curved space-time, which depends only on the electromagnetic field in a specific way. This map is valid for any value of the two lorentz invariants $F$…