相关论文: Some Variations on Maxwell's Equations

The Maxwell-Lorentz theory of electrodynamics cannot readily be applied to a system of point charges: the electromagnetic field is not well-defined at the position of a point charge, an energy conservation argument is not obvious, an…

Maxwell's equations are modified to incorporate a scalar field to account for the London's superconductivity. Assuming the electromagnetic field is described by the Klein-Gordon equation, London's equations of superconductivity are then…

The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…

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,…

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 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 foundation of a…

While the electromagnetic force is microscopically simply the Lorentz force, its macroscopic form is more complicated, and given by expressions such as the Maxwell stress tensor and the Kelvin force. Their derivation is fairly opaque, at…

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…

In this note, we propose an exegesis of the Maxwell equations for electromagnetism. We begin with an analogy between the homogeneous Maxwell equations and the equations needed to describe the vorticity field of an incompressible inviscid…

In the recent work~\cite{Wang:2021p2}, the author proposed the expanded Maxwell's equations for moving charged media system, which seems subtle. Considering a very short time, we can approximately define the inertial frame of reference. If…

We begin by reviewing the derivation of generalized Maxwell equations from an operational definition of the electromagnetic field and the most basic notions of what constitutes a dynamical field theory. These equations encompass the…

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…

A general law for electromagnetic induction phenomena is derived from Lorentz force and Maxwell equation connecting electric field and time variation of magnetic field. The derivation provides with a unified mathematical treatment the…

After having obtained previously an extended first approximation of Maxwell's equations in Fock's nonlinear relativity, we propose here the corresponding exact form. In order to achieve this goal, we were inspired mainly by the special…

In this paper, we discuss the Maxwell equations in terms of differential forms, both in the 3-dimensional space and in the 4-dimensional space-time manifold. Further, we view the classical electrodynamics as the curvature of a line bundle,…

We establish global existence and uniqueness of the dynamics of classical electromagnetism with extended, rigid charges and fields which need not to be square integrable. We consider also a modified theory of electromagnetism where no…

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…

We consider non-Lorentzian expansions, Galilean and Carrollian, of the Lorentz force equation in which both the particle position and the electro-magnetic field are expanded. There are two well-known limits in the case of a constant field,…

The differential form of the Maxwell's equations was first derived based on an assumption that the media are stationary, which is the foundation for describing the electro-magnetic coupling behavior of a system. For a general case in which…

In this work, we study the magnetic effects of gravity in the framework of special relativity. Imposing covariance of the gravitational force with respect to the Lorentz transformations, we show from a thought experiment that a…