Related papers: Some Variations on Maxwell's Equations
It is shown that the set of equations known as Maxwell's equations perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices,…
We express Maxwell's equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two…
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure…
Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…
Many papers have been published over the years that either conjecture or even (claim to) prove the universality of the form of Maxwell's equations. We present yet another derivation of Maxwell's equations and discuss the conclusions…
A new term describing interactions between charge and potentials may be added to the right hand side of the Einstein equations. In the proposed term an additional tensor has been introduced containing a charge density, analogous to the…
The derivation of the Maxwell equations is reproduced whereby magnetic charges are included. This ansatz yields the results: 1) Longitudinal Ampere forces in a differential magnetostatic force law are improbable. Otherwise an electric…
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 propose a modification of Maxwell's macroscopic fundamental set of equations in vacuum in order to clarify Faraday's law of induction. Using this procedure, the Lorentz force is no longer separate from Maxwell's equations. The Lorentz…
Maxwell's equations describe the relation of charge and electric force almost perfectly even though electrons and permanent charge were not in his equations, as he wrote them. For Maxwell, all charge depended on electric field. Charge was…
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…
We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is…
Some mathematical inconsistencies in the conventional form of Maxwell's equations extended by Lorentz for a single charge system are discussed. To surmount these in framework of Maxwellian theory, a novel convection displacement current is…
We discuss a previously unpublished description of electromagnetism outlined by Richard P. Feynman in the 1960s in five handwritten pages, recently uncovered among his papers, and partly developed in later lectures. Though similar to the…
It is shown that the Galilean limit (V << c, or L/T <<c)) of the Maxwell equations admits three different limits: the magneto-quasi-static, electro-quasi-static, and electromagnetic-quasi-static limits, in addition to the two obvious static…
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…
A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the…
A fully relativistically covariant formulation of the classical Maxwell electrodynamics of an arbitrarily-moving point charge is presented, purely in terms of gauge invariant potentials without entailing any gauge fixing. A new,…
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…
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…