相关论文: The Maxwell-Volterra reciprocity law in electrodyn…
An analysis of the concept of orientation used in electrodynamics is presented. At least two different versions are encountered in the literature. Both are clearly identified and comparisons are made.
In the framework of the classical Maxwell-Lorentz electrodynamics the energy conservation law is reconsidered.
For a convex polytope P with rational vertices, we count the number of integer points in integral dilates of P and its interior. The Ehrhart-Macdonald reciprocity law gives an intimate relation between these two counting functions. A…
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…
The paper formulates Maxwell's equations in 4-dimensional Euclidean space by embedding the electromagnetic vector potential in the frame vector $g_0$. Relativistic electrodynamics is the first problem tackled; in spite of using a geometry…
The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if…
Despite its importance, in the introductory disciplines of exact science courses, the demonstration of the Maxwell-Boltzmann velocity distribution law is not explained, only its final equation is shown. In order to fill this deficiency, in…
We extend an axiomatic approach to classical electrodynamics, which we developed recently, to the case of non-vanishing magnetic charge. Then two axioms, namely those of the existence of the Lorentz force (Axiom 2) and of magnetic flux…
The paper contained a preliminary version of a general theory of reciprocity laws on vector spaces.
We consider an elastic-plastic medium whose motion equations are isomorphic to Maxwell's equations. Electrical charges are modeled by pressure centers of the medium. The electric interaction is shown to be concerned with the conservation…
Lorentz's reciprocity lemma and Feld-Tai reciprocity theorem show the effect of interchanging the action and reaction in Maxwell's equations. We derive a free-space version of these reciprocity relations which generalizes the conservation…
In a previous paper (El. J. Combin. 6 (1999), R37), the author generalized Ehrhart's idea of counting lattice points in dilated rational polytopes: Given a rational polytope, that is, a polytope with rational vertices, we use its…
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 outline a regular way for solving Maxwell's equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwell's equations is seemingly…
We embed general boundary value problems for the time-harmonic Maxwell equations into the elliptic boundary value theory. This is achieved by introducing two new scalar functions to the electromagnetic field and imposing additional boundary…
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…
In this note, we would like to find the laws of electrodynamics in simple economic systems. In this direction, we identify the chief economic variables and parameters, scalar and vector, which are amenable to be put directly into the crouch…
Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant…
The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the…