Related papers: Maxwell's Equations in Arbitrary Coordinate System
In this article we have illustrated how is possible to formulate Maxwell's equations in vacuum in an independent form of the usual systems of units. Maxwell's equations, are then specialized to the most commonly used systems of units:…
The covariant formulation of Maxwell's equations can be expressed in a form independent of the usual systems of units by introducing the constants alpha, beta and gamma into these equations. Maxwell's equations involving these constants are…
A new formulation of the Maxwell equations based on two vector and two scalar potentials is proposed. The use of these potentials allows the electromagnetic field equations to be written in the form of a hyperbolic system. In contrast to…
We develop a differential-form approach to systematically derive the Newman-Penrose null-tetrad equations for Lorentz-violating extensions of Maxwell electrodynamics. The coordinate-independent nature of differential forms allows the…
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.
A Hamiltonian field theory for the macroscopic Maxwell equations with fully general polarization and magnetization is stated in the language of differential forms. The precise procedure for translating the vector calculus formulation into…
Maxwellian approximations to linear general relativity are revisited in light of relatively recent results on the degrees of freedom in the linear gravitational field. The well-known Maxwellian formalism obtained in harmonic coordinates is…
This paper aims to show that making use of Newton's view on equations of motion of a physical system and of the Maxwell stress tensor we come to a natural nonlinearization of Maxwell equations in vacuum making use only of nonrelativistic…
Using equations of motion with the anisotropic dissipative term for quantum particle and quantum-mechanical commutation rules, the general Maxwell-type differential equations are derived. The direct modifications of the well-known Maxwell…
For an elliptic complex of first order differential operators on a smooth manifold, we define a system of two equations which can be thought of as abstract Maxwell equations. The formal theory of this system proves to be very similar to…
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…
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…
This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations of a generic autonomous system along a particular solution. The main result of this paper is a compact yet explicit and…
This paper provides a view of Maxwell's equations from the perspective of complex variables. The study is made through complex differential forms and the Hodge star operator in $\mathbb{C}^2$ with respect to the Euclidean and the Minkowski…
Multipolar solutions of Maxwell's equations are used in many practical applications and are essential for the understanding of light-matter interactions at the fundamental level. Unlike the set of plane wave solutions of electromagnetic…
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,…
Variables are separated in Maxwell equations by the Newman-Penrose method of isotropic complex tetrade in the uniformly accelerated spherical coordinate system. Particular solutions are obtained in terms of spin 1 spherical harmonics. PACS:…
A covariant formalism is used in order to examine the status of Maxwell equations and to unify the concept of balances, for all chemical engineering applications in relation with electrodynamics. The resulting formal structure serves as a…
We present a small computer algebra program for use in Maxwell's theory. The Maxwell equations and the energy-momentum current of the electromagnetic field are formulated in the language of exterior differential forms. The corresponding…
Two questions connected to the macroscopic Maxwell equations are addressed: First, which form do they assume in the hydrodynamic regime, for low frequencies, strong dissipation and arbitrary field strengths. Second, what does this tell us…