Related papers: An educational path for the magnetic vector potent…
It is shown that electromagnetic potentials convey physical information beyond that supplied by electric and magnetic fields alone, and are thus more fundamental. Observable physical properties can impose conditions on the selection of…
We show that the known expressions for the force on a point-like dipole are incompatible with the relativistic transformation of force, and in this respect we apply the Lagrangian approach to the derivation of the correct equation for force…
The question of an instantaneous action (A M Stewart 2003 Eur. J. Phys. 24, 519) can be approached in a systematic way applying the Helmhotz vector decomposition theorem to a two-parameter Lorenz-like gauge. We thus show that only the…
Although gauge invariance preserves the values of physical observables, a gauge transformation can introduce important alterations of physical interpretations. To understand this, it is first shown that a gauge transformation is not, in…
Gauss integral theorems for electric and magnetic fields, Faradays law of electromagnetic induction, magnetic field circulation theorem, theorems on the flux and circulation of vector potential, which are valid in curved spacetime, are…
The fallacies associated with the gauge concept in electromagnetism are illustrated. A clearer and more valid formulation of the basics of classical electromagnetism is provided by recognizing existing physical constraints as well as the…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
The magnetic scalar potential can be used to design electromagnets accurately and efficiently. I will describe a practical construction algorithm: the prescribed field in a "Target" region (constrained only by Maxwell's equations) specifies…
We study the gauge invariance of laser-matter interaction. The velocity gauge where the vector potential is expanded to the $n$-th order with respect to the spatial coordinate, and the length gauge where the electric and magnetic fields are…
The Ampere-Maxwell's law and the displacement current constitute one of the most difficult aspects of electromagnetic theory for students in introductory electromagnetics courses. Here we present a set of examples that go beyond the…
In the self-sufficient potential formalism, treating all electromagnetic phenomena as natural or forced oscillations of some distributed electromagnetic oscillating system (Minkowski space-time), the electromagnetic potential must be…
Electromagnetism is a simple example of a gauge theory where the underlying potentials -- the vector and scalar potentials -- are defined only up to a gauge choice. The vector potential generates magnetic fields through its spatial…
We describe the potential produced by a point electric charge placed into a constant magnetic field, so strong that the electron Larmour length is much shorter than its Compton length. The standard Coulomb law is modified due to the vacuum…
The maximum current in a vacuum tube prescribed by the classical Child-Langmuir law can be overcome, when the space-charge effect of the induced potential is mitigated by the mirror effect in a spatially varying magnetic field. The current…
We investigate the ground state energies of vector $\rho^{\pm}$ and $K^{\pm *}$ mesons depending on the magnetic field value in the $SU(3)$ lattice gauge theory. It has been shown that the energy of a vector particle depends on its spin…
In the first part of this paper we review the fundamental difference between the usual transformations of the three-dimensional (3D) vectors of the electric field $\mathbf{E}$, the magnetic field $\mathbf{B}$, the polarization $\mathbf{P}$,…
I address the view that the classical electromagnetic potentials are shown by the Aharonov-Bohm effect to be physically real (which I dub: 'the potentials view'). I give a historico-philosophical presentation of this view and assess its…
This is the first paper of a five part work in which we study the Lagrangian and Hamiltonian structure of classical field theories with constraints. Our goal is to explore some of the connections between initial value constraints and gauge…
In recent years, the $H$ formulation of Maxwell's equation has become the de facto standard for simulating the time-dependent electromagnetic behavior of superconducting applications with commercial software. However, there are cases where…
It is demonstrated how the right hand sides of the Lorentz Transformation equations may be written, in a Lorentz invariant manner, as 4--vector scalar products. This implies the existence of invariant length intervals analogous to invariant…