Related papers: An educational path for the magnetic vector potent…
We present an alternative formulation of the magnetostatic boundary value problem which is useful for calculating the magnetic field around a magnetic material placed in the vicinity of steady currents. The formulation differs from the…
A forgotten experiment by Andr\'e Blondel (1914) proves, as held on the basis of theoretical arguments in a previous paper, that the time variation of the magnetic flux is not the cause of the induced $emf$: the physical agent is instead…
Though sufficient for local conservation of charge, Maxwells displacement current is not necessary. An alternative to the Ampere-Maxwell equation is exhibited and the alternatives electric and magnetic fields and scalar and vector…
In the present work we argue that the usual assumption that magnetic currents possess the vector structure characteristic of electric currents may be the source of several difficulties in the theory of magnetic monopoles. We propose an {\it…
Vector and scalar potential formulation is valid from quantum theory to classical electromagnetics. The rapid development in quantum optics calls for electromagnetic solutions that straddle quantum physics as well as classical physics. The…
We investigated how students apply the concept of circulation when faced with problems related to the Ampere-Maxwell law. For this purpose, we designed a metacognitive pencil-and-paper question, presented it to 65 students, and analysed…
The main purposes of this paper are (i) to illustrate explicitly by a number of examples the gauge functions chi(x, t) whose spatial and temporal derivatives transform one set of electromagnetic potentials into another equivalent set; and…
We consider a quantum spinless nonrelativistic charged particle moving in the $xy$ plane under the action of a time-dependent magnetic field, described by means of the linear vector potential ${\bf A}=B(t)\PG{-y(1+\alpha),x(1-\alpha)}/2$,…
In the introductory courses on electromagnetism, the Biot-Savart law is generally explained by a simple example to find the magnetic field created at any point in space by a small wire element that carries a current. The simplest system…
Vector and scalar potentials are used for convenience in solving boundary value problems involving electromagnetic (EM) fields. The potentials are made unique by choosing a non-unique gauge relationship. The most commonly used gauges are…
The interaction between a quantum charge and a dynamic source of a magnetic field is considered in the Aharonov-Bohm scenario. It is shown that, in weak interactions with a post-selection of the source, the effective vector potential is,…
The magnetic field is traditionally presented as a (pseudo)vector quantity, tied closely to the cross product. Though familiar to experts, many students find these ideas challenging and full of subtleties. Building on earlier work in…
The Coulomb-gauge vector potential of a uniformly moving point charge is obtained by calculating the gauge function for the transformation between the Lorenz and Coulomb gauges. The expression obtained for the difference between the vector…
Teaching magnetism is one of the most challenging topics at undergraduate level in programmes with scientific background. A basic course includes the description of the magnetic interaction along with empirical results such as the…
A fully relativistically covariant and manifestly gauge invariant formulation of classical Maxwell electrodynamics is presented, purely in terms of gauge invariant potentials without entailing any gauge fixing. We show that the…
Several mathematical formulae are used nowadays in order to compute a magnetic torque. We demonstrate that its more general expression is the vectorial product of the current density with the vector potential. We associate this Larmor's…
In ZM theory the direction of time has a non-zero projection onto space and this projection corresponds to the local velocity relative to the observer. Classical trajectories can be obtained by following the local direction of time. The…
We study a class of fractional parabolic equations involving a time-dependent magnetic potential and formulate the corresponding inverse problem. We determine both the magnetic potential and the electric potential from the exterior partial…
The development of smooth particle magnetohydrodynamic (SPMHD) has significantly improved the simulation of complex astrophysical processes. However, the preservation the solenoidality of the magnetic field is still a severe problem for the…
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. The formalism is shown to provide a short derivation, in which the 4--vector…