Related papers: An educational path for the magnetic vector potent…
The instantaneous nature of the potentials of the Coulomb gauge is clarified and a concise derivation is given of the vector potential of the Coulomb gauge expressed in terms of the instantaneous magnetic field.
The expression for the Coulomb-gauge vector potential in terms of the `instantaneous' magnetic field derived by Stewart [2003 Eur. J. Phys. 24, 519] by employing Jefimenko's equation for the magnetic field and Jackson's formula for the…
Modern undergraduate textbooks in electricity and magnetism typically focus on a force representation of electrodynamics with an emphasis on Maxwell's Equations and the Lorentz Force Law. The vector potential $\mathbf{A}$ and scalar…
The retarded vector potential of a point magnetic dipole with an arbitrary time dependence undergoing accelerated relativistic motions is derived. A novel expression for the angular distribution of the radiated power of an arbitrary moving…
A solution is proposed for finding the vector potential and magnetic field of any distribution of currents with axial symmetry. In this approach, the magnetic field and the vector potential are looked for not by solving a differential…
If potential energy is the timelike component of a four-vector, then there must be a corresponding spacelike part which would logically be called the potential momentum. The potential four-momentum consisting of the potential momentum and…
When the magnetic vector potential is expressed in terms of the magnetic field it, is found to be explicitly non-local in space. This gives support to the conclusions of Aharonov et al. in a recent comment, that the Aharonov-Bohm effect may…
We derive an analytic solution for the electromagnetic vector potential in any gauge directly from Maxwell's equations for potentials for an arbitrary time-dependent charge-current distribution. No gauge condition is used in the derivation.…
The most popular interpretation of the Aharonov-Bohm (AB) effect is that the electromagnetic potential locally affects the complex phase of a charged particle's wave function in the magnetic field free region. However, since the vector…
The existence of gauge conditions involving second-order derivatives of potentials is not well known in classical electrodynamics. We introduce one of these gauges, the Coulomb static gauge, in which the scalar potential is given by the…
The Liouville equation with non-constant magnetic field is obtained as a limit in the Planck constant \hbar of the Heisenberg equation with the same magnetic field. The convergence is with respect to an appropriate semi-classical pseudo…
Results obtained for the antisymmetric gauge A=[Hy,-Hx]/2 by Brown and Zak are compared with those based on pure group-theoretical considerations and corresponding to the Landau gauge A=[0,Hx]. Imposing the periodic boundary conditions one…
Electromagnetic vector potential has physical significance in quantum mechanics as revealed by the Aharonov-Bohm effect for charged particles. However, till date it is thought that we cannot measure the vector potential directly as this is…
We give an integral expression for the vector potential of a time-independent, steady azimuthal current density. Our derivation is substantially simpler and somewhat more general than others given in the literature. As an illustration, we…
It is well-known that the electric and magnetic Aharonov-Bohm effects may be formally described on equal footing using the four-vector potential in a relativistic framework. We propose an illustrative manifestation of both effects in a…
Though sufficient for local conservation of charge, we show that Maxwells displacement current is not necessary. An alternative to the Ampere Maxwell equation is exhibited and the alternative s electric and magnetic fields and scalar and…
Radiation from magnetic and electric dipole moments is a key subject in theory of electrodynamics. Although people treat the problem thoroughly in the context of frequency domain, the problem is still not well understood in the context of…
The fact that electromagnetic effects propagate at the speed of light suggests how the Lorenz-gauge scalar and vector potentials of a uniformly moving point charge must be modified when the charge was initially at rest and then set suddenly…
In this work we substantiate the applying of the Helmholtz vector decomposition theorem (H-theorem) to vector fields in classical electrodynamics. Using the H-theorem, within the framework of the two-parameter Lorentz-like gauge (so called…
The time-dependent, geometric method for high-energy limits and inverse scattering is applied to nonrelativistic quantum particles in external electromagnetic fields. Both the Schr"odinger- and the Pauli equations in R^2 and R^3 are…