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V. Hnizdo

Publications and source records attributed to V. Hnizdo.

At least 19 recordsLinked to original sources
arXiv2025

Note on Jackson's formalism of gauge transformation

An outline is given of how Jackson may have obtained the inhomogeneous wave equations for the auxiliary functions $\Psi$ and $\bf V$ in his influential 2002 AJP paper on the transformation from the Lorenz gauge to other electromagnetic gauges. It clarifies the roles of these functions in the calculation of the Coulomb-gauge vector potential ${\bf A}_C$ by showing that while ${\bf A}_C$ is given directly $\nabla\times{\bf V}$, only the subtraction of $\nabla\Psi$ from the Lorenz-gauge vector potential ${\bf A}_L$ yields ${\bf A}_C$.

physics.class-ph↗
arXiv2025

Novel distributional Laplacians and a Coulomb-gauge problem

Novel distributional Laplacians of an arsinh function and a related logarithm function are derived. The method used to establish the former result is employed in a calculation of the gauge transformation function for the case of a uniformly moving point charge.

physics.class-ph↗
arXiv2025

Note on the transformation from the Lorenz gauge to the Coulomb gauge

There is a simple formula for the gauge function of the transformation from the Lorenz gauge to the Coulomb gauge, valid under a condition that is satisfied by some charge densities employed in the literature. An equation for the gauge function of this transformation that is alternative but equivalent to a formula of Jackson is derived also.

physics.class-ph↗
arXiv2024

Potentials and fields of a charge set suddenly from rest into uniform motion

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 into uniform motion. The modified potentials are shown to satisfy the requisite inhomogeneous wave equations. The gauge function of the transformation of these potentials to the Coulomb gauge is calculated in closed form. It is validated by confirming that the Coulomb-gauge vector potential that is calculated using it yields together with the Coulomb-gauge scalar potential the same electric and magnetic fields as those calculated with the Lorenz-gauge potentials.

physics.class-ph↗
arXiv2021

Finite and divergent parts of the self-force of a point charge from its spherically averaged self-field

The electromagnetic self-force of a point charge moving arbitrarily on a rectilinear trajectory is calculated by averaging its retarded electric self-field over a sphere of infinitesimal radius centered on the charge's present position. The finite part of the self-force obtained is the well-established relativistic radiation reaction, while its divergent part implies the pre-relativistic longitudinal electromagnetic mass of Abraham.

physics.class-ph↗
arXiv2020

Comment on "Basic observables for the accelerated electron and its field"

We show that the "defective" terms in the expression that Dondera [Phys. Rev. D 98, 096008 (2018)] obtained for the momentum of the retarded field of an accelerating point charge are mathematically well justified. The repair should not be sought in assigning an accelerating "bare" charge ad hoc compensating attributes. We advance a conjecture, supported by published work, concerning the Hadamard finite part of the divergent integral for the retarded-field momentum in question.

physics.class-ph↗
arXiv2015

What's the Use of Bound Charge?

Bound charge is a useful construct for calculating the electrostatic field of polarized material, and it represents a perfectly genuine accumulation of charge. But is such a material in every respect equivalent to a particular configuration of bound charge? The answer is no, and the same goes for bound current and (in the time-dependent case) polarization current.

physics.class-ph↗
arXiv2013

Mansuripur's Paradox

A recent article claims that the Lorentz force law is incompatible with special relativity. We discuss the "paradox" on which this claim is based. The resolution depends on whether one assumes a "Gilbert" model for the magnetic dipole (separated monopoles) or the standard "Ampere" model (current loop). The former was presented in these pages many years ago; the latter requires the inclusion of "hidden momentum."

physics.class-ph↗
arXiv2013

Time-dependent fields of a current-carrying wire

The electric and magnetic fields of an infinite straight wire carrying a steady current which is turned on abruptly are determined using Jefimenko's equations, starting from the standard assumption that the wire is electrically neutral in its rest frame. Some nontrivial aspects of the solution are discussed in detail.

physics.class-ph↗
arXiv2012

Magnetic dipole moment of a moving electric dipole

The current density of a moving electric dipole is expressed as the sum of polarization and magnetization currents. The magnetic field due to the latter current is that of a magnetic dipole moment that is consistent with the relativistic transformations of the polarization and magnetization of macroscopic electrodynamics.

physics.class-ph↗
arXiv2012

Spin-orbit coupling and the conservation of angular momentum

In nonrelativistic quantum mechanics, the total (i.e. orbital plus spin) angular momentum of a charged particle with spin that moves in a Coulomb plus spin-orbit-coupling potential is conserved. In a classical nonrelativistic treatment of this problem, in which the Lagrange equations determine the orbital motion and the Thomas equation yields the rate of change of the spin, the particle's total angular momentum in which the orbital angular momentum is defined in terms of the kinetic momentum is generally not conserved. However, a generalized total angular momentum, in which the orbital part is defined in terms of the canonical momentum, is conserved. This illustrates the fact that the quantum-mechanical operator of momentum corresponds to the canonical momentum of classical mechanics.

physics.class-ph↗
arXiv2007

Comment on "How the potentials in different gauges yield the same retarded electric and magnetic fields," by J. A. Heras [Am. J. Phys. 75, 176 (2007)]

Heras purports to show without solving the requisite dynamic equations how the non-causal term generated by the scalar potential of the Coulomb, Kirchhoff, or velocity gauge is canceled by an equal and opposite term in the contribution to the electric field that is generated by the vector potential. Heras's procedure is criticized as being just an algebraic manipulation that has no explanatory content.

physics.class-ph↗
arXiv2006

Regularization of the second-order partial derivatives of the Coulomb potential of a point charge

The second-order partial derivatives of the Coulomb potential of a point charge can be regularized using the Coulomb potential of a charge of the oblate spheroidal shape that a moving rest-frame-spherical charge acquires by the Lorentz contraction. This `physical' regularization is shown to be fully equivalent to the standard delta-function identity involving these derivatives.

physics.class-ph↗