The Kirchhoff gauge

We discuss the Kirchhoff gauge in classical electrodynamics. In this gauge the scalar potential satisfies an elliptical equation and the vector potential satisfies a wave equation with a nonlocal source. We find the solutions of both equations and show that, despite of the unphysical character of the scalar potential, the electric and magnetic fields obtained from the scalar and vector potentials are given by their well-known retarded expressions. We note that the Kirchhoff gauge pertains to the class of gauges known as the velocity gauge.Comment: 12 page

Reply to "Comment(s) on `Preacceleration without radiation: The non-existence of preradiation phenomenon," by J. D. Jackson [Am. J. Phys. 75, 844-845 (2007)] and V. Hnizdo [Am. J. Phys. 75, 845-846 (2007)

This paper replies the comments by J. D. Jackson [Am. J. Phys. 75, 844-845 (2007)] and V. Hnizdo [Am. J. Phys. 75, 845-846 (2007)].Comment: 9 pages. See also the related paper: "E. Eriksen and O. Gron, Does preradiation exist? [Phys. Scr. 76, 60-63 (2007)].

Preacceleration without radiation: the non-existence of preradiation phenomenon

An unexpected prediction of classical electrodynamics is that a charge can accelerate before a force is applied. We would expect that a preaccelerated charge would radiate so that there would be spontaneous preradiation, an acausal phenomenon. We reexamine the subtle relation between the Larmor formula for the power radiated by a point charge and the Abraham-Lorentz equation and find that for well-behaved external forces acting for finite times, the charge does not radiate in time intervals where there is preacceleration. That is, for these forces preradiation does not exist even though the charge is preaccelerated. The radiative energy is emitted only in time intervals when the external force acts on the charge.Comment: Equation (37) of the published paper in AJP has been correcte

A short proof that the Coulomb-gauge potentials yield the retarded fields

A short demonstration that the potentials in the Coulomb gauge yield the retarded electric and magnetic fields is presented. This demonstration is relatively simple and can be presented in an advanced undergraduate curse of electromagnetic theory

Comment on 'Helmholtz theorem and the v-gauge in the problem of superluminal and instantaneous signals in classical electrodynamics,' by Chubykalo et al [Found. of Phys. Lett, 19, 37-46 (2006)]

Fundamental errors in the Chubykalo et al paper [Found. of Phys. Lett, 19, 37-46 (2006)] are highlighted. Contrary to their claim that "... the irrotational component of the electric field has a physical meaning and can propagate exclusively instantaneously," it is shown that this instantaneous component is physically irrelevant because it is always canceled by a term contained into the solenoidal component. This result follows directly from the solution of the wave equation that satisfies the solenoidal component. Therefore the subsequent inference of these authors that there are two mechanisms of transmission of energy and momentum in classical electrodynamics, one retarded and the other one instantaneous, has no basis. The example given by these authors in which the full electric field of an oscillating charge equals its instantaneous irrotational component on the axis of oscillations is proved to be false.Comment: An alternative discussion can be found in the paper: Jose A. Heras, "How potentials in different gauges yield the same retarded electric and magnetic fields," Am. J. Phys. 75, 176-183 (2007

Generalization of the Schott energy in electrodynamic radiation theory

We discuss the origin of the Schott energy in the Abraham-Lorentz version of electrodynamic radiation theory and how it can be used to explain some apparent paradoxes. We also derive the generalization of this quantity for the Ford-O'Connell equation, which has the merit of being derived exactly from a microscopic Hamiltonian for an electron with structure and has been shown to be free of the problems associated with the Abraham-Lorentz theory. We emphasize that the instantaneous power supplied by the applied force not only gives rise to radiation (acceleration fields), but it can change the kinetic energy of the electron and change the Schott energy of the velocity fields. The important role played by boundary conditions is noted

Comment on 'A generalized Helmholtz theorem for time-varying vector fields by A. M. Davis, [Am. J. Phys. 74, 72-76 (2006)]'

In a recent paper Davis formulated a generalized Helmholtz theorem for a time-varying vector field in terms of the Lorenz gauge retarded potentials. The purposes of this comment are to point out that Davis's generalization of the theorem is a version of the extension of the Helmholtz theorem formulated some years ago by McQuistan and also by Jefimenko and more recently by the present author and to show that Davis's expression for the time-dependent vector field is also valid for potentials in gauges other than the Lorenz gau

The exact relation between the displacement current and the conduction current: Comment on a paper by Griffiths and Heald

I introduce the exact relation between the displacement current $\epsilon_0 \partial \v{E}/\partial t$ and the ordinary current $\v{J}$. I show that $\epsilon_0 \partial \v{E}/\partial t$ contains a local term determined by the present values of $\v{J}$ plus a non-local term determined by the retarded values of $\v{J}$. The non-local term implements quantitatively the suggestion made by Griffiths and Heald that the displacement current at a point is a surrogate for ordinary currents at other locations.Comment: 7 page