266 research outputs found
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 and the ordinary current . I show that
contains a local term determined by the
present values of plus a non-local term determined by the retarded
values of . 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
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