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Jose A. Heras

Publications and source records attributed to Jose A. Heras.

At least 19 recordsLinked to original sources
arXiv2011

A formal interpretation of the displacement current and the instantaneous formulation of Maxwell's equations

Maxwell's displacement current has been the subject of controversy for more than a century. Questions on whether the displacement current represents a true current like the conduction current and whether it produces a magnetic field have recently been discussed in the literature. Similar interpretations for the Faraday induction current have also been controversial. These basic questions are answered in this paper by considering the relation between the displacement and conduction currents as well as the relation between Faraday induction and conduction currents. It is pointed out that the displacement current contributes to the magnetic field and that the induction current contributes to the electric field. However, the displacement and induction currents cannot be considered as the conduction current because they are nonlocal. Both relations are used to implement an instantaneous formulation of Maxwell's equations with local and nonlocal sources.

physics.class-ph↗
arXiv2010

Can the Lorenz-gauge potentials be considered physical quantities?

Two results support the idea that the scalar and vector potentials in the Lorenz gauge can be considered to be physical quantities: (i) they separately satisfy the properties of causality and propagation at the speed of light and not imply spurious terms and (ii) they can naturally be written in a manifestly covariant form. In this paper we introduce expressions for the Lorenz-gauge potentials at the present time in terms of electric and magnetic fields at the retarded time. These expressions provide a third result in favor of a physical interpretation of the Lorenz-gauge potentials: (iii) they can be regarded as causal effects of the observed electric and magnetic fields.

physics.class-ph↗
arXiv2010

The c equivalence principle and the correct form of writing Maxwell's equations

It is well-known that the speed $c_u=1/\sqrt{ε_0μ_0}$ is obtained in the process of defining SI units via action-at-a-distance forces, like the force between two static charges and the force between two long and parallel currents. The speed $c_u$ is then physically different from the observed speed of propagation $c$ associated with electromagnetic waves in vacuum. However, repeated experiments have led to the numerical equality $c_u=c,$ which we have called the $c$ equivalence principle. In this paper we point out that $\nabla\times{\bf E}=-[1/(ε_0μ_0 c^2)]\partial{\bf B}/\partial t$ is the correct form of writing Faraday's law when the $c$ equivalence principle is not assumed. We also discuss the covariant form of Maxwell's equations without assuming the $c$ equivalence principle.

physics.class-ph↗
arXiv2010

The Galilean limits of Maxwell's equations

We show that if Maxwell's equations are expressed in a form independent of specific units, at least three Galilean limits can be extracted. The electric and magnetic limits can be regarded as nonrelativistic limits because they are obtained using the condition $|\bf{v}| \ll c$ and restrictions on the magnitudes of the sources and fields. The third limit is called the instantaneous limit and is introduced by letting $c\to \infty$. The electric and instantaneous limits have the same form, but their interpretation is different because the instantaneous limit cannot be considered as a nonrelativistic limit. We emphasize the double role that the speed of light $c$ plays in Maxwell's equations.

physics.class-ph↗
arXiv2009

The covariant formulation of Maxwell's equations expressed in a form independent of specific units

The covariant formulation of Maxwell's equations can be expressed in a form independent of the usual systems of units by introducing the constants alpha, beta and gamma into these equations. Maxwell's equations involving these constants are then specialized to the most commonly used systems of units: Gaussian, SI and Heaviside-Lorentz by giving the constants alpha, beta and gamma the values appropriate to each system.

physics.class-ph↗
arXiv2008

Can Maxwell's equations be obtained from the continuity equation?

We formulate an existence theorem that states that given localized scalar and vector time-dependent sources satisfying the continuity equation, there exist two retarded fields that satisfy a set of four field equations. If the theorem is applied to the usual electromagnetic charge and current densities, the retarded fields are identified with the electric and magnetic fields and the associated field equations with Maxwell's equations. This application of the theorem suggests that charge conservation can be considered to be the fundamental assumption underlying Maxwell's equations.

physics.class-ph↗
arXiv2008

Author's response

This paper replies to the comment by Jefimenko: "Causal equations for electric and magnetic fields and Maxwell's equations: Comment on a paper by Heras" [Am. J. Phys. 76, 101-101 (2008)]."

physics.class-ph↗
arXiv2008

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 $ε_0 \partial Ě/\partial t$ and the ordinary current $vJ$. I show that $ε_0 \partial Ě/\partial t$ contains a local term determined by the present values of $vJ$ plus a non-local term determined by the retarded values of $vJ$. 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.

physics.class-ph↗
arXiv2008

The Coulomb static gauge

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 Coulomb static potential. We obtain an explicit expression for the associated vector potential and show how the scalar and vector potentials in this gauge yield the retarded electric and magnetic fields. We note the close relation between the proposed gauge and the temporal gauge.

physics.class-ph↗
arXiv2007

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.

physics.class-ph↗
arXiv2007

How potentials in different gauges yield the same retarded electric and magnetic fields

This paper presents a simple and systematic method to show how the potentials in the Lorentz, Coulomb, Kirchhoff, velocity and temporal gauges yield the same retarded electric and magnetic fields. The method appropriately uses the dynamical equations for the scalar and vector potentials to obtain two wave equations, whose retarded solutions lead to the electric and magnetic fields. The advantage of this method is that it does not use explicit expressions for the potentials in the above gauges, which are generally simple to obtain for the scalar potential but generally difficult to calculate for the vector potential. The spurious character of the term generated by the scalar potential in the Coulomb, Kirchhoff and velocity gauges is noted. The non spurious character of the term generated by the scalar potential in the Lorenz gauge is emphasized.

physics.class-ph↗
arXiv2006

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 gaug

physics.class-ph↗
arXiv2006

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.

physics.class-ph↗
arXiv2006

Instantaneous fields in classical electrodynamics

In this paper we express the retarded fields of Maxwell's theory in terms of the instantaneous fields of a Galilei-invariant electromagnetic and we find the vector function whose spatial and temporal derivatives transform the instantaneous fields into the retarded ones. We conclude that the instantaneous fields can formally be introduced as unphysical objects into classical electrodynamics which can be used to find the physical retarded fields.

physics.class-ph↗