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

Heras, José A.

doi:10.1119/1.3533223

Cited by 28 publications

(35 citation statements)

References 20 publications

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“…9, where the decrease in time of the electric field within the capacitor results in a spatially uniform displacement current, I D [10,11], which is confined to the region between the plates and is numerically equal to the conduction current, I. Both of these currents are accounted for by Ampère's generalized law [2] …”

Section: Application Of Generalized Aclmentioning

confidence: 99%

Intrinsic symmetry of Ampère’s circuital law and other educational issues

2012

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This paper explores Ampère's circuital law (ACL) from an educational perspective. The interchangeability of the ampèrian loop with the current loop, an intrinsic symmetry of ACL that is seldom addressed in the literature or textbooks, is illustrated here. It is verified that the symmetry axis of a circular current is an ampèrian loop. The attempt to apply ACL to a finite wire, a common source of student misunderstanding, is used to highlight the limitations of ACL. The generalisation of ACL is illustrated using an instructive example where the displacement current is unconfined and not spatially uniform. This work is primarily intended for teachers and more advanced undergraduate students, who may benefit from the ideas that are presented here.PACS Nos: 03.50. De, 01.40.Fk Résumé : Nous réétudions ici le théorème d'Ampère, dans une perspective pédagogique. Nous illustrons l'interchangeabilité de la boucle d'Ampère et la boucle de courant, une symétrie intrinsèque du théorème qui est rarement discutée dans la litté-rature ou les manuels. Nous vérifions que l'axe de symétrie d'un courant circulaire est une boucle d'Ampère. Afin d'illustrer les limitations du théorème, nous utilisons l'application du théorème à un fil de longueur finie, une source fréquente de malentendus chez les étudiants. Nous illustrons la généralisation du théorème d'Ampère à l'aide d'un exemple pédagogique où le courant de déplacement n'est pas confiné ni spatialement uniforme. Ce travail vise surtout les enseignants et les étudiants des 2 e et 3 e cycles qui peuvent profiter des idées présentées ici.[Traduit par la Rédaction]

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Section: Application Of Generalized Aclmentioning

confidence: 99%

Intrinsic symmetry of Ampère’s circuital law and other educational issues

2012

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“…The electrostatic potential φ satisfies the Poisson equation,

MathClass-bin- MathClass-rel\nabla MathClass-bin\cdot (ϵ MathClass-rel\nabla φ) MathClass-rel= ρ_{0} MathClass-bin+ {MathClass-op\sum}_{i MathClass-rel= 1}^{N} z_{i} q c_{i}

where ϵ is the dielectric constant, ρ 0 the permanent charge density in the system, z i is the valence of i th ion species, and q is the unit charge. Together, these equations are the form of Maxwell's equations appropriate when magnetic forces are insignificant .…”

Section: Energetic Variational Approach and Conservation Lawsmentioning

confidence: 99%

An energetic variational approach to ion channel dynamics

Hyon

Eisenberg

2013

Math. Meth. Appl. Sci.

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We introduce a mathematical model to study the transport of ions through ion channels. The system is derived in the framework of the energetic variational approach, taking into account the coupling between electrostatics, diffusion, and protein (ion channel) structure. The geometric constraints of the ion channel are introduced through a potential energy controlling the local maximum volume inside the ion channel. A diffusive interface (labeling) description is also employed to describe the geometric configuration of the channels. The surrounding bath and channel are smoothly connected with the antechamber region by this label function. A corresponding modified Poisson–Nernst–Planck channel system for ion channels is derived using the variational derivatives of the total energy functional. The functional consists of the entropic free energy for diffusion of the ions, the electrostatic potential energy, the repulsive potential energy for the excluded volume effect of the ion particles, and the potential energy for the geometric constraints of the ion channel. For the biological application of such a system, we consider channel recordings of voltage clamp to measure the current flowing through the ion channel. The results of one‐dimensional numerical simulations are presented to demonstrate some signature effects of the channel, such as the current output produced by single‐step and double‐step voltage inputs. Copyright © 2013 John Wiley & Sons, Ltd.

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“…Heras [14] discusses the true nature of the displacement current in connection with Faraday"s induction. This is especially interesting, since the actual conference paper makes use of the displacement current in order to explain electromagnetic induction.…”

Section: Other Critics Of Faraday's Law Of Inductionmentioning

confidence: 99%

The Use of Finite Differences on Electric Currents Gives Credit to Coulomb‟s Law as Causing Electromagnetic Forces, thereby Explaining Electromagnetic Induction

Jonson¹

2013

IJMO

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Abstract-Using differential calculus rigorously on electric currents, thereby using the method of finite elements, it has been possible to derive expressions for the total electromagnetic force between two electric currents, based solely on Coulomb's law, thereby applying the effects of propagation delay. These results, explored in earlier publications, have been used in order to attain a new explanation to electromagnetic induction, thereby simultaneously rejecting Faraday's Law of Induction. It is being shown that Faraday's Law of Induction fails to account for the behavior of the induced signal in a secondary loop of a typical transformer circuit, since it has been found a mathematical deficiency in the traditional analysis of electric measurements, which implies a phase fault. Instead it is successfully being shown that the usage of the Displacement Current Density, based on Coulomb's Law, and the Continuity Equation of Electricity are able to account for the correct phase behavior.Index Terms-Coulomb's law, Faraday's law of induction, the displacement current density, the continuity equation of electricity, new definition of propagation delay, transformer circuit, wrong analysis of measurements I.

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

Cited by 28 publications

References 20 publications

Intrinsic symmetry of Ampère’s circuital law and other educational issues

Intrinsic symmetry of Ampère’s circuital law and other educational issues

An energetic variational approach to ion channel dynamics

The Use of Finite Differences on Electric Currents Gives Credit to Coulomb‟s Law as Causing Electromagnetic Forces, thereby Explaining Electromagnetic Induction

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