We discuss the electromagnetic energy-momentum distribution and the mechanical forces of the electromagnetic field in material media. There is a long-standing controversy on these notions. The Minkowski and the Abraham energy-momentum tensors are the most well-known ones. We propose a solution of this problem which appears to be natural and self-consistent from both a theoretical and an experimental point of view.
We obtain the fields and electromagnetic self-force of a charge distributed on the surface of a sphere undergoing rigid motion at constant proper acceleration, where the charge distribution has axial symmetry about the direction of motion. A closed-form expression for the self-force is given in terms of the multipole moments of the charge distribution. Applications to the electrodynamics of a dipole, and to electromagnetic self-force near a horizon (in spacetime) are discussed.
We calculate the electromagnetic self-force of a uniformly charged spherical ball moving on a rectilinear trajectory, neglecting the Lorentz contraction.
From the energy-momentum tensors of the electromagnetic field and the mechanical energy-momentum, the equations of energy conservation and balance of electromagnetic and mechanical forces are obtained. The equation for the Abraham force in a dielectric medium with losses is obtained
It is proposed a natural and consistent division of the momentum of electromagnetic waves in linear, non-dispersive and non-absorptive dielectric and magnetic media into material and electromagnetic parts. The material part is calculated using directly the Lorentz force law and the electromagnetic momentum density has the same form than in vacuum, without an explicit dependence on the properties of the media. The consistency of the treatment is verified through the obtention of a correct momentum balance equation in many examples and showing the compatibility of the division with the Einstein'…
Using the Lagrangian formalism, the electromagnetic force on a moving dipole derived by Kholmetskii, Missevitch and Yarman (2011, Eur. J. Phys. 32, 873) is found to be missing some important terms.
We present an elementary discussion of the momentum transferred to a conducting sheet by an electromagnetic wave propagating in a polarizable medium. We show that conservation of momentum is consistent with Minkowski's expression for the momentum density.
The incorporation of a relativistic momentum of a nonelectromagnetic nature into macroscopic problems of electrodynamics obviates the lack of correspondence between the electromagnetic mass and the electromagnetic momentum of macroscopic bodies, allowing, in particular, the resolution of the well-known 4/3 paradox.
The article describes a new approach to obtaining the energy-momentum tensor of electromagnetic field in medium without the use of Maxwell's equations and Poynting theorem. The energy-momentum tensor has new qualities and consequences. Its linear invariant is Lagrange density of the electromagnetic field. From the tensor follows the equation of conservation of energy density, the equation of flux energy density and wave equations for these energy values. Wave equation for momentum density describes simultaneous transfer of momentum and angular momentum regardless of radiation polarization. Fro…
The problem of the `infinite energy' of a point charge is well known in connection with the Lorentz--Abraham--Dirac equation and, more significantly, in quantum electrodynamics. Though it is not stated usually, this is strongly related to the old problem of what the electromagnetic energy-momentum tensor is. Electromagnetic energies and forces will be examined thoroughly from a new point of view in the framework of Distribution Theory.
The symmetric tensor energy-impulse of interaction of collective of electric charges with an electromagnetic field is received. A system of covariant energy and momentum conservation equations or a system of equations for the collective motion of charged particles is derived from this tensor. From this system Expressions are derived for collective electrodynamics forces. From the energy-momentum tensor derived the tensor of collective electrodynamics forces is.
Several noncovariant formulations of the electromagnetic self-force of extended charged bodies, as have been developed in the context of classical models of charged particles, are compared. The mathematical equivalence of the various dissimilar self-force expressions is demonstrated explicitly by deriving these expressions directly from one another. The applicability of the self-force formulations and their significance in the wider context of classical charged particle models are discussed.
Recently there have been suggestions that the Lorentz force law is inconsistent with special relativity. This is difficult to understand, since Einstein invented relativity in order to reconcile electrodynamics with mechanics. Here we investigate the momentum of an electric charge and a magnetic dipole in the frame in which both are at rest, and in an infinitesimally boosted frame in which both have a common velocity. We show that for a dipole composed of a magnetic monopole-antimonopole pair the torque is zero in both frames, while if the dipole is a point dipole, the torque is not zero, but …
This article was published as Sec.4 of the "Roadmap on Structured Light" in Journal of Optics 19 (2017) 013001. Section 4 describes the essential elements of the classical theory of electromagnetic force and momentum.
We present an elementary discussion of the momentum transferred by an electromagnetic wave propagating in a dispersive medium. Our analysis is based on Minkowski's electromagnetic momentum density which have been recently seen to be consistent with a fully covariant expression of the energy-momentum tensor of the electromagnetic field in a dispersive medium and with all the experimental evidence. We show that the medium may be either pulled or pushed as the electromagnetic pulse enters in it depending on the value of the frequency.
The Abraham--Minkowski momentum controversy is the outwardly visible symptom of an inconsistency in the use of the energy-momentum tensor in the case of a plane quasimonochromatic field in a simple linear dielectric. We show that the Gordon form of the electromagnetic momentum is conserved in a thermodynamically closed system. We regard conservation of the components of the four-momentum in a thermodynamically closed system as a fundamental property of the energy--momentum tensor. Then the first row and column of the energy--momentum tensor is populated by the electromagnetic energy density an…
A model calculation using the Darwin Lagrangian is carried out for a magnet consisting of two current-carrying charges constrained by centripetal forces to move in a circular path in the presence of the electric field from a distant external point charge. In the limit that the magnet's two charges are non-interacting, the calculation recovers the only valid calculation for hidden mechanical momentum. However, if the magnet's charges are mutually interacting, then there is internal electromagnetic linear momentum associated with the perturbed magnet's electrostatic charge distribution and the m…
We determine the invariant expression of the force density that the electromagnetic field exerts on dipolar matter and construct the non-symmetric energy-momentum tensor of the electromagnetic field in matter which is consistent with that force and with Maxwell equations. We recover Minkowski's expression for the momentum density. We use our results to discuss momentum exchange of an electromagnetic wave-packet which falls into a dielectric block. In particular we show that the wave-packet pulls the block when it enters and drags it when it leaves. The usual form of the center of mass motion t…
We consider the Einstein equation, where the common electromagnetic energy momentum tensor is replaced by its generalized equivalent as suggested in our earlier paper (A.L. Kholmetskii et al. Phys. Scr. 83, 055406 (2011)). Now we show that with this new electromagnetic energy-momentum tensor, the scalar curvature at the location of charges is significantly altered in comparison with the common result, and it even may change its sign. Some implications of the obtained results are discussed.
The total linear electromagnetic field momentum $\mathbf P_{\mathrm{em}}$ of a stationary electric dipole $\mathbf p$ in a static magnetic field $\mathbf B$ is considered. The expression $\mathbf P_{\mathrm{em}} = \frac12\mathbf B \times \mathbf p$, which has previously been implied to hold in all static magnetic field situations, is not valid in general. The contribution of the electromagnetic momentum of the fringing fields of the dipole is discussed. It is shown that when either the static magnetic field or the electric dipole moment is changed, the mechanical impulse on the system equals $…
We investigate here the question raised in literature about the correct expression for the electromagnetic field-momentum, especially when static fields are involved. For this we examine a couple of simple but intriguing cases. First we consider a system configuration in which electromagnetic field momentum is present even though the system is static. We trace the electromagnetic momentum to be present in the form of a continuous transport of electromagnetic energy from one part of the system to another, without causing any net change in the energy of the system. In a second case we show that …
Invoking Maxwell's classical electrodynamics in conjunction with expressions for the electromagnetic (EM) energy, momentum, force, and torque, we use a few simple examples to demonstrate the nature of linear and angular momentum exchange between a wave-packet and a small spherical particle. The linear and angular momenta of the EM field, when absorbed by the particle, will be seen to elicit different responses from the particle.
The self-force of a point charge moving on a rectilinear trajectory is obtained, with no need of any explicit removal of infinities, as the negative of the time rate of change of the momentum of its retarded self-field.
Electromagnetic force and torque are typically derived from a stress tensor in conjunction with Maxwell's equations of classical electrodynamics. In some instances, the Principle of Least Action (built around a Lagrangian) can be used to arrive at the same mathematical expressions of force and torque as those derived from a stress tensor. This paper describes some of the underlying arguments for the existence of a Lagrangian in the case of certain simple physical systems. While some formulations of electromagnetic force and torque admit a Lagrangian, there are other formulations for which a La…
Simply by assuming the first postulate of Special Relativity and by exploring Gedankenexperiments with electromagnetic forces, we suggest that there is a speed limit in the universe, which can be determined as a relation between vacuum permeability and permittivity. We also derive space contraction and time dilatation without referring to light. Finally, we argue that, based on previous works on the derivation of Lorentz s Transformation without light and from our results, it is possible to transform the epistemological status of the Einstein s second postulate from principle into derivation.
The force exerted by an electromagnetic body on another body in relative motion, and its minimal expression, the force on moving charges or \emph{Lorentz' force} constitute the link between electromagnetism and mechanics. Expressions for the force were produced first by Maxwell and later by H. A. Lorentz, but their expressions disagree. The construction process was the result, in both cases, of analogies rooted in the idea of the ether. Yet, the expression of the force has remained despite its production context. We present a path to the electromagnetic force that starts from Ludwig Lorenz' re…
On the basis of a non-local Lagrangian for Maxwell equations in a dispersive medium, the energy-momentum tensor of the field is derived. We obtain the Field equations through variational methods and an extension of Noether theorem for a non-local Lagrangian is obtained as well. The electromagnetic energy-momentum tensor obtained in the general context is then specialized to the case of a field with slowly varying amplitude on a rapidly oscillating carrier.
To model momentum exchange in nonlinear wave-particle interaction, as in amplification devices like traveling-wave tubes, we use an $N$-body self-consistent hamiltonian description based on Kuznetsov's discrete model, and we provide new formulations for the electromagnetic power and the conserved momentum. This approach leads to fast and accurate numerical simulations in time domain and in one dimensional space.
The Lorentz force law of classical electrodynamics requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetic material. In contrast, the Einstein-Laub formulation does not invoke hidden entities. The total force and torque exerted by electromagnetic fields on a given object are independent of whether the force and torque densities are evaluated using the law of Lorentz or that of Einstein and Laub. Hidden entities aside, the two formulations differ only in their predicted force and torque distributions throughout material media.
The Schott term is the third order term in the electromagnetic self force of a charged point particle. The self force may be obtained by integrating the electromagnetic stress-energy-momentum tensor over the side of a narrow hypertube enclosing a section of worldline. This calculation has been repeated many times using two different hypertubes known as the Dirac Tube and the Bhabha Tube, however in previous calculations using a Bhabha Tube the Schott term does not arise as a result of this integration. In order to regain the Lorentz-Abraham-Dirac equation many authors have added an ad hoc comp…
The form of the energy-momentum tensor when a quasimonochromatic field propagates into and through an antireflection-coated, sourceless, transparent, continuous, linear magneto-dielectric medium, initially at rest in the local frame, remains controversial. The Minkowski energy-momentum tensor is the main component of the electromagnetic conservation law. It has been known for over a century that the electromagnetic conservation law is unsound as evidenced by alternative energy-momentum tensors that have been proposed to ameliorate known physical deficiencies (violation of conservation of angul…
The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy-momentum tensor for an electromagnetic field interacting with a linear dielectric medium. Here we investigate the energy and momentum in a closed system composed of a propagating electromagnetic field and a negligibly reflecting dielectric. The Gordon momentum is easily identified as the total momentum by the fact that it is, by virtue of being invariant in time, conserved. We construct continuity equat…
It is shown that the mathematical form, obtained in a recent paper, for the angular momentum of the electromagnetic field in the vicinity of electric charge is equivalent to another form obtained previously by Cohen-Tannoudji, Dupont-Roc and Gilbert. In this version of the paper an improved derivation is given.
When the parameters of electron - extreme power laser interaction enter the regime of dominated radiation reaction, the electron dynamics changes qualitatively. The adequate theoretical description of this regime becomes crutially important with the use of the radiation friction force either in the Lorentz-Abraham-Dirac form, which possess unphysical runaway solutions, or in the Landau-Lifshitz form, which is a perturbation valid for relatively low electromagnetic wave amplitude. The goal of the present paper is to find the limits of the Landau-Lifshitz radiation force applicability in terms o…
Using the Finite Difference Time Domain method, we solve Maxwell's equations numerically and compute the distribution of electromagnetic fields and forces inside material media. The media are generally specified by their dielectric permittivity epsilon(w) and magnetic permeability mu(w), representing small, transparent dielectric and magnetic objects such as platelets and micro-beads. Using two formulations of the electromagnetic force-density, one due to H. A. Lorentz [Collected Papers 2, 164 (1892)], the other due to A. Einstein and J. Laub [Ann, Phys. 331, 541 (1908)], we show that the forc…
A new classical electromagnetic analysis is presented suggesting that the Aharonov-Bohm phase shift is overwhelmingly likely to arise from a classical lag effect based upon classical electromagnetic forces. The analysis makes use of several aspects of classical electromagnetic theory which are unfamiliar to most physicists, including the Darwin Lagrangian, acceleration-based electric fields, internal electromagnetic momentum in a magnet, and a magnet model involving at least three mutually-interacting particles. Only when the acceleration-based electric forces acting on the passing charge are …
We present arguments in favor of the proposition that the momentum of light inside a transparent dielectric medium is the arithmetic average of the Minkowski and Abraham momenta. Using the Lorentz transformation of the fields (and of the coordinates) from a stationary to a moving reference frame, we show the consistent transformation of electromagnetic energy and momentum between the two frames. We also examine the momentum of static (i.e., time-independent) electromagnetic fields, and show that the close connection that exists between the Poynting vector and the momentum density extends all t…
Starting from Stratton-Panofsky-Phillips-Jefimenko equations for the electric and magnetic fields generated by completely arbitrary charge and current density distributions at rest, we derive far-zone approximations for the fields, containing all components, dominant as well as sub-dominant. Using these approximate formulas, we derive general formulas for the total electromagnetic linear momentum and angular momentum, valid at large distances from arbitrary, non-moving charge and current sources.
The problem of assigning a momentum to an electromagnetic wave packet propagating inside an insulator has become known under the name of the Abraham-Minkowski controversy. In the present paper we re-examine the question, first through a power expansion in the polarizability of the medium and assuming the simplest and most natural choice for the force exerted on a dielectric material by an electromagnetic field. It is shown that the Abraham expression is highly favoured. We then show the complete generality of these results.
We examine the force of the electromagnetic radiation on linear, isotropic, homogeneous media specified in terms of their permittivity epsilon and permeability mu. A formula is proposed for the electromagnetic Lorentz force on the magnetization M, which is treated here as an Amperian current loop. Using the proposed formula, we demonstrate conservation of momentum in several cases that are amenable to rigorous analysis based on the classical Maxwell equations, the Lorentz law of force, and the constitutive relations. Our analysis yields precise expressions for the density of the electromagneti…
In this letter we show that for isolated systems for which the energy current density is not equal to the momentum density, that means for systems with non-symmetric energy-momentum, the usual statements of the center of mass motion theorem are not valid. We also discuss the modified version of the theorem that is always valid. Then we present a simple and exactly workable example of an electromagnetic interacting system which illustrates the violation of those standard versions of the center of mass motion theorem. We show that for this system Minkowski's density of linear momentum which yiel…
In a previous work, Optics Communications 284 (2011) 2460--2465, we considered a dielectric medium with an anti-reflection coating and a spatially uniform index of refraction illuminated at normal incidence by a quasimonochromatic field. Using the continuity equations for the electromagnetic energy density and the Gordon momentum density, we constructed a traceless, symmetric energy--momentum tensor for the closed system. In this work, we relax the condition of a uniform index of refraction and consider a dielectric medium with a spatially varying index of refraction that is independent of tim…
