Potential In Electrodynamics Research Articles

NUMERICAL DISSIPATIVE METHOD FOR THE ELECTROSTATIC PROBLEM OF A TWO-DIMENSIONAL SYSTEM OF DIELECTRICS AND CONDUCTORS

A numerical method is implemented for solving the damped wave equation for the electrodynamic potential in regions with no charges and no free currents. The damping is obtained by the artificial introduction of a dissipative term, proportional to the rate of change of the potential, in the wave equation. This is carried out in order to obtain the potential and electric field of a two-dimensional electrostatic system of conductors and dielectrics with arbitrary spatial arrangements once the system has reached equilibrium. As an immediate application, the capacity per unit length of the system is calculated from the obtained electrostatic energy. In particular, the method is applied for typical values of the dielectric constant of reinforced concrete columns.

Modeling Electromagnetic Wave Phenomena in Large Quantum Systems [Special Series: Guest Editorial

The articles in this special section focuses on quantum technologies. This is a third article in a special series on this topic. While the first two were concerned with basic theory, this article is the first to tackle the practical simulation of realistic systems, such as nanoantennas. Furthermore, it departs from the classical electromagnetics homogenization of material properties, conventionally represented by permittivity and permeability, by turning to the time-dependent density functional theory (TDDFT), which aims at a quantum mechanics-based analysis of light–matter interactions on the atomistic level. Following a basic introduction into the DFT and TDDFT theory, its formulation in the Lorenz gauge is presented. It is shown how the efficient computation of the electrodynamic potentials in the Lorenz gauge can help to achieve the goal of atomic-scale simulations of nanodevices, which include both quantum atomistic and longer-range electromagnetic retardation effects. Finally, the computational challenge and a road map for future calculations are shown.

Three-Dimensional Simulation of Solution-Contact Electrolytic Dissolution

Electrochemical dissolution is a process where a metal is dissolved via oxidation and can be controlled through electrolyte properties, electrolyte flow, and applied potential. Electrochemical dissolution is employed in many manufacturing applications such as electrochemical machining, electrochemical pickling, metal refining, metal surface finishing, etc. Most of these dissolution applications use a traditional metal-contact method (metal being dissolved is in direct contact with the anode); however, some applications will have phenomena that cause operational issues, safety issues, or damage to the dissolver components. These phenomena include (1) difficulty maintaining contact, (2) arcing/sparking[1] in a flammable environment, which occurs because of a build-up of oxide, or (3) overheating, which can cause melting during dissolution. To avoid unsafe or destructive phenomena, a solution-contact electrolytic dissolution (SCED) method (metal being dissolved is only in contact with electrolyte) can be employed. Here, a three-dimensional model is developed to simulate solution-contact electrolytic dissolution in a small-scale system for the first time.A representation of a small-scale SCED system is shown in Figure 1. This system takes place within a HNO3 solution and includes a Pt anode and cathode where water-splitting and hydrogen formation occur, respectively. The sample coupon (our target for dissolution) acts as a physical barrier, so hydrogen ions gather on the anode-side of the sample coupon, forming a positively charged region, while H+ ions are consumed on the cathode-side of the coupon, leaving a negatively charged region. This imbalance of charge, along with the potential profile that forms within the system when voltage is applied to the anode, drive reactions to occur on the surface of the sample coupon. The reactions include the ejection of a metal ion, Mν+, towards the negatively charged region, while H+ ions combine with the free e-s released from the metal dissolution reaction to form hydrogen gas. The model theory developed here is able to predict stray currents in the solution-phase, a useful design tool to avoid corrosion of other components within an electrochemical system. [2-3] Discussion over important phenomena that must be properly represented to simulate this electrolytic dissolution process will take place, including electrochemical species transport, local surface reaction rates (using Butler-Volmer kinetics), and electrodynamic potential.

Retarded Potentials in Fractional Electrodynamics

A general expression is obtained for retarded potentials for a system of equations of macroscopic electrodynamics with fractional Caputo derivatives with respect to time. An analog of the Lienard–Wiechert potentials is obtained. All expressions contain a nonlocal (time-distributed) delay, which takes the temporal dispersion in the system into account.

A study on the static field of a point charge in three-dimensional electrodynamics

The static field potential in quantum electrodynamics in the space of three dimensions (QED3) produced by a point charge was investigated taking into account the polarization of the vacuum. The polarization operator is taken in the approximation which was previously used to study the dynamic violation of chiral symmetry in QED3. An approximate analytical analysis is accompanied by numerical calculations; there is a good quantitative agreement between the results obtained using these methods. The case of massive dynamical fermions is considered. The limiting transition to the massless case is analyzed, as well as the confinement problem occurring in this model.

Векторный потенциал, эффект Ааронова-Бома и электродинамика в токамаке

В статье показано, что векторный потенциал в электродинамике является вспомогательной функцией, а в некоторых случаях может включать в себя одновременно не силовое магнитное поле. В связи с этим в эффекте Ааронова-Бома обладающая зарядом квантовая частица взаимодействует не с потенциалом, а с не силовым магнитным полем. При этом теорема Стокса, примененная к векторному потенциалу, остается верной и применимой для объяснения эффекта Ааронова-Бома за счет присутствия в векторном потенциале не силового тороидального магнитного поля. Электродинамика в токамаке находит объяснение также в терминах силовых и не силовых магнитных полей.

Contextualização e tradução do artigo “Demonstração dos teoremas relativos às ações Eletrodinâmicas”, escrito por J. Bertrand.

J. Bertrand costuma ser conhecido por suas contribuições para a mecânica e para a matemática, mas pouco se sabe sobre sua predileção para a eletrodinâmica. Assim, de maneira inédita, apresentamos a contextualização e a tradução comentada, do francês para o português, do artigo “Demonstração dos teoremas relativos às ações eletrodinâmicas”. Nesse artigo, Bertrand deduz catorze teoremas fundamentais da eletrodinâmica. Entre outros pontos, tece considerações a respeito da validade da 3a lei de Newton na eletrodinâmica, deduz a Força de Ampère de apenas dois fatos experimentais – diminuindo o número dos casos de equilíbrio necessários de quatro para dois – obtém o teorema equivalente ao divergente do campo magnético (uma das equações de Maxwell), faz considerações sobre o potencial eletrodinâmico, e deduz a relação entre um dipolo magnético e um circuito fechado plano.

The quantum-optics Hamiltonian in the Multipolar gauge

This article deals with the fundamental problem of light-matter interaction in the quantum theory. Although it is described through the vector potential in quantum electrodynamics, it is believed by some that a hamiltonian involving only the electric and the magnetic fields is preferable. In the literature this hamiltonian is known as the Power-Zienau-Woolley hamiltonian. We question its validity and show that it is not equivalent to the minimal-coupling hamiltonian. In this article, we show that these two hamiltonians are not connected through a gauge transformation. We find that the gauge is not fixed in the Power-Zienau-Woolley hamiltonian. The interaction term is written in one gauge whereas the rest of the hamiltonian is written in another gauge. The Power-Zienau-Woolley hamiltonian and the minimal-coupling one are related through a unitary transformation that does not fulfill the gauge fixing constraints. Consequently, they predict different physical results. In this letter, we provide the correct quantum theory in the multipolar gauge with a hamiltonian involving only the physical fields.

On limiting velocity with Weber-like potentials

This work analyses the problem of a charge moving perpendicularly to the plates of a charged capacitor. The results obtained from the current theoretical framework (Maxwell–Lorentz electromagnetism and special relativity theory) are compared with the results obtained from Weber’s electrodynamic potential, with the Phipps’s potential and a new potential proposed here. The aim of this comparison is to analyse the causes of the inability of these Weber-like potentials to predict the existence of a limiting velocity for this problem, as special relativity theory does indeed predict and many experimental results confirm. To overcome this incapacity, the need to employ an effective potential to solve the capacitor problem is shown. In the adoption of this strategy, it is shown that the potential proposed here reproduces the same relativistic result. Finally, the origin and possible interpretation of the aforementioned effective potential are analysed.

Lanczos potential for some non-vacuum spacetimes

The Lanczos potential is a general relativity analogue of potential in electrodynamics. This potential can be obtained by solving Weyl-Lanczos relations. This computation is easy in the case of vacuum spacetimes and/or spacetimes of particular Petrov type, while obtaining the Lanczos potential for arbitrary spacetime is very difficult. In this paper, we have obtained the Lanczos potential for non-vacuum spacetimes: Vaidya spacetime and Van Stockum spacetime (which is not of any Petrov type).

Electromagnetic potential in pre-metric electrodynamics: Causal structure, propagators and quantization

An axiomatic approach to electrodynamics reveals that Maxwell electrodynamics is just one instance of a variety of theories for which the name electrodynamics is justified. They all have in common that their fundamental input are Maxwell's equations $\textrm{d} F = 0$ (or $F = \textrm{d} A$) and $\textrm{d} H = J$ and a constitutive law $H = # F$ which relates the field strength two-form $F$ and the excitation two-form $H$. A local and linear constitutive law defines what is called local and linear pre-metric electrodynamics whose best known application are the effective description of electrodynamics inside media including, e.g., birefringence. We analyze the classical theory of the electromagnetic potential $A$ before we use methods familiar from mathematical quantum field theory in curved spacetimes to quantize it in a locally covariant way. Our analysis of the classical theory contains the derivation of retarded and advanced propagators, the analysis of the causal structure on the basis of the constitutive law (instead of a metric) and a discussion of the classical phase space. This classical analysis sets the stage for the construction of the quantum field algebra and quantum states. Here one sees, among other things, that a microlocal spectrum condition can be formulated in this more general setting.

Eigenfunctions for a Quantum Wire on a Single Electron at Its Surface and in the Quantum Well with Beaded Fractional Quantized States for the Fractional Charges

We developed energy profiles for the fractional quantized states both on the surface of electron due to overwhelming centrifugal potentials and inside the electron at different locations of the quantum well due to overwhelming attractive electrodynamic potentials. The charge as a physical constant and single entity is taken as density and segments on their respective sub-quanta (floats on sub quanta) and hence the fractional charge quantiz at in. There is an integrated oscillatory effect which ties all fractional quantized states both on the surface and in the interior of the volume of an electron. The eigenfunctions, i.e., the energy profiles for the electron show the shape of a string or a quantum wire in which fractional quantized states are beaded. We followed an entirely different approach and indeed thesis to reproducing the eigenfunctions for the fractional quantized states for a single electron. We produced very fascinating mathematical formulas for all such cases by using Hermite and Laguerre polynomials, spherical based and Neumann functions and indeed asymptotic behavior of Bessel and Neumann functions. Our quantization theory is dealt in the momentum space.

Vector potentials in gauge theories in flat spacetime

A recent suggestion that vector potentials in electrodynamics (ED) are nontensorial objects under four-dimensional (4D) frame rotations is found to be both unnecessary and confusing. As traditionally used in ED, a vector potential $A$ always transforms homogeneously under 4D rotations in spacetime, but if the gauge is changed by the rotation, one can restore the gauge back to the original gauge by adding an inhomogeneous term. It is then not a 4-vector, but two 4-vectors: one for rotation and one for translation. For such a gauge, it is much more important to preserve explicit homogeneous Lorentz covariance by simply skipping the troublesome gauge-restoration step. A gauge-independent separation of $A$ into a dynamical term and a nondynamical term in Abelian gauge theories is redefined more generally as the terms caused by the presence and absence, respectively, of the 4-current term in the inhomogeneous Maxwell equations for $A$. Such a separation cannot in general be extended to non-Abelian theories where $A$ satisfies nonlinear differential equations. However, in the linearized iterative solution that is perturbation theory, the usual Abelian quantizations in the usual gauges can be used. Some nonlinear complications are briefly reviewed.

One-Loop Contribution to the Matter-Driven Expansion of the Universe

Standard perturbative quantum gravity formalism is applied to compute the lowest order corrections to the spatially flat cosmological FLRW solution governed by ordinary matter. The presented approach is analogous to the one used to compute quantum corrections to the Coulomb potential in electrodynamics, or to the approach applied in computation of quantum corrections to the Schwarzschild solution in gravity. In this framework, it is shown that the corrections to the classical metric coming from the one-loop graviton vacuum polarization (self-energy) have (UV cutoff dependent) repulsive properties, which could be not negligible in the very early Universe.

The influence of the leg cutting on the core losses in the amorphous modular transformers

Purpose – In a modular transformer with a wounded amorphous core, the authors should make some cutting to limit the eddy currents in its magnetic ribbon. The purpose of this paper is to deal with 3D magnetic field analysis, including the eddy currents induced by varying frequency of power. The influence of the core leg cutting on the power losses values, in the three variants of a one-phase modular transformer structure, has been presented. Design/methodology/approach – 3D field problems including eddy currents of various frequency were analysed using the electrodynamic potentials and V within the finite element method. The wave method and iterative one of the laminated core homogenization, have been employed. The values of the calculated losses have been verified experimentally. Findings – The reduction of the core losses by axial cutting of the transformer legs is an efficient approach for the loss limitation. The wave method is not acceptable for homogenization of the amorphous core for its operation a...

Finite field-energy and interparticle potential in logarithmic electrodynamics

We pursue an investigation of logarithmic electrodynamics, for which the field energy of a point-like charge is finite, as happens in the case of the usual Born–Infeld electrodynamics. We also show that, contrary to the latter, logarithmic electrodynamics exhibits the feature of birefringence. Next, we analyze the lowest-order modifications for both logarithmic electrodynamics and for its non-commutative version, within the framework of the gauge-invariant path-dependent variables formalism. The calculation shows a long-range correction ( $$1/r^5$$ -type) to the Coulomb potential for logarithmic electrodynamics. Interestingly enough, for its non-commutative version, the interaction energy is ultraviolet finite. We highlight the role played by the new quantum of length in our analysis.

On the ‘second potential’ in electrodynamics

In the strict absence of charge, it is manifestly possible to introduce two potentials in electrodynamics, one of which is well known and can be said to be of magnetic character whilst the other is rather less well known and can be said to be of electric character. Remarkably, both potentials make explicit and seemingly natural appearances in the fundamental description of the angular momentum of freely propagating light. In the present paper, we review and examine the ‘second potential’ and, in particular, consider its significance in the presence of charge.

Reflector Impulse Antenna of High Electrodynamic Potential

A few versions of impulse antennas are studied with the aim of suggesting an optimal design of the feed line and radiator for the reflector-based antenna and ensuring operation of the facility at high voltages and under field conditions. The high-voltage system described as the final choice is intended for shaping and radiating electromagnetic pulses of ultrashort duration, while maintaining the proper electric strength of its components. It is characterized by an electrodynamic potential (field-range product) W = 1.2 MV. The system is a variant of the half-reflector impulse antenna design, involving a half-circular parabolic reflector that is excited through a nonuniform dual-line feeder of simple geometry.

On retardation, radiation and Liénard–Wiechert type potentials in electrodynamics and elastodynamics

The aim of this paper is to investigate the fundamental problems of retardation and radiation caused by non-uniformly moving point sources using the theories of electrodynamics and elastodynamics. This paper investigates and compares the retarded electromagnetic fields and the retarded elastodynamic fields. For the non-uniform motion of a general point source, the Liénard–Wiechert type potentials and the radiation and nonradiation fields are derived for a point charge and for a point force.

Gauge-free Coleman–Weinberg potential

The gauge-dependence of the one loop Coleman-Weinberg effective potential in scalar electrodynamics is resolved using a gauge-free approach not requiring any gauge-fixing of quantum fluctuations of the photon degrees of freedom. This leads to a unique dynamical ratio at one loop of the Higgs mass to the photon mass. We compare our approach and results with those obtained in geometric framework of DeWitt and Vilkovisky, which maintains invariance under field redefinitions as well as invariance under background gauge transformations, but {\it requires}, in contrast to our approach, gauge fixing of {\it fluctuating} photon fields. We also discuss possible modifications of the Coleman-Weinberg potential if we adapt the DeWitt-Vilkovisky method to our gauge-free approach for scalar QED.