Modeling a Stationary Electromagnetic Field Based on the Maxwell Equations

2021 ◽  
Vol 13 (2) ◽  
pp. 254-262
Author(s):  
M. B. Markov ◽  
S. V. Parot’kin
Keyword(s):  
Electromagnetic Field ◽  
Maxwell Equations

SOLITARY WAVES OF THE NONLINEAR KLEIN-GORDON EQUATION COUPLED WITH THE MAXWELL EQUATIONS

2002 ◽  
Vol 14 (04) ◽  
pp. 409-420 ◽  
Author(s):  
VIERI BENCI ◽  
DONATO FORTUNATO FORTUNATO
Keyword(s):  
Electromagnetic Field ◽  
Solitary Wave ◽  
Electric Field ◽  
Solitary Waves ◽  
Maxwell Equations ◽  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation

This paper is divided in two parts. In the first part we construct a model which describes solitary waves of the nonlinear Klein-Gordon equation interacting with the electromagnetic field. In the second part we study the electrostatic case. We prove the existence of infinitely many pairs (ψ, E), where ψ is a solitary wave for the nonlinear Klein-Gordon equation and E is the electric field related to ψ.

scholarly journals GENERALIZED EINSTEIN–MAXWELL FIELD EQUATIONS IN THE PALATINI FORMALISM

2013 ◽  
Vol 22 (04) ◽  
pp. 1350017 ◽  
Author(s):  
GINÉS R. PÉREZ TERUEL
Keyword(s):  
Electromagnetic Field ◽  
Algebraic Equation ◽  
Ricci Tensor ◽  
Maxwell Equations ◽  
Natural Generalization ◽  
New Method ◽  
Maxwell Field ◽  
Field Equations ◽  
Palatini Formalism

We derive a new set of field equations within the framework of the Palatini formalism. These equations are a natural generalization of the Einstein–Maxwell equations which arise by adding a function [Formula: see text], with [Formula: see text] to the Palatini Lagrangian f(R, Q). The result we obtain can be viewed as the coupling of gravity with a nonlinear extension of the electromagnetic field. In addition, a new method is introduced to solve the algebraic equation associated to the Ricci tensor.

Bound state in a model of electromagnetic field interacting with a material plan

2020 ◽  
Vol 35 (21) ◽  
pp. 2050170
Author(s):  
Yu. M. Pismak ◽  
D. Shukhobodskaia
Keyword(s):  
Electromagnetic Field ◽  
Maxwell Equations ◽  
Singular Potential ◽  
Bound State ◽  
Material Object ◽  
Two Dimensional ◽  
Isotropic Plane ◽  
Chern Simons ◽  
Material Plane ◽  
State Of Field

In the model with Chern-Simons potential describing the coupling of electromagnetic field with a two-dimensional material, the possibility of the appearance of bound field states, vanishing at sufficiently large distances from interacting with its macro-objects, is considered. As an example of such two-dimensional material object we consider a homogeneous isotropic plane. Its interaction with electromagnetic field is described by a modified Maxwell equation with singular potential. The analysis of their solution shows that the bound state of field cannot arise without external charges and currents. In the model with currents and charges the Chern-Simons potential in the modified Maxwell equations creates bound state in the form of the electromagnetic wave propagating along the material plane with exponentially decreasing amplitude in the orthogonal to its direction.

A Working of Eddy Current Transducers under Control of Ferromagnetic Pipes in Condition of Insufficient Magnetic Saturation

2013 ◽  
Vol 467 ◽  
pp. 528-530
Author(s):  
Kai Yu Hao ◽  
Vadim Miroshnikov
Keyword(s):  
Electromagnetic Field ◽  
Numerical Calculation ◽  
Eddy Current ◽  
Maxwell Equations ◽  
Control Sample ◽  
Magnetic Saturation ◽  
Method Of Calculation ◽  
Current Transducer ◽  
Object Of Control ◽  
Eddy Current Transducer

The numerical method of calculation of electromagnetic field in a control sample at a time of work of encircling eddy current transducer is offered. The method is based on a numerical solution of the two Maxwell equations, which connect a change of electrical and magnetic fields. It allows to make calculations taking into account the actual value of magnetic inductivity of metal and to get results in any form, convenient for further interpretations. For the calculation of the encircling eddy current transducer the equivalent circuit of defect as step junction is offered. The numerical calculation shows, that the greatest sensitivity of the transducer is achieved when the value of magnetic permeability of the object of control is approximately 10-30. Therefore, it is not necessary to lead the material of the object of control up to satiety, as it considered before.

scholarly journals THE MAXWELL LAGRANGIAN IN PURELY AFFINE GRAVITY

2008 ◽  
Vol 23 (03n04) ◽  
pp. 567-579 ◽  
Author(s):  
NIKODEM J. POPŁAWSKI
Keyword(s):  
Electromagnetic Field ◽  
Ricci Tensor ◽  
Maxwell Equations ◽  
Legendre Transformation ◽  
Conformal Transformations ◽  
Field Tensor ◽  
Metric Tensor ◽  
Hamiltonian Density ◽  
Electromagnetic Field Tensor ◽  
Affine Gravity

The purely affine Lagrangian for linear electrodynamics, that has the form of the Maxwell Lagrangian in which the metric tensor is replaced by the symmetrized Ricci tensor and the electromagnetic field tensor by the tensor of homothetic curvature, is dynamically equivalent to the Einstein–Maxwell equations in the metric–affine and metric formulation. We show that this equivalence is related to the invariance of the Maxwell Lagrangian under conformal transformations of the metric tensor. We also apply to a purely affine Lagrangian the Legendre transformation with respect to the tensor of homothetic curvature to show that the corresponding Legendre term and the new Hamiltonian density are related to the Maxwell–Palatini Lagrangian for the electromagnetic field. Therefore the purely affine picture, in addition to generating the gravitational Lagrangian that is linear in the curvature, justifies why the electromagnetic Lagrangian is quadratic in the electromagnetic field.

scholarly journals The Dual Continuity Equations

2018 ◽  
Author(s):  
Arbab Arbab ◽  
Norah N. Alsaawi
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Gauge Invariance ◽  
Maxwell Equations ◽  
Continuity Equation ◽  
Mathematical Structure ◽  
Magnetic Monopoles ◽  
System Of Equations ◽  
Duality Transformation ◽  
Continuity Equations

The ordinary continuity equation relating the current and density of a system is extended to incorporate systems with dual (longitudinal and transverse) currents. Such a system of equations is found to have the same mathematical structure as that of Maxwell equations. The horizontal and transverse currents and the densities associated with them are found to be coupled to each other. Each of these quantities are found to obey a wave equation traveling at the velocity of light in vacuum. London's equations of super-conductivity are shown to emerge from some sort of continuity equations. The new London's equations are symmetric and are shown to be dual to each other. It is shown that London's equations are Maxwell's equations with massive electromagnetic field (photon). These equations preserve the gauge invariance that is broken in other massive electrodynamics. The duality invariance may allow magnetic monopoles to be present inside superconductors. The new duality is called the comprehensive duality transformation.

The Maxwell equations

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Variational Principle ◽  
Maxwell Equations ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Field Energy ◽  
Total Charge ◽  
Faraday’S Law ◽  
System Energy

This chapter presents Maxwell equations determining the electromagnetic field created by an ensemble of charges. It also derives these equations from the variational principle. The chapter studies the equation’s invariances: gauge invariance and invariance under Poincaré transformations. These allow us to derive the conservation laws for the total charge of the system and also for the system energy, momentum, and angular momentum. To begin, the chapter introduces the first group of Maxwell equations: Gauss’s law of magnetism, and Faraday’s law of induction. It then discusses current and charge conservation, a second set of Maxwell equations, and finally the field–energy momentum tensor.

scholarly journals A Class of Solutions of Einstein-Maxwell Equations with the Cosmological Constant

1974 ◽  
Vol 64 ◽  
pp. 188-190
Author(s):  
J. F. Plebański
Keyword(s):  
Electromagnetic Field ◽  
Cosmological Constant ◽  
Maxwell Equations ◽  
Type D ◽  
The Common ◽  
Image Position

Working in the signature (+ + + -) and units such that G = 1 = c, it was found a solution of Einstein-Maxwell equations with λ (without current and pseudo-current). In real coordinates xμ=(p, σ, q, τ) the solutions is: (1)(2) where (3) is pure imaginary; in (1) ‘d’ denotes the external differential]. Not all constants m0, n0, e0, g0, b, ∊, λ are physically significant: by re-scaling coordinates ∊ can be made equal to +1,0, or −1. The solution is of the type D: the double Debever-Penrose vectors (4) have the common complex expansion Z = (q + ip)-1. Among C(a)'s only C(3) given by: (5) is in general ≠0. The invariants of the electromagnetic field are: (6)

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