scholarly journals Some remarks on the charging capacitor problem

2018 ◽  
Vol 7 (2) ◽  
pp. 10-12
Author(s):  
C. J. Papachristou
Keyword(s):  
Electromagnetic Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Displacement Current ◽  
Standard Textbook ◽  
Maxwell Displacement Current

The charging capacitor is the standard textbook and classroom example for explaining the concept of the so-called Maxwell displacement current. A certain aspect of the problem, however, is often overlooked. It concerns the conditions for satisfaction of the Faraday-Henry law inside the capacitor. Expressions for the electromagnetic field are derived that properly satisfy all four of Maxwell’s equations in that region.

A Decomposition of the Electromagnetic Field — Application to the Darwin Model

1997 ◽  
Vol 07 (08) ◽  
pp. 1085-1120 ◽  
Author(s):  
P. Ciarlet ◽  
E. Sonnendrücker
Keyword(s):  
Electromagnetic Field ◽  
Electric Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Computational Cost ◽  
Field Application ◽  
Displacement Current ◽  
Computational Domain ◽  
Numerical Resolution ◽  
Simply Connected

In many cases, the numerical resolution of Maxwell's equations is very expensive in terms of computational cost. The Darwin model, an approximation of Maxwell's equations obtained by neglecting the divergence free part of the displacement current, can be used to compute the solution more economically. However, this model requires the electric field to be decomposed into two parts for which no straightforward boundary conditions can be derived. In this paper, we consider the case of a computational domain which is not simply connected. With the help of a functional framework, a decomposition of the fields is derived. It is then used to characterize mathematically the solutions of the Darwin model on such a domain.

scholarly journals Convection Displacement Current and Generalized Form of Maxwell–Lorentz Equations

1997 ◽  
Vol 12 (01) ◽  
pp. 1-24 ◽  
Author(s):  
Andrew E. Chubykalo ◽  
Roman Smirnov-Rueda
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Gauge Condition ◽  
Classical Electrodynamics ◽  
Displacement Current ◽  
Field Equations ◽  
Charge System ◽  
Basic Field ◽  
Maxwell Displacement Current ◽  
Magnetic Potentials

Some mathematical inconsistencies in the conventional form of Maxwell's equations extended by Lorentz for a single charge system are discussed. To surmount these in the framework of Maxwellian theory, a novel convection displacement current is considered as additional and complementary to the famous Maxwell displacement current. It is shown that this form of the Maxwell–Lorentz equations is similar to that proposed by Hertz for electrodynamics of bodies in motion. Original Maxwell's equations can be considered as a valid approximation for a continuous and closed (or going to infinity) conduction current. It is also proved that our novel form of the Maxwell–Lorentz equations is relativistically invariant. In particular, a relativistically invariant gauge for quasistatic fields has been found to replace the non-invariant Coulomb gauge. The new gauge condition contains the famous relationship between electric and magnetic potentials for one uniformly moving charge that is usually attributed to the Lorentz transformations. Thus, for the first time, using the convection displacement current, a physical interpretation is given to the relationship between the components of the four-vector of quasistatic potentials. A rigorous application of the new gauge transformation with the Lorentz gauge transforms the basic field equations into a pair of differential equations responsible for longitudinal and transverse fields, respectively. The longitudinal components can be interpreted exclusively from the standpoint of the instantaneous "action at a distance" concept and leads to necessary conceptual revision of the conventional Faraday–Maxwell field. The concept of electrodynamics dualism is proposed for self-consistent classical electrodynamics. It implies simultaneous coexistence of instantaneous long-range (longitudinal) and Faraday–Maxwell short-range (transverse) interactions that resembles in this aspect the basic idea of Helmholtz's electrodynamics.

Electromagnetic field behavior of 3D Maxwell's equations for chiral media

2019 ◽  
Vol 379 ◽  
pp. 118-131 ◽  
Author(s):  
Tsung-Ming Huang ◽  
Tiexiang Li ◽  
Ruey-Lin Chern ◽  
Wen-Wei Lin
Keyword(s):  
Electromagnetic Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Chiral Media ◽  
Field Behavior

XI.—Electromagnetic Phenomena in a Uniform Gravitational Field

1932 ◽  
Vol 51 ◽  
pp. 71-79 ◽  
Author(s):  
D. Meksyn
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Suitable Choice ◽  
Fundamental Tensor

In two recent papers Professor E. T. Whittaker has solved the electromagnetic equations for the case of a uniform gravitational field. The fundamental tensor associated with such a field makes the Riemannian tensor vanish, since such a field can be transformed away by a suitable choice of coordinates. This property enables us to find the electromagnetic field in a uniform gravitational field without solving Maxwell's equations, but by a mere transformation of co-ordinates.

scholarly journals Origin of Gauge Theories in Electrodynamics

2021 ◽  
Author(s):  
Jay Solanki
Keyword(s):  
Field Theory ◽  
Electromagnetic Field ◽  
Gauge Theory ◽  
Gauge Invariance ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Gauge Theories ◽  
Degree Of Freedom ◽  
Potential Formulation ◽  
Electromagnetic Field Theory

<div>The potential formulation has significant advantages over field formulation in solving complicated problems in electromagnetic field theory. One essential part of electromagnetic field theory's potential formulation is gauge invariance and gauge theories because it provides an extra degree of freedom. By using this extra degree of freedom, we can solve complicated electromagnetic problems quickly. Thus, it is necessary to include a systematic explanation of gauge theories in teaching electromagnetic theory. However, textbooks usually formulate gauge theories by using Maxwell's equations of electromagnetism, by using vector calculus identities. However, this method of formulation of gauge theories does not give a clear idea about the origin of gauge theories and gauge invariance in electromagnetism. Here the author formulates gauge theories from wave equations of the electric and magnetic fields instead of directly using Maxwell's equations. This method generalizes all gauge theories like Lorenz gauge theory, Coulomb gauge theory, Etc. Gauge theory, because of the way the author derives it, gives a distinct idea about the mathematical origin of the gauge theories and gauge invariance in electromagnetic field theory. Thus, the author reviews the origin of gauge theories in electromagnetic field theory and develops a distinct and effective method to introduce gauge theory in the teaching of electromagnetic field theory that can provide better understanding of the topic to undergraduate students.</div><div><br></div>

Fields—Maxwell’s Equations

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Dipole Moments ◽  
Scalar Fields ◽  
Vector Calculus ◽  
Klein Gordon ◽  
Energy And Momentum ◽  
Scalar Potentials

Chapter 3 explores the concept of the field, which is necessary to describe forces without resorting to action at a distance, and uses it to describe electromagnetism, as encapsulated by the Maxwell equations. First, scalar fields and the Klein–Gordon equation are discussed. Vector calculus is introduced. The physical meaning of Maxwell’s equations is explained. The equations are then solved for electrostatic fields. Non-uniform charge distributions and dipole moments are discussed. The vector and scalar potentials are introduced. Electromagnetic wave solutions of Maxwell’s equations are found and the Hertz experiment is described. Magnetostatics is discussed briefly. The Lorentz force is described and used to determine the motion of a charged particle in a cyclotron or synchrotron. The action principle for electromagnetism is described. The energy and momentum carried by the electromagnetic field are calculated. The reaction of a charged particle to its own electromagnetic field is considered.

On the instability of localized EM pulses in nonlinear electrodynamics with account of temperature effects

2021 ◽  
Vol 35 (10) ◽  
pp. 2150176
Author(s):  
Mikhail B. Belonenko ◽  
Natalia N. Konobeeva ◽  
Alexander V. Zhukov
Keyword(s):  
Electromagnetic Field ◽  
Pair Production ◽  
Temperature Effects ◽  
Electromagnetic Pulse ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Nonlinear Electrodynamics ◽  
Influence Of Temperature ◽  
Schwinger Mechanism

Based on Maxwell’s equations, we study the development of electromagnetic pulse instability in nonlinear electrodynamics beyond approximation of slowly varying amplitudes and phases. The action was chosen from the Heisenberg–Euler Lagrangian based on the invariants of the electromagnetic field. We analyze the scenario for the evolution of instability, which turns out to be consistent with the earlier conclusion done within the approximation of slowly varying amplitudes and phases. In this study, we take into account the influence of temperature. The rate of pair production under the Schwinger mechanism is estimated.

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