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.

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 Aplikasi Aljabar Geometris Pada Teori Elektrodinamika Klasik

2012 ◽  
Vol 1 (2) ◽  
pp. 89
Author(s):  
Joko Purwanto
Keyword(s):  
Geometric Algebra ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Classical Electrodynamic ◽  
Classical Electrodynamics ◽  
Theoretical Formulation

In this paper geometric algebra and its aplication in the theory of classical electrodynamic will  be studied. Geometric algebra provide many simplification and new insight in the theoretical formulation and physical aplication of theory. In this work has been studied aplication of geometric algebra in classical electrodynamics especially Maxwell’s equations. Maxwell’s equations was formulated in one compact equation ÑF=J. The various equation parts are easily identified by their  grades.

scholarly journals The quantum theory of dispersion in metallic conductors

1929 ◽  
Vol 124 (794) ◽  
pp. 409-422 ◽  
Keyword(s):  
Electrical Conductivity ◽  
Dielectric Constant ◽  
Electromagnetic Field ◽  
Quantum Theory ◽  
Isotropic Medium ◽  
Electromagnetic Waves ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Classical Electrodynamics ◽  
Metallic Conductivity

1. Formulation of the problem. - The propagation of electromagnetic waves in a homogeneous isotropic medium showing metallic conductivity has been treated phenomenologically on the basis of classical electrodynamics. If in Maxwell's equations for the electromagnetic field curl E = - 1/ c ∂B/∂ t , curl H = 1/ c (∂D/∂ t + 4πI), div D = 4πρ, div B = 0, we assume that D = εE, B = μH, I = σE, (1) where e is the dielectric constant, u the permeability and q the electrical conductivity, we get curl E = - μ/c ∂H/∂ t , curl H = 1/ c (ε ∂E/∂ t 4πσE), div E = 4πρ/ε. div H =0.

scholarly journals Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 987
Author(s):  
Tomasz P. Stefański ◽  
Jacek Gulgowski
Keyword(s):  
Wave Propagation ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Momentum Conservation ◽  
Point Of View ◽  
Classical Electrodynamics ◽  
Classical Solutions ◽  
Systems With Memory ◽  
Energy And Momentum ◽  
With Memory

In this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their properties from the point of view of classical electrodynamics, i.e., energy and momentum conservation, reciprocity, causality. Afterwards, we derive classical solutions for wave-propagation problems, assuming helical, spherical, and cylindrical symmetries of solutions. The results are supported by numerical simulations and their analysis. Discussion of relations between the TF Schrödinger equation and TF electrodynamics is included as well.

Sign in / Sign up

Export Citation Format

Share Document