Galilean symmetry of Maxwell's equations in classical electrodynamics

1985 ◽  
Vol 28 (8) ◽  
pp. 672-676
Author(s):  
G. A. Kotel'nikov
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Classical Electrodynamics ◽  
Galilean Symmetry

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 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 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.

Sumudu Applications to Maxwell's Equations

PIERS Online ◽  
2009 ◽  
Vol 5 (4) ◽  
pp. 355-360 ◽  
Author(s):  
Fethi Bin Muhammad Belgacem
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations

Maxwell’s Equations versus Newton’s Third Law

2018 ◽  
Author(s):  
Glyn Kennell ◽  
Richard Evitts
Keyword(s):  
Electric Fields ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Simulated Data ◽  
Numerical Data ◽  
Transport Equations ◽  
Concentration Gradients ◽  
Third Law

The presented simulated data compares concentration gradients and electric fields with experimental and numerical data of others. This data is simulated for cases involving liquid junctions and electrolytic transport. The objective of presenting this data is to support a model and theory. This theory demonstrates the incompatibility between conventional electrostatics inherent in Maxwell's equations with conventional transport equations. <br>

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