On the Relativistic Invariance of Maxwell's Equation

1999 ◽  
Vol 54 (10-11) ◽  
pp. 637-644 ◽  
Author(s):  
Oleg D. Jefimenko
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Common Knowledge ◽  
Physical Significance ◽  
Relativistic Invariance ◽  
Maxwell’S Equation ◽  
Maxwell's Equation

It is common knowledge that Maxwell's electromagnetic equations are invariant under relativistic transformations. However the relativistic invariance of Maxwell's equations has certain heretofore over-looked peculiarities. These peculiarities point out to the need of reexamining the physical significance of some basic electromagnetic formulas and equations.

The Electric Field in Maxwell's Equations

1978 ◽  
Vol 15 (2) ◽  
pp. 169-171 ◽  
Author(s):  
Z. L. Budrikis
Keyword(s):  
Electric Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Coulomb Force ◽  
Maxwell’S Equation ◽  
Ohm’S Law ◽  
Ohm's Law ◽  
Maxwell's Equation

The field E in Maxwell's equation curl E = – δB/δ t is limited to induction and Coulomb force. It does not extend to all phenomena that are included in E of Ohm's law, J = σE. Maxwell's equation would need another term to account for additional vorticity of the E in Ohm's law.

scholarly journals Gauge independent quantum gravitational corrections to Maxwell’s equation

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
S. Katuwal ◽  
R. P. Woodard
Keyword(s):  
Field Equation ◽  
Maxwell Equation ◽  
Maxwell’S Equations ◽  
Vacuum Polarization ◽  
Maxwell's Equations ◽  
Flat Space ◽  
Effective Field ◽  
Maxwell’S Equation ◽  
Gauge Dependence ◽  
Maxwell's Equation

Abstract We consider quantum gravitational corrections to Maxwell’s equations on flat space background. Although the vacuum polarization is highly gauge dependent, we explicitly show that this gauge dependence is canceled by contributions from the source which disturbs the effective field and the observer who measures it. Our final result is a gauge independent, real and causal effective field equation that can be used in the same way as the classical Maxwell equation.

scholarly journals Unification of force and substance

2016 ◽  
Vol 374 (2075) ◽  
pp. 20150257 ◽  
Author(s):  
Frank Wilczek
Keyword(s):  
Dynamical Systems ◽  
Gauge Symmetry ◽  
Gauge Invariance ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Physical Significance ◽  
Fundamental Physics ◽  
Present Understanding

Maxwell’s mature presentation of his equations emphasized the unity of electromagnetism and mechanics, subsuming both as ‘dynamical systems’. That intuition of unity has proved both fruitful, as a source of pregnant concepts, and broadly inspiring. A deep aspect of Maxwell’s work is its use of redundant potentials, and the associated requirement of gauge symmetry. Those concepts have become central to our present understanding of fundamental physics, but they can appear to be rather formal and esoteric. Here I discuss two things: the physical significance of gauge invariance, in broad terms; and some tantalizing prospects for further unification, building on that concept, that are visible on the horizon today. If those prospects are realized, Maxwell’s vision of the unity of field and substance will be brought to a new level. This article is part of the themed issue ‘Unifying physics and technology in light of Maxwell's equations’.

Solving Maxwell's Equation in Meta-Materials by a CG-DG Method

2016 ◽  
Vol 19 (5) ◽  
pp. 1242-1264 ◽  
Author(s):  
Ziqing Xie ◽  
Jiangxing Wang ◽  
Bo Wang ◽  
Chuanmiao Chen
Keyword(s):  
Error Estimate ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Numerical Results ◽  
Time Dependent ◽  
Spatial Discretization ◽  
Maxwell’S Equation ◽  
Temporal Discretization ◽  
Dg Method ◽  
Theoretical Results

AbstractIn this paper, an approach combining the DG method in space with CG method in time (CG-DG method) is developed to solve time-dependent Maxwell's equations when meta-materials are involved. Both the unconditional L2-stability and error estimate of order are obtained when polynomials of degree at most r is used for the temporal discretization and at most k for the spatial discretization. Numerical results in 3D are given to validate the theoretical results.

scholarly journals Homogeneous and Inhomogeneous Maxwell’s Equations in Terms of Hodge Star Operator

2018 ◽  
Vol 37 ◽  
pp. 15-27
Author(s):  
Zakir Hossine ◽  
Md Showkat Ali
Keyword(s):  
Riemannian Manifolds ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Differential Forms ◽  
Flat Space ◽  
Space Time ◽  
Exterior Algebra ◽  
Important Ingredient ◽  
Maxwell’S Equation ◽  
Hodge Star Operator

The main purpose of this work is to provide application of differential forms in physics. For this purpose, we describe differential forms, exterior algebra in details and then we express Maxwell’s equations by using differential forms. In the theory of pseudo-Riemannian manifolds there will be an important operator, called Hodge Star Operator. Hodge Star Operator arises in the coordinate free formulation of Maxwell’s equation in flat space-time. This operator is an important ingredient in the formulation of Stoke’stheorem.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 15-27

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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