Solutions of Maxwell’s equations for electric and magnetic fields in arbitrary media

1992 ◽  
Vol 60 (10) ◽  
pp. 899-902 ◽  
Author(s):  
Oleg D. Jefimenko
Keyword(s):  
Magnetic Fields ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Electric And Magnetic Fields

Basic Electromagnetic Theory

2020 ◽  
pp. 68-77
Author(s):  
Magdalene Wan Ching Goh
Keyword(s):  
Electromagnetic Wave ◽  
Magnetic Fields ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Electromagnetic Theory ◽  
Electromagnetic Spectrum ◽  
Wave Polarization ◽  
Basic Principles ◽  
Electric And Magnetic Fields

Electromagnetic theory covers the basic principles of electromagnetism. This chapter explores relationships between electric and magnetic fields. The chapter describes the behaviour of electromagnetic wave. The four sets of Maxwell's equations which underpin the principles of electromagnetism are briefly explained. An illustration on wave polarization and propagation is presented. The author describes the classification of waves according to their wavelengths (i.e. the electromagnetic spectrum).

scholarly journals GRAVITOELECTROMAGNETISM AND THE INTEGRAL FORMULATION OF MAXWELL'S EQUATIONS

2001 ◽  
Vol 10 (05) ◽  
pp. 633-647 ◽  
Author(s):  
DONATO BINI ◽  
CRISTIANO GERMANI ◽  
ROBERT T. JANTZEN
Keyword(s):  
Magnetic Fields ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Integral Formulation ◽  
Curved Spacetime ◽  
Electric And Magnetic Fields ◽  
Lines Of Force

The integral formulation of Maxwell's equations expressed in terms of an arbitrary observer family in a curved spacetime is developed and used to clarify the meaning of the lines of force associated with observer-dependent electric and magnetic fields.

Maxwell's Equations and Shear Waves in the Vortex Sponge

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1367-1373
Author(s):  
Edward M. Kelly
Keyword(s):  
Magnetic Fields ◽  
Shear Wave ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Shear Waves ◽  
Plane Shear ◽  
Electric And Magnetic Fields ◽  
Hollow Vortex ◽  
Vortex Tubes

AbstractThe vortex sponge is a fluid substratum which is criss-crossed by innumerable fine hollow vortex tubes. Bending of tubes causes them to drift; the combination of drift and bending turns out to have effects mathematically identical to those of electric and magnetic fields. Thus, electromagnetism can be viewed mechanically, with Maxwell's curl equations governing the translation and rotation of the substratum. Shear and shear waves are illustrated by a plane shear wave.

scholarly journals Reevaluation and correction of Maxwell’s Equations: a magnetic field has a source, a moving electric charge

F1000Research ◽  
2020 ◽  
Vol 9 ◽  
pp. 1092
Author(s):  
M.J. Koziol
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Electric Charge ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Electric And Magnetic Fields ◽  
The World ◽  
New Equation ◽  
The Magnetic Field

Maxwell’s Equations are considered to summarize the world of electromagnetism in four elegant equations. They summarize how electric and magnetic fields propagate, interact, how they are influenced by other objects and what their sources are. While it is widely accepted that the source of a magnetic field is a moving charge, one of the equations instead states that the magnetic field has no source. However, it is widely accepted that a magnetic field cannot be created without a moving electric charge. As such, here, after carefully reevaluating how Maxwell derived his equation, a limitation was identified. After adjustments, a new equation was derived that instead demonstrates that the source of a magnetic field is a moving charge, confirming experimentally verified and widely accepted observations.

Development of an Explicit Symplectic Scheme that Optimizes the Dispersion-Relation Equation of the Maxwell’s Equations

2013 ◽  
Vol 13 (4) ◽  
pp. 1107-1133 ◽  
Author(s):  
Tony W. H. Sheu ◽  
L. Y. Liang ◽  
J. H. Li
Keyword(s):  
Dispersion Relation ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Angular Frequency ◽  
Numerical Dispersion ◽  
Local Conservation ◽  
Symplectic Scheme ◽  
Electric And Magnetic Fields ◽  
The Difference ◽  
Explicit Finite Difference

AbstractIn this paper an explicit finite-difference time-domain scheme for solving the Maxwell’s equations in non-staggered grids is presented. The proposed scheme for solving the Faraday’s and Ampere’s equations in a theoretical manner is aimed to preserve discrete zero-divergence for the electric and magnetic fields. The inherent local conservation laws in Maxwell’s equations are also preserved discretely all the time using the explicit second-order accurate symplectic partitioned Runge-Kutta scheme. The remaining spatial derivative terms in the semi-discretized Faraday’s and Ampere’s equations are then discretized to provide an accurate mathematical dispersion relation equation that governs the numerical angular frequency and the wavenumbers in two space dimensions. To achieve the goal of getting the best dispersive characteristics, we propose a fourth-order accurate space centered scheme which minimizes the difference between the exact and numerical dispersion relation equations. Through the computational exercises, the proposed dual-preserving solver is computationally demonstrated to be efficient for use to predict the long-term accurate Maxwell’s solutions.

scholarly journals Maxwell’s Equations on Cantor Sets: A Local Fractional Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yang Zhao ◽  
Dumitru Baleanu ◽  
Carlo Cattani ◽  
De-Fu Cheng ◽  
Xiao-Jun Yang
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Cold Dark Matter ◽  
Differential Forms ◽  
Cantor Sets ◽  
Unified Theory ◽  
Fractional Operators ◽  
Vector Calculus ◽  
Electric And Magnetic Fields ◽  
Fractional Differential

Maxwell’s equations on Cantor sets are derived from the local fractional vector calculus. It is shown that Maxwell’s equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields. Local fractional differential forms of Maxwell’s equations on Cantor sets in the Cantorian and Cantor-type cylindrical coordinates are obtained. Maxwell's equations on Cantor set with local fractional operators are the first step towards a unified theory of Maxwell’s equations for the dynamics of cold dark matter.

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