Iterative solution of Maxwell's equations-a bridge between static and time-varying solutions

1990 ◽  
Vol 33 (1) ◽  
pp. 69-72 ◽  
Author(s):  
H.A. Kalhor ◽  
K. Audenaerde
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Iterative Solution ◽  
Time Varying

Essentials of Electricity and Magnetism

2019 ◽  
pp. 3-42
Author(s):  
Richard Freeman ◽  
James King ◽  
Gregory Lafyatis
Keyword(s):  
Angular Momentum ◽  
Steady State ◽  
Electromagnetic Radiation ◽  
Electric Fields ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Electromagnetic Energy ◽  
Time Dependent ◽  
Time Varying ◽  
Electricity And Magnetism

A review of the basic elements of electricity and magnetism is presented with an introduction to Maxwell’s equations for steady-state in a vacuum. The modifications to these equations necessary to account for time varying sources are shown to produce to a causal unification of magnetic and electric fields. The application of Maxwell’s equations in the presence of matter leads to the concepts of electric and magnetic polarization of matter. Electromagnetic radiation arises directly from Maxwell’s time-dependent equations and the basic response of materials to this radiation is discussed. Finally, electromagnetic conservation laws are derived, including electromagnetic energy and linear and angular momentum.

scholarly journals A derivation of Maxwell's equations using the Heaviside notation

2018 ◽  
Vol 376 (2134) ◽  
pp. 20170447
Author(s):  
Damian P. Hampshire
Keyword(s):  
Differential Equations ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Lorentz Invariance ◽  
Local Equilibrium ◽  
Local System ◽  
Equation Of Motion ◽  
Time Varying ◽  
Theme Issue ◽  
Faraday’S Law

Maxwell's four differential equations describing electromagnetism are among the most famous equations in science. Feynman said that they provide four of the seven fundamental laws of classical physics. In this paper, we derive Maxwell's equations using a well-established approach for deriving time-dependent differential equations from static laws. The derivation uses the standard Heaviside notation. It assumes conservation of charge and that Coulomb's law of electrostatics and Ampere's law of magnetostatics are both correct as a function of time when they are limited to describing a local system. It is analogous to deriving the differential equation of motion for sound, assuming conservation of mass, Newton's second law of motion and that Hooke's static law of elasticity holds for a system in local equilibrium. This work demonstrates that it is the conservation of charge that couples time-varying E -fields and B -fields and that Faraday's Law can be derived without any relativistic assumptions about Lorentz invariance. It also widens the choice of axioms, or starting points, for understanding electromagnetism. This article is part of the theme issue ‘Celebrating 125 years of Oliver Heaviside's ‘Electromagnetic Theory’’.

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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