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On the derivation of Maxwell's equations
Physics Letters, 1964Maxwell's equations in material media can be derived from (~ electron theory ~> in two steps. First, from the electromagnetic equations for fields with point sources (electrons and nuclei), valid at what we shall call the steb-atomic lecel, the equations, which take into account the existence of stable atoms, molecules o1" ions must he derived.
de Groot, S. R., Vlieger, J.
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ON THE HOMOGENIZATION OF MAXWELL EQUATIONS
COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, 1995We discuss the following general problem: given a composite, made from at least two different materials with each its own (scalar, and possibly complex‐valued) ε and μ, distributed in space in a regular, crystal‐like, pattern, find the equivalent permittivity and permeability (they will, in general, be tensors). This is homogenization. A computation in
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On the strength of Maxwell’s equations
Journal of Mathematical Physics, 1987The ‘‘strength’’ of a set of field equations (first defined by Einstein as the number of Taylor coefficients of field variables that could be chosen arbitrarily) is used to show that the amount of initial data required by the electromagnetic formulation of Maxwell’s theory in free space is equal, without approximation, to that required by the potential
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2014
This chapter is devoted to the review of Maxwell’s equations in differential and integral forms as well as the electromagnetic boundary conditions. We will also discuss the electromagnetic potentials and wave equations. The solution to inhomogeneous wave equation using field representations by the Green’s function will be presented.
Kasra Barkeshli, Sina Khorasani
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This chapter is devoted to the review of Maxwell’s equations in differential and integral forms as well as the electromagnetic boundary conditions. We will also discuss the electromagnetic potentials and wave equations. The solution to inhomogeneous wave equation using field representations by the Green’s function will be presented.
Kasra Barkeshli, Sina Khorasani
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Maxwell’s Quaternion Equations
Space Science JournalThe equations of electrodynamics must, first of all, satisfy the law of conservation of energy. It is shown that Maxwell's equations can be obtained from the Cauchy-Riemann conditions for a quaternion in 4D space. Electrons are written as 4D vectors in energy space, in which the first elements represent the real part of the quaternion (scalar), and the
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2021
Since Maxwell established a foundation of the modern electromagnetic theory in 1873 [1], electromagnetics has undergone a rapid development and has been one of the most important research areas in engineering and science. It demands the study of Maxwell’s equations and their application to the analysis and design of devices and systems.
Gang Bao, Peijun Li
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Since Maxwell established a foundation of the modern electromagnetic theory in 1873 [1], electromagnetics has undergone a rapid development and has been one of the most important research areas in engineering and science. It demands the study of Maxwell’s equations and their application to the analysis and design of devices and systems.
Gang Bao, Peijun Li
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1983
We have analyzed, up to this point, the origin and the consequences of four physical laws associated with static electromagnetic phenomena. The first of them, Gauss’s law, relates the electric field to its sources. In differential form it is written as $$\nabla \cdot E = 4\pi \rho .$$ (7.1) Within the area of application of electromagnetism ...
Allan W. Snyder, John D. Love
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We have analyzed, up to this point, the origin and the consequences of four physical laws associated with static electromagnetic phenomena. The first of them, Gauss’s law, relates the electric field to its sources. In differential form it is written as $$\nabla \cdot E = 4\pi \rho .$$ (7.1) Within the area of application of electromagnetism ...
Allan W. Snyder, John D. Love
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2012
The empirical basis of electrodynamics is defined by Faraday’s law of induction, by Gauss’ law, by the law of Biot and Savart and by the Lorentz force and the principle of universal conservation of electric charge. These laws can be tested – confirmed or falsified – in realistic experiments.
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The empirical basis of electrodynamics is defined by Faraday’s law of induction, by Gauss’ law, by the law of Biot and Savart and by the Lorentz force and the principle of universal conservation of electric charge. These laws can be tested – confirmed or falsified – in realistic experiments.
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1984
In this chapter we collect together the basic equations of electromagnetism and express them in the form first devised by Maxwell to represent correctly the relationships between the electric field E and the magnetic field B in the presence of electric charges and electric currents, whether steady or rapidly fluctuating, in a vacuum or in matter. These
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In this chapter we collect together the basic equations of electromagnetism and express them in the form first devised by Maxwell to represent correctly the relationships between the electric field E and the magnetic field B in the presence of electric charges and electric currents, whether steady or rapidly fluctuating, in a vacuum or in matter. These
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2013
Time-varying currents and charges are known to produce time-varying electromagnetic fields. Time-varying electromagnetic fields are governed by Faraday’s law and Ampere’s law, which are two fundamental equations in electrodynamics. Two additional Gauss’s laws can be derived from Faraday’s law and Ampere’s law.
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Time-varying currents and charges are known to produce time-varying electromagnetic fields. Time-varying electromagnetic fields are governed by Faraday’s law and Ampere’s law, which are two fundamental equations in electrodynamics. Two additional Gauss’s laws can be derived from Faraday’s law and Ampere’s law.
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