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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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1971
The preceding sections have introduced all the basic concepts needed for the treatment of electromagnetic fields. The various ideas, developed more or less independently above, together form the basis for further development. It will not be out of place, therefore, to summarize the most important equations below.
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The preceding sections have introduced all the basic concepts needed for the treatment of electromagnetic fields. The various ideas, developed more or less independently above, together form the basis for further development. It will not be out of place, therefore, to summarize the most important equations below.
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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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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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2020
Maxwell’s equations are the key to understand electromagnetic (EM) waves because these equations summarize the most important and useful knowledge of EM fields. In order to help readers get the key easily and quickly, two mathematical operators: divergence and curl, are introduced by ignoring lengthy mathematics but focusing on their physical meanings.
Ming-Seng Kao, Chieh-Fu Chang
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Maxwell’s equations are the key to understand electromagnetic (EM) waves because these equations summarize the most important and useful knowledge of EM fields. In order to help readers get the key easily and quickly, two mathematical operators: divergence and curl, are introduced by ignoring lengthy mathematics but focusing on their physical meanings.
Ming-Seng Kao, Chieh-Fu Chang
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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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2016
In this chapter we will study the Maxwell equations . These equations, together with the material relationships (constitutive) of the system to be analyzed, contain all classical macroscopic information we can obtain from an electromagnetic viewpoint. In fact, the electric and magnetic fields studied in the previous chapters are particular cases of a ...
Félix Salazar Bloise +3 more
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In this chapter we will study the Maxwell equations . These equations, together with the material relationships (constitutive) of the system to be analyzed, contain all classical macroscopic information we can obtain from an electromagnetic viewpoint. In fact, the electric and magnetic fields studied in the previous chapters are particular cases of a ...
Félix Salazar Bloise +3 more
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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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