Models, structure, and generality in Clerk Maxwell’s theory of electromagnetism

2017 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Physical Theory ◽  
Electromagnetic Theory ◽  
System Of Equations ◽  
Structural Requirements ◽  
Electricity And Magnetism ◽  
Lagrangian Form ◽  
Gradual Development ◽  
William Thomson ◽  
Fundamental Equations ◽  
Lines Of Force

This article examines the gradual development of James Clerk Maxwell’s electromagnetic theory, arguing that he aimed at general structures through his models, illustrations, formal analogies, and scientific metaphors. It also considers a few texts in which Maxwell expounds his conception of physical theories and their relation to mathematics. Following a discussion of Maxwell’s extension of an analogy invented by William Thomson in 1842, the article analyzes Maxwell’s geometrical expression of Michael Faraday’s notion of lines of force. It then revisits Maxwell’s honeycomb model that he used to obtain his system of equations and the concomitant unification of electricity, magnetism, and optics. It also explores Maxwell’s view about the Lagrangian form of the fundamental equations of a physical theory. It shows that Maxwell was guided by general structural requirements that were inspired by partial and temporary models; these requirements were systematically detailed in Maxwell’s 1873 Treatise on electricity and magnetism.

XVI.—On the Faraday-Tube Theory of Electro-Magnetism

1923 ◽  
Vol 42 ◽  
pp. 225-246
Author(s):  
William Gordon Brown
Keyword(s):  
Mathematical Theory ◽  
Physical Theory ◽  
Quantitative Form ◽  
Electrical Theory ◽  
Lines Of Force

The method of describing a field of force by means of lines or tubes of induction, which originated with Faraday, was given a quantitative form by Sir J. J. Thomson, and further discussed by N. Campbell in his book Modern Electrical Theory. Since Maxwell himself looked on his work as a mathematical theory of Faraday's lines of force, one is tempted to examine the original physical theory for hints as to the modification of the Maxwellian theory to suit certain modern requirements.

XIX. On the electromagnetic theory of the reflection and refraction of light

1880 ◽  
Vol 171 ◽  
pp. 691-711 ◽  
Keyword(s):  
Electromotive Force ◽  
Electric Displacement ◽  
Electromagnetic Theory ◽  
Point Of View ◽  
Electrostatic Energy ◽  
Magnetic Media ◽  
Reflection And Refraction ◽  
Electricity And Magnetism

In the second volume of his ‘Electricity and Magnetism’ Professor J. Clerk Maxwell has proposed a very remarkable electromagnetic theory of light, and has worked out‘ the results as far as the transmission of light through uniform crystalline and magnetic media are concerned, leaving the questions of reflection and refraction untouched. These, however, may be very conveniently studied from his point of view. If we call W the electrostatic energy of the medium, it may be expressed in terms of the electromotive force and the electric displacement at each point as is done in Professor Maxwell’s ‘Electricity and Magnetism,’ vol. ii., part iv., ch. 9. I shall adopt his notation and call the electromotive force and its components P, Q, R, and the electric displacement D and its components f, g, h . As several of the results of this paper admit of a very elegant expression in Quaternion notation I shall give the work and results in both Cartesian and Quaternion form, confining the German letters to the Quaternion notation. Between these quantities then we have the equation W = -1/2∭S D . dxdydz = 1/2∭(P f + Q y + R h ) dxdydz

scholarly journals On electrostatic screening by gratings, nets, or perforated sheets of conducting material

1891 ◽  
Vol 49 (296-301) ◽  
pp. 405-418
Keyword(s):  
Two Dimensional ◽  
Conducting Material ◽  
Plate Xiii ◽  
Electricity And Magnetism ◽  
Perforated Sheets ◽  
Lines Of Force

1. Maxwell, in his “Theory of a Grating of Parallel Wires” (‘Electricity and Magnetism,’ Arts. 203— 205, and Plate XIII), gives a very valuable and interesting two-dimensional investigation of electrostatic screening, and a most instructive diagram of “Lines of Force near a Grating,” which powerfully helps to understand and extend the theory, and to acquit it of an accusation wrongly made against it in the last two sentences of Art, 205.

The Influence of Modern Physics

2015 ◽  
Author(s):  
Leemon B. McHenry
Keyword(s):  
Quantum Theory ◽  
Physical Theory ◽  
Electromagnetic Theory ◽  
Relativity Theory ◽  
Unified Theory ◽  
Physical Evidence ◽  
Current State ◽  
Unified Theories ◽  
Modern Physics ◽  
Event Ontology

This chapter investigates the influence of Maxwell’s electromagnetic theory, Einstein’s relativity theory and the early quantum theory on the development of the event ontology in the 1920s with particular focus on Whitehead’s view. These were the three key ideas that led to a transformation of our view of reality as comprised fundamentally of energy events. The two main themes of this chapter include: (1) physical evidence in support of an ontology of events, and (2) the increasing unification of physical theory until we arrive at the current state of two highly successful, unified theories that are presently disunified within the search for a comprehensive, unified theory.

Electrodynamics from Thomson and Maxwell to Hertz

2017 ◽  
Author(s):  
Jed Z. Buchwald
Keyword(s):  
Field Theory ◽  
Energy Conservation ◽  
Electric Current ◽  
Electromagnetic Theory ◽  
James Clerk Maxwell ◽  
Heinrich Hertz ◽  
William Thomson ◽  
First Time ◽  
Electric Waves

This article examines developments in the field of electrodynamics from William Thomson and James Clerk Maxwell to Heinrich Hertz. It begins with a discussion of Michael Faraday’s work, focusing on his discovery of what was later termed ‘dielectric capacity’ and his role in the birth of field theory. It then considers Thomson’s unification of Faraday’s understanding of both electro- and magnetostatics with energy conservation, along with Maxwell’s extension of Thomson’s structure to cover electrodynamics, which for the first time brought to the fore issues concerning the electric current. It also describes Maxwellian electrodynamics and electromagnetic theory, Hermann Helmholtz’s development of a different form of electrodynamics, and Hertz’s work on electric waves.

Aspects of French Theoretical Physics in the Nineteenth Century

1966 ◽  
Vol 3 (2) ◽  
pp. 109-132 ◽  
Author(s):  
J. W. Herivel
Keyword(s):  
Nineteenth Century ◽  
Physical Theory ◽  
European Countries ◽  
Theoretical Physics ◽  
Theory Of Evolution ◽  
Claude Bernard ◽  
Electricity And Magnetism ◽  
Great Progress ◽  
Pierre Duhem

In France, as in other European countries, especially Britain and Germany, the nineteenth century was a period of great progress and achievement in science. This would still have been true if Claude Bernard and Louis Pasteur had been the only outstanding French scientists of the nineteenth century, whereas there were, of course, many others apart from an impressive number of brilliant French mathematicians. Nevertheless, although it was a great century for French science there was perhaps something rather disappointing about it, and something rather ingrowing about the attitude of French scientists towards scientific developments in other countries. For example, the French took it hard that the creator of the theory of evolution should have been an Englishman, remembering too late Darwin's predecessor Lamarck, and they certainly were very slow in accepting Darwin's theory of evolution.1 Again, the French may have felt that after the important contributions of French scientists such as Coulomb, Poisson, Biot and, above all, Ampère, the theory of electricity and magnetism which is today principally associated with the names of Faraday and Maxwell should have been created by a Frenchman. Once again this new theory was only accepted very slowly and hesitantly, and even unwillingly, in France—one thinks, for example, of the criticisms levelled at the theory by Pierre Duhem in his “The Aim and Structure of Physical Theory”.2 Of course it might be that if one knew how to weigh properly the various achievements of French scientists in different branches of science one would find that, allowing for her rather static population during the nineteenth century, the total contribution of France compared well with those of Britain and Germany. Nevertheless, in one case at least, that of theoretical physics, there seems to have been an unmistakable failure to live up to the promise of the beginning of the century. The purpose of this paper is to advance possible reasons to explain this failure.

On the missed opportunities of classical physics

2021 ◽  
Vol 34 (4) ◽  
pp. 475-479
Author(s):  
Toir Makhsudovich Radzhabov
Keyword(s):  
Physical Theory ◽  
Finite Size ◽  
Physical Field ◽  
Classical Approach ◽  
Structural Elements ◽  
Missed Opportunities ◽  
Classical Physics ◽  
Lines Of Force

This study considers a variant of the realization of Dirac’s ideas regarding the limited number of Faraday force lines and allowance for the finite size of microparticles in physical theory. It is shown that within the framework of the classical approach, consideration of the limited number of Faraday force lines opens additional possibilities for describing and characterizing the physical field and associated phenomena. Specifically, it is shown that it becomes possible to obtain in a facile manner an expression for describing the discrete radiation of an atom, which agrees well with the empirical Balmer relation. An assumption is made about the possibility of the material existence of Faraday force lines as structural elements of the physical field. It is suggested that the natural fields of physical bodies can be considered as a set of materially existing lines of force, i.e., as a luminiferous ether.

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