Rogers: Physics for the Inquiring mind/Louisell: Coupled Mode and Parametric Electronics/Pugh: Principles of Electricity and Magnetism/Reitz u. Milford: Foundations of Electromagnetic Theory/Herforth und Koch: Radiophysikalisches und Radiochemisches Grund

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.

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

Philosophical Transactions of the Royal Society of London ◽

10.1098/rstl.1880.0019 ◽

1880 ◽

Vol 171 ◽

pp. 691-711 ◽

Cited By ~ 9

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

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