Abstract
In the previous reading selection, Maxwell argued that Faraday’s lines of electric and magnetic force “must not be regarded as mere mathematical abstractions.” Rather, they represent deformations or strains within an elastic medium—the electromagnetic field—by which forces are communicated between electric charges and currents. But while Faraday represented these strains pictorially using elegant diagrams, Maxwell represented them mathematically in terms of space- and time-dependent variables which obey a set of partial differential equations. Specifically, in an essay read before the Royal Society in 1864, Maxwell formulated his “Dynamical theory of the Electromagnetic Field” in the form of 20 equations involving 20 variable quantities. The reading selection in the present chapter is the introductory section of Maxwell’s 1864 publication. Herein, he provides an overview of his “General Equations of the Electromagnetic Field.”
Certain phenomena in electricity and magnetism lead to the same conclusion as those of optics, namely, that there is an æthereal medium pervading all bodies, and modified only in degree by their presence.
—James Clerk Maxwell
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Notes
- 1.
The original article is Maxwell, J. C., A Dynamical Theory of the Electromagnetic Field, Philosophical Transactions of the Royal Society of London, 155, 459–512, 1865. A nice historical introduction to Maxwell’s 1864 essay, along with an edited version of the essay itself, was written by Thomas F. Torrance; see Maxwell, J. C., A Dynamical Theory of the Electromagnetic Field, Wipf and Stock Publishers, 1996.
- 2.
Electrodynamische Maassbestimmungen. Leipzig Trans. vol. i. 1849, and Taylor’s Scientific Memoirs, vol. v. art. xiv.
- 3.
“Explicare testator quo modo fiat ut lucid planum polarization’s per fires electrical gel magnetic as declinetur.”—Halis Saxonum, 1838.
- 4.
“On the Possible Density of the Luminiferous Medium, and on the Mechanical Value of a Cubic Mile of Sunlight,” Transactions of the Royal Society of Edinburgh (1854), p. 57.
- 5.
Experimental Researches, Series 19.
- 6.
Comptes Rendus (1856, second half year, p. 529, and 1857, first half year, p. 1209).
- 7.
Proceedings of the Royal Society, June 1856 and June 1861.
- 8.
Faraday, Exp. Res. Series xi.; Mossotti, Mem. della Soc. Italiana (Modena), vol. xxiv. part 2. p. 49.
- 9.
Faraday, Exp. Res. 1233–1250.
- 10.
Reports of British Association, 1859, p. 248; and Report of Committee of Board of Trade on Submarine Cables, pp. 136 & 464.
- 11.
As, for instance, the composition of glue, treacle, &c., of which small plastic figures are made, which after being distorted gradually recover their shape.
- 12.
“Conservation of Force,” Physical Society of Berlin, 1847; and Taylor’s Scientific Memoirs, 1853, p. 11:4.
- 13.
Reports of the British Association, 1848; Philosophical Magazine, Dec. 1851.
- 14.
Philosophical Magazine, May 1846, or Experimental Researches, iii. p. 447.
- 15.
Heaviside, O., Electromagnetic Theory, vol. 1, “The Electrician” Printing and Publishing Company, London, 1893. See especially Chap. 2, §33–§36 and Chap. 3.
- 16.
Faraday refers to an “electro-tonic state” established within matter subject to an electro-motive force. See Faraday, M., Experimental Researches in Electricity, vol. 1, Taylor and Francis, London, 1839, §3. New Electrical State or Condition of Matter, 59–80.
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Kuehn, K. (2016). Maxwell’s Equations. In: A Student's Guide Through the Great Physics Texts. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-21816-8_31
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