Faraday, Maxwell, and the Electromagnetic Field

by Nancy Forbes

  9. Maxwell himself described the third equation, curl E = −μ∂H/∂t, though not using these symbols, in a “Note on the Electromagnetic Theory of Light” in 1868. This was a note added to a report on his experiment with Charles Hockin to determine the ratio of the electromagnetic and electrostatic units of charge. Maxwell did not include the equation in his Treatise; nor, it seems, did he mention it to his students, and it stayed in the dark until his collected papers were published in two volumes in The Scientific Papers of James Clerk Maxwell, edited by W. D. Niven in 1890, five years after Heaviside had published the four now-famous equations.

  10. Heaviside published his reformulation of Maxwell's theory in section 4 of a long series of papers, “Electromagnetic Induction and Its Propagation,” which appeared in installments in the weekly journal the Electrician, starting in 1885. The first half of this series (including section 4) was reprinted in vol. 1 of his collected Electrical Papers as article 30, and the second half in vol. 2 as article 35.

  11. In vector algebra the vector product of two vectors is itself a vector. Its magnitude is the arithmetic product of those of the two vectors multiplied by the sine of the angle between them, and its direction is at right angles to both the two vectors.

  12. Heaviside also gave the formula for energy flow in Section 4 of the series of papers “Electromagnetic Induction and its Propagation,” reprinted as Article 30 in Vol. 1 of his collected Electrical Papers.

  13. Lodge decided to edit out the words eccentric and repellent when he published his collected papers on lightning protection in 1892. (He had by then become a good friend of Heaviside.)

  14. The French physicist and philosopher Pierre Duhem gave this description of Lodge's book as an example of what he saw as British physicists’ over-reliance on physical models in his own book, which has been translated as The Aim and Structure of Physical Theory, pages 70–71.

  15. Heaviside wrote this tribute to Fitzgerald in a January 1901 letter. Bruce Hunt quotes it in The Maxwellians, page 187.

  16. Fitzgerald wrote of this “great difficulty” to J. J. Thomson on December 23, 1884. The letter is quoted by Bruce Hunt in The Maxwellians, page 45.

  17. Hermann Helmholtz was ennobled (acquired the von) in 1882.

  18. This passage is from a letter Hertz wrote to Heaviside on March 21, 1889, quoted by Rollo Appleyard in his book Pioneers of Electrical Communication, page 238. In the same letter, he emphatically endorsed Heaviside's abandonment of the electric and magnetic potentials.

  19. Heaviside made this comment about Helmholtz's theory being “Maxwell's run mad” in a June 15, 1892, letter to Lodge, quoted by Bruce Hunt in The Maxwellians, page 198.

  20. Heaviside congratulated Hertz on giving a death blow to “these theories” (those employing action at a distance) in a July 13, 1889, letter, quoted by Paul Nahin in Oliver Heaviside: Sage in Solitude, page 111. Had Heaviside known how much Hertz revered Helmholtz (whose own theory had action-at-a-distance elements), he may not have rubbed salt in the wound so forcefully. But with Heaviside one cannot be sure.

  CHAPTER SEVENTEEN: A NEW EPOCH

  1. Tait called Heaviside's and Gibb's vector analysis “a hermaphrodite monster” in the preface to the third (1890) edition of his book An Elementary Treatise on Quaternions. Heaviside's response, and other comments mocking Tait's devotion to quaternions, are recorded in vol. 1, chapter 3 of his treatise Electromagnetic Theory. Tait would have seen them when they appeared earlier in journals, mostly the Electrician.

  2. The coherer was a kind of switch that was activated by electromagnetic radiation—a tubeful of metallic powder that was ordinarily a very poor conductor of electricity but became a very good one when the magnetic effect of radiation caused its particles to cohere and thus provide a low-resistance path.

  3. For many years nobody knew for certain how Marconi's transatlantic signals managed to follow the curvature of Earth. Oliver Heaviside and Arthur Kennelly, an expatriate Briton living in America, independently postulated an ionized layer in the upper atmosphere that reflected the waves. Experiments by Edward Victor Appleton and Miles Barnett in the 1920s confirmed that they were correct.

  4. Hertz made this much-quoted observation in his 1892 book, translated as Electric Waves: Being Researches on the Propagation of Electric Action with Finite Velocity through Space, page 21.

  5. The quotation is from “Maxwell's Influence on the Development of the Conception of Physical Reality,” an essay by Albert Einstein in James Clerk Maxwell, A Commemorative Volume, published in 1931.

  6. Planck wrote of his “act of desperation” to Professor Robert Williams Wood of Johns Hopkins University, Baltimore, on October 7, 1931. The letter is given and discussed by Malcolm Longair in his book Theoretical Concepts in Physics, pages 222–23.

  7. Feynman's comment on the importance of potentials in quantum electrodynamics is recorded in The Feynman Lectures on Physics, by Richard Feynman, Robert Leighton, and Matthew Sands, vol. 2, chapter 1, p. 3 (1964).

  8. In Michelson and Morley's experiment, each part of the light beam was reflected back toward the point where the beam was split and the experiment was designed to detect a difference in their average speeds, back and forth. The average speed of part of the beam traveling closer to the direction of the aether drift was expected to be slightly slower. The reason for this can be seen by considering the components of each part of the beam along the line of the aether drift and transverse to it. Light traveling back and forth along the line of aether drift would lose more time traveling upstream than it would gain traveling downstream, and although light traveling transverse to the aether drift would also be slowed (because, relative to the aether, it was covering a greater distance), this slowing effect could be shown mathematically to be less than that on light traveling back and forth along the line of aether drift.

  9. Poincaré first made this statement on the nonexistence of absolute motion and time in his paper “La théorie de Lorenz et le principe de réaction,” published in 1900, available in Archives néerlandaises des sciences exactes et naturelles 5, pages 252–78.

  10. Poincaré also gave this result in 1890 in his paper “La théorie de Lorentz et le principe de Réaction,” published in Archives néerlandaises des sciences exactes et naturelles 5, series 2, pages 252–78.

  11. Einstein published the main part of the special theory of relativity in his 1905 paper “On the Electrodynamics of Moving Bodies” and the derivation of E = mc2 in a short follow-up paper. This paper appeared in the Annalen der Physik, vol. 18, pages 639–41 (1905).

  12. Einstein's statement is reported by Frederick Seitz in his article about Maxwell in the Proceedings of the American Philosophical Society 145, no.1, March 2001.

  13. In 1979, Abdus Salam, Sheldon Glashow, and Steven Weinberg gained the Nobel Prize in Physics for showing the electromagnetic force and the weak nuclear force to be different aspects of a single force, now called the electroweak force.

  Appleyard, Rollo. Pioneers of Electrical Communication. London: Macmillan, 1930.

  Bell, Eric Temple. Men of Mathematics. 2 vols. Harmondsworth: Penguin Books, 1965. First published 1937.

  Bence Jones, Henry. The Life and Letters of Faraday. 2 vols. Philadelphia: Lippincott, 1870.

  Blackburn, Simon. Think: A Compelling Introduction to Philosophy. Oxford: Oxford University Press, 1991.

  Bowers, Brian, and Lenore Symons. Curiosity Perfectly Satisfied: Faraday's Travels in Europe, 1813–1815. London: Peter Peregrinus in association with the Science Museum, 1991.

  Brown, George Ingham. Scientist, Soldier, Statesman, Spy: Count Rumford, the Extraordinary Life of a Scientific Genius. Stroud: Sutton Publishing, 1999.

  Brown, L., B. Pippard, and A. Pais, eds. Twentieth Century Physics. New York: IOP Publishing, AIP Press, 1995.

  Buchwald, Jed Z. From Maxwell to Microphysics. Chicago: University of Chicago Press, 1985.

  Campbell, Lewis, and William Garnett. The Life of James Clerk Maxwell. London:
Macmillan, 1882. Second edition published 1884. We have used the online version by Sonnet Software (second edition, 1999), available at www.sonnetsoftware.com/bio/maxbio.pdf, accessed December 9, 2013.

  Darrigol, Olivier. Electrodynamics from Ampère to Einstein. Oxford: Oxford University Press, 2000.

  Davy, John. Memoirs of the Life of Sir Humphry Davy. London: Smith Elder, 1836.

  de Launay, Louis, ed. Corréspondance du Grand Ampère. 3 vols. Paris: Gauthier Villars, 1936–1943.

  Duhem, Pierre. The Aim and Structure of Physical Theory. Princeton: Princeton University Press, 1954.

  Dumas, M. Éloge historique de Michael Faraday. Paris: Firmin Didot, 1868.

  Dyson, Freeman J. “Why Is Maxwell's Theory So Hard to Understand?” In the James Clerk Maxwell Commemorative Booklet. Edinburgh: James Clerk Maxwell Foundation, 1999.

  Einstein, Albert. “Maxwell's Influence on the Development of the Conception of Physical Reality.” In James Clerk Maxwell, A Commemorative Volume. Cambridge: Cambridge University Press, 1931.

  ———. Relativity: The Special and General Theory. London: Methuen, 1920.

  Einstein, Albert, and Leopold Infeld. The Evolution of Physics. New York: Simon and Schuster, 1938.

  Everitt, C. W. Francis. James Clerk Maxwell: Physicist and Natural Philosopher. New York: Charles Scribner's Sons, 1975.

  ———. “Maxwell's Scientific Creativity.” In Springs of Scientific Creativity, edited by Rutherford Aris, H. Ted David, and Roger Stuewer. Minneapolis: University of Minnesota Press, 1983.

  ———. “Maxwell's Scientific Papers.” Applied Optics 6, no. 4 (1967).

  Faraday, Michael. Common Place Book. London: Institution of Electrical Engineers.

  ———. Experimental Researches in Electricity. New York: Dover Publications, 1965. Originally published in the Philosophical Transactions of the Royal Society, 1831–1852.

  ———. Faraday's Diary, Being the Various Philosophical Notes of Experimental Investigation. Edited by Thomas Martin. London: Bell and Sons, 1932–1936.

  Feynman, Richard P., Robert B. Leighton, and Matthew Sands. Lectures on Physics. New York: Addison Wesley, 1965.

  Fleisch, Daniel. A Student's Guide to Maxwell's Equations. Cambridge: Cambridge University Press, 2008.

  Fleming, Ambrose. “Some Memories.” In James Clerk Maxwell, A Commemorative Volume. Cambridge: Cambridge University Press, 1931.

  Forfar, David O. “Generations of Genius.” In the James Clerk Maxwell Commemorative Booklet. Edinburgh: James Clerk Maxwell Foundation, 1999.

  Forfar, David O., and Chris Prichard. “The Remarkable Story of Maxwell and Tait.” In the James Clerk Maxwell Commemorative Booklet. Edinburgh: James Clerk Maxwell Foundation, 1999.

  Garnett, William. “Maxwell's Laboratory.” In James Clerk Maxwell, A Commemorative Volume. Cambridge: Cambridge University Press, 1931.

  Gilbert, William. De Magnete. New York: Dover Publications, 1958. First published in Latin, 1600. English translation by P. Fleury Mottelay, 1893.

  Gill, David. History and Description of the Royal Observatory Cape of Good Hope. Edinburgh: Neill, 1913.

  Gladstone, John Hall. Michael Faraday. London: Macmillan, 1872.

  Glazebrook, Richard T. “Early Days of the Cavendish Laboratory.” In James Clerk Maxwell, A Commemorative Volume. Cambridge: Cambridge University Press, 1931.

  ———. James Clerk Maxwell and Modern Physics. London: Cassell, 1901.

  Goldman, Martin. The Demon in the Aether: The Life of James Clerk Maxwell. Edinburgh: Paul Harris Publishing, 1983.

  Gooding, David, and Frank A. J. L. James. Faraday Rediscovered: Essays on the Life and Work of Michael Faraday. New York: American Institute of Physics, 1989.

  Hamilton, James. Faraday: The Life. London: Harper Collins, 2002.

  Harman, Peter M. Energy, Force and Matter: The Conceptual Development of Nineteenth-Century Physics. Cambridge: Cambridge University Press, 1982.

  ———. The Natural Philosophy of James Clerk Maxwell. Cambridge: Cambridge University Press, 1998.

  ———, ed. The Scientific Papers and Letters of James Clerk Maxwell. 3 vols. Cambridge: Cambridge University Press, 1990–2002.

  Heaviside, Oliver. Electrical Papers. 2nd ed. 2 vols. Providence, RI: Chelsea Publishing, 1970. Originally published 1892.

  ———. Electromagnetic Theory. 3 vols. New York: Dover Publications, 1950. First published 1893–1912.

  Hertz, Heinrich. Electric Waves: Being Researches on the Propagation of Electric Action with Finite Velocity through Space. Translated from the German by Daniel Evan Jones. London: Macmillan, 1893.

  Hirshfeld, Alan. The Electric Life of Michael Faraday. New York: Walker, 2006.

  Hoffmann, Banesh. The Strange Story of the Quantum. Harmondsworth: Penguin Books, 1963. First published 1947.

  Hunt, Bruce J. The Maxwellians. Ithaca, NY: Cornell University Press, 1994.

  James, Frank, A. J. L., ed. The Correspondence of Michael Faraday. 6 vols. London: Institution of Engineering and Technology, 1991–2011.

  ———. Michael Faraday: A Very Short Introduction. Oxford: Oxford University Press, 2010.

  Jeans, James. “James Clerk Maxwell's Method.” In James Clerk Maxwell, A Commemorative Volume. Cambridge: Cambridge University Press, 1931.

  Jones, Reginald Victor. “The Complete Physicist: James Clerk Maxwell, 1831–79.” In Yearbook Royal Society of Edinburgh, 1980.

  Knott, Cargill Gilston. Life and Scientific Work of Peter Guthrie Tait. Cambridge: Cambridge University Press, 1911.

  Kuhn, Thomas S. The Structure of Scientific Revolutions. Chicago: University of Chicago Press, 1962.

  Lamb, Horace. “Clerk Maxwell as Lecturer.” In James Clerk Maxwell, A Commemorative Volume. Cambridge: Cambridge University Press, 1931.

  Larmor, Joseph. “The Scientific Environment of James Clerk Maxwell.” In James Clerk Maxwell, A Commemorative Volume. Cambridge: Cambridge University Press, 1931.

  Leff, Harvey S., and Andrew F. Rex. Maxwell's Demon, Entropy, Information, Computing. Bristol: Adam Hilger, 1990.

  Lindley, David. Degrees Kelvin: A Tale of Genius, Invention and Tragedy. Washington, DC: Joseph Henry, 2004.

  Lodge, Oliver. “Clerk Maxwell and the Wireless Telegraph.” In James Clerk Maxwell, A Commemorative Volume. Cambridge: Cambridge University Press, 1931.

  Longair, Malcolm S. Theoretical Concepts in Physics. Cambridge: Cambridge University Press, 1984.

  Mahon, Basil. The Man Who Changed Everything: The Life of James Clerk Maxwell. Chichester: Wiley, 2003.

  ———. Oliver Heaviside: Maverick Mastermind of Electricity. London: Institution of Engineering and Technology, 2009.

  Marcet, Jane Haldimand. Conversations on Chemistry. 9th American ed. Hartford, CT: Cooke, 1824. First published in London, 1806.

  Maxwell, James Clerk. “A Dynamical Theory of the Electromagnetic Field.” Edited and introduced by Thomas F. Torrance. Edinburgh: Scottish Academic Press, 1982.

  ———. Matter and Motion. Reprinted with notes and appendices by Joseph Larmor, 1920. New York: Dover Publications, 1991.

  ———. A Treatise on Electricity and Magnetism. 3rd ed. Oxford: Clarendon, 1891. Reprinted by Oxford University Press 1998. First edition published 1873.

  Nahin, Paul J. Oliver Heaviside: Sage in Solitude. New York: IEEE Press, 1987.

  Niven, William Davidson, ed. The Scientific Papers of James Clerk Maxwell. 2 vols. Cambridge: Cambridge University Press, 1890.

  Paris, John Ayrton. The Life of Sir Humphry Davy. London: Colburn and Bentley, 1831.

  Planck, Max. “Maxwell's Influence on Theoretical Physics in Germany.” In James Clerk Maxwell, A Commemorative Volume. Cambridge: Cambridge University Press, 1931.

  Poincaré, Henri. La science et l'hypothèse. Paris: E. Flammarion, 1917. First published 1902.

  Pritchard, Chris. “Aspects of the Life and Work of Peter Guthrie Tait.” In the James Clerk Maxwell Commemorative Booklet. Edinburgh: James Clerk M
axwell Foundation, 1999.

  Segrè, Emilio. From Falling Bodies to Radio Waves: Classical Physicists and Their Discoveries. New York: W. H. Freeman, 1984.

  Siegel, Daniel M. Innovation in Maxwell's Electromagnetic Theory. Cambridge: Cambridge University Press, 1991.

  Simpson, Thomas K. Maxwell on the Electromagnetic Field. New Brunswick, NJ: Rutgers University Press, 1997.

  Reid, John S. “James Clerk Maxwell's Scottish Chair.” In the James Clerk Maxwell Commemorative Booklet. Edinburgh: James Clerk Maxwell Foundation, 1999.

  Templeton, John Marks, and Robert L. Herrmann. The God Who Would Be Known: Revelations of Divine Contemporary Science. Philadelphia and London: Templeton Foundation, 2002.

  Thompson, Sylvanus P. Michael Faraday, His Life and Work. London: Cassell, 1901.

  Thomson, J. J. “James Clerk Maxwell.” In James Clerk Maxwell, A Commemorative Volume. Cambridge: Cambridge University Press, 1931.

  Tolstoy, Ivan. James Clerk Maxwell: A Biography. Edinburgh: Canongate, 1981.

  Tyndall, John. Faraday as a Discoverer. London: Longmans, Green, 1868.

  Watts, Isaac. The Improvement of the Mind, Also His Posthumous Works. Edited by Philip Doddridge and David Jennings. London: William Baynes, 1819.

  Weaver, Jefferson Hane, and Lloyd Motz. The Story of Physics. New York: Avon Books, 1989.

  Weightman, Gavin. Signor Marconi's Magic Box. London: Harper Collins, 2003.

  Whittaker, E. T. A History of the Theories of Aether and Electricity. New York: Dover Publications, 1989. First published by Thomas Nelson and Sons, 1951.

  Williams, L. Pearce. Michael Faraday: A Biography. New York: Basic Books, 1965.

  ———. The Origins of Field Theory. Lanham, MD: University Press of America, 1980.

  Yavetz, Ido. From Obscurity to Enigma: The Work of Oliver Heaviside, 1872–1889. Basel: Birkhäuser Verlag, 1995.

  Abbott, Benjamin, 274n6, 275n11, 275nn2, 276n8, 276n10