3.4.1 Ohm's Law

"A Physicist Who Professed Such Heresies Was Unworthy to Teach Science"

Modern practice assumes there are four Maxwell’s equations: the two Gauss’ Laws (one each for electricity and magnetism), Faraday’s Law, and Ampère’s Law. We’ll discuss these presently. However, these four vector relations, broken out into components as originally written, comprise only thirteen of Maxwell’s original twenty equations. Where did the rest go?

Three of the seven “missing” relations are Ohm’s Law: potential or voltage (V in volts) equals current (I in amps) times resistance (R in ohms) or V = I R, broken out into three vector components [[i]]. As generalized by Gustav Kirchhoff (1824–1887), this relation may be written J = σ E where J is the vector current density in amps per square meter, σ is the conductivity in inverse ohm-meters, and E is the electric field vector in volts/meter. Ohm’s Law, relating as it does voltage to current, is a fundamental relationship underlying all electronics. As Heaviside put it, “Ohm found that the results could be summed up in such a simple law that he who runs may read it, and a schoolboy now can predict what a Faraday then could only guess at roughly” [[ii]]. Figure 3.14 shows Georg Simon Ohm (1789–1854) and his law.

Figure 3.14: Georg Simon Ohm (1789–1854) [[iii]], left, and the remarkable relation he found between voltage (V), current (I), and resistance (R) in an electrical circuit, right.

“Here men of science long groped in darkness, when in the year 1827,” declared Irish physicist John Tyndall (1820–1893) in the year 1852, “the theory of galvanism by Ohm, then of Berlin, now of Nürnberg, rose like a polestar to illumine the obscurity” [[vi]]. “When I first read Ohm’s theory, a light arose within me like the sudden illumination of a dark room by lightning,” explained the American physicist Joseph Henry (1797–1878) [[vii]].

Figure 3.15: John Tyndall (1820–1893) [[iv]], left, and Joseph Henry (1797–1878) [[v]], right.

Brilliant investigators like Tyndall and Henry appreciated Ohm’s merit, and with the benefit of hindsight, Ohm’s Law seems obvious. At the time, however, Ohm’s work was poorly received. One critic called it:

…“a web of naked fantasies” which could never find the semblance of support from the most superficial observation of facts; “he who looks on the world,” proceeds the writer, “with the eye of reverence must turn aside from this book as the result of an incurable delusion, whose sole effort is to detract from the dignity of nature” [[viii], [ix]].

Some have argued the poor reception to Ohm’s work followed from the difficulty in understanding his sometimes complex and obscure writings [[x]], or from a conceptual shift in Ohm’s experimental work quite different from prevailing electrical thinking of the period [[xi]]. Others argue that Ohm was out of step with the philosophical tenor of his contemporaries. Ohm’s discovery came in the 1820s, while German culture was under the sway of the philosophies of Immanuel Kant (1724–1804) and Georg Wilhelm Friedrich Hegel (1770–1831) who, like Descartes before them, championed the practice of deducing scientific truth through pure reason. Hegel, for instance, is said to have “proved” there could be only seven planets (although this story may be apocryphal [[xii]]).

Whatever the reason, the Prussian Minister of Education, himself, concluded “a physicist who professed such heresies was unworthy to teach science” [[xiii]]. The nine years Ohm labored on his measurements and theory while working as a high school teacher and aspiring for a position as a university professor earned him only abuse and derision. Ohm resigned his high school teaching position in 1827, and for the next six years, he worked in poverty and obscurity as a tutor.

Happily for Ohm, his work began to draw attention from outside Germany. Heinrich Friedrich Emil Lenz (1804–1865) of Russia, Charles Wheatstone (1802–1875) from England, and Joseph Henry (1797–1878) in the U.S. all noted and built upon Ohm’s pioneering work.

Figure 3.16: Charles Wheatstone (1802–1875) [[xiv]], left, and Heinrich Friedrich Emil Lenz (1804–1865) [[xv]], right.

Ohm found a position at the Polytechnic School of Nuremberg in 1833, in 1841 the Royal Society of London awarded Ohm the Copley medal in recognition of his achievements, and in 1849 he became a professor of experimental physics at the University of Munich [[xvii]].

Figure 3.17: Henry Cavendish (1731-1810) [[xvi]]..

Ironically, Ohm’s law appears to have been first discovered by Henry Cavendish (1731–1810), the shy and reclusive scientist who also discovered hydrogen. Perhaps best known for his careful measurements of gravitational attraction that defined the constant in Newton’s Law of Universal Gravitation, his result yielded the first accurate estimates for the density and mass of the Earth. Cavendish calculated the mass of the Earth to an accuracy of 1% by measuring the period of oscillation of the torsion balance shown in cross section.

Figure 3.18: Henry Cavendish (1731-1810) used a delicate torsion balance to measure gravitational attraction and determine the constant in Newton’s Law of Universal Gravitation [[xviii]].

Cavendish was so reclusive, however, that much of his work remained buried in his notes. Cavendish anticipated the discovery of Ohm’s Law, Coulomb’s Law of Electric Force, Dalton’s Law of Partial Pressure, and the kinetic theory of gases. He carefully studied the composition of air, removing the oxygen and nitrogen. Cavendish discovered a residue he could not make react. A century later, researchers realized Cavendish had isolated argon. Very few people knew about the extent of his work at the time because Cavendish rarely published his results.

Decades after the death of Cavendish, Maxwell spent much time bringing to light the forgotten gems among the rich ore of Cavendish’s overlooked work. Maxwell carefully replicated many of the experiments Cavendish reported. “This absorbed a lot of Maxwell’s time,” one of Maxwell’s biographers notes, “which, it has been said might have been better spent on research” [[xix]]. Yet, in this meticulous concern for the experimental basis of electromagnetic science, we see Maxwell keeping himself well-grounded in the foundations underlying his theory.

Next time, 3.4.3 Maxwell’s Original Equations.

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References

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[[i]]         Gupta, Madhu. (1980). Georg Simon Ohm and Ohm's Law. Education, IEEE Transactions on. 23. 156 - 162. 10.1109/TE.1980.4321401. See: https://www.researchgate.net/publication/3052303_Georg_Simon_Ohm_and_Ohm's_Law

[[ii]]        Heaviside, EMT vol. 1, p. 13.

[[iii]]       Portrait of G. S. Ohm, head and shoulders. Credit: Wellcome Collection. CC BY.

[[iv]]        Portrait of John Tyndall, Smithsonian. Credit: https://snl.no/John_Tyndall/ .

[[v]]        Photo of Joseph Henry. See: https://infogalactic.com/info/File:Joseph_Henry_(1879).jpg

[[vi]]        Tyndall, John, “XLVI. Reports on the Progress of the Physical Sciences,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 3(19), 1852, p. 321. doi:10.1080/14786445208647013

[[vii]]       Ibid. p. 322.

[[viii]]      Tyndall, Op. Cit. p. 322.

[[ix]]       Hart, Ivor B., Makers of Science, London: Oxford University Press, 1924, pp. 242-244.

[[x]]        Winter, H.J.J., “The Reception of Ohm’s Electrical Researches by his Contemporaries,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Series 7, vol. 35, No. 245, June 1944, pp. 371-386.

[[xi]]       Schagrin, Morton, “Resistance to Ohm’s Law,” Am. J. Phys. 31, 536 (1963); doi: 10.1119/1.1969620

[[xii]]       Beaumont, Bertrand, “Hegel and the Seven Planets,” Mind Vol. 63, No. 250, April 1954, pp. 246-248.

[[xiii]]      Hart, Ivor B., Op. Cit.

[[xiv]]      Drawing of Sir Charles Wheatstone, the English scientist and inventor, 1868, by Samuel Laurence. See: https://en.wikipedia.org/wiki/File:Wheatstone_Charles_drawing_1868.jpg

[[xv]]       See https://en.wikipedia.org/wiki/File:Heinrich_Friedrich_Emil_Lenz.jpg

[[xvi]]      Henry Cavendish, Chemist. 1731-1810. Credit: Wellcome Collection. CC BY.

[[xvii]]      Hart, Ivor B., Op. Cit.

[[xviii]]     Cavendish, H. (1798), ‘Experiments to determine the Density of the Earth’ in McKenzie, A.S. ed. Scientific Memoirs Vol.9: The Laws of Gravitation, American Book Co. 1900, p.62 see: https://commons.wikimedia.org/wiki/File:Cavendish_Experiment.png

[[xix]]      Tolstoy, Ivan, James Clerk Maxwell: A Biography, Edinburgh: Canongate, 1981, p. 148.

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