3.4 James Clerk Maxwell & His Equations

He Colored in Faraday’s Lines of Force

Born in 1831, the same year in which Faraday discovered electromagnetic induction, James Clerk Maxwell (1831–1879) made fundamental contributions to statistical mechanics, to the theory of fluids and solids, and to our understanding of color perception. His greatest discovery, however, was his systematization of the laws governing electricity and magnetism and their relation to light. In 1864, Maxwell presented “A Dynamical Theory of the Electromagnetic Field,” summarizing the behavior of electric and magnetic fields in about 20 equations [[ii]].

Figure 3.13: James Clerk Maxwell (1831-1879) colored in Faraday’s lines of force, providing them with a rigorous mathematical foundation [[i]].

Two decades later, Oliver Heaviside (1850–1925) derived a more compact form of Maxwell’s equations, using his own novel vector approach to reduce Maxwell’s twenty equations to the four “Maxwell’s equations” used by physicists and engineers today [[iii]]. Maxwell’s equations are really just a compilation of relationships, earlier discovered by Gauss, Faraday, and Ampère, but with a few Maxwellian twists. Figure 3.13 shows Maxwell. The next chapter discusses Heaviside’s contributions to Maxwell’s theory in more detail. So much of Maxwell’s work was filtered through interpretations provided by Heaviside, however, that we’ll be seeing Heaviside’s name appear frequently in our examination of Maxwell.

Maxwell’s life and accomplishments are too vast to be captured in a single post. As a synthesizer of previously existing work, he compiled, revised, and extended upon the works of others. Today’s post may be cursory, but in forthcoming posts, we will examine Maxwell’s twenty original equations, consider their origins, and see how they evolved into our modern understanding of electromagnetic physics:

• 3.4.1 Ohm’s Law: “A Physicist Who Professed Such Heresies Is Unworthy to Teach Science”

• 3.4.2 Maxwell’s Original Equations: How Twenty Equations Became Four

• 3.4.3 Gauss’s Laws: The Famed Geophysicist Was Also Reputed to be an Excellent Mathematician

• 3.4.4 Ampère’s Law: Two Different Right-Hand Rules - For Currents & Radiation

• 3.4.5 Faraday’s Law & Electromagnetic Waves: Maxwell’s Theory Suggests Light is an Electromagnetic Wave

• 3.4.6 Permittivity & Permeability: Mr. Heaviside’s “Not So Helpful Terms”

• 3.4.7 What is “Free Space?”: An Æther By Any Other Name…

• 3.4.8 Maxwell's Methods and Views: The Profound Meaning Behind His Math

Next time, 3.4.1 Ohm’s Law: “A Physicist Who Professed Such Heresies Is Unworthy to Teach Science.”

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References

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[[i]]         George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, 1890. https://amzn.to/43oeZJu

[[ii]]        Maxwell, James Clerk, “A Dynamical Theory of the Electromagnetic Field,” Royal Society Transactions, Vol. CLV (1864), as reprinted in W. D. Niven, ed., The Scientific Papers of James Clerk Maxwell, Vol. 1, Cambridge: At the University Press, 1890, pp. 526‑597. See: https://amzn.to/43oeZJu

[[iii]]       Bork, Alfred M., “Maxwell and the Electromagnetic Wave Equation,” American Journal of Physics, Vol. 35, 1967, pp. 844‑849. Bork provides an excellent analysis linking Maxwell’s original Cartesian formulation to the currently accepted vector form.

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