On Physical Lines of Force

In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch performed an experiment with a Leyden jar and established the ratio of electric charge as measured statically to the same electric charge as measured electrodynamically. Maxwell used this ratio in Isaac Newton's equation for the speed of sound, as applied using the density and transverse elasticity of his sea of molecular vortices. He obtained a value which was very close to the speed of light, as recently measured directly by Hippolyte Fizeau. Maxwell then wrote[3]

"we can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena"

It was also in this 1861 paper that Maxwell first introduced the displacement current term which is now included in Ampère's circuital law. But it wasn't until his next paper in 1865, "A Dynamical Theory of the Electromagnetic Field" that Maxwell used this displacement current term to derive the electromagnetic wave equation.

${\displaystyle \mathbf {\nabla } \times \mathbf {B} =\mu _{0}\mathbf {J} +\underbrace {\mu _{0}\epsilon _{0}{\frac {\partial }{\partial t}}\mathbf {E} } _{\mathrm {Maxwell's\ term} }}$

The four modern Maxwell's equations, as laid down in a publication by Oliver Heaviside in 1884, had all appeared in Maxwell's 1861 paper. Heaviside however presented these equations in modern vector format using the nabla operator (∇) devised by William Rowan Hamilton in 1837,

Of Maxwell's work, Albert Einstein wrote:[4]

"Imagine [Maxwell's] feelings when the differential equations he had formulated proved to him that electromagnetic fields spread in the form of polarised waves, and at the speed of light! To few men in the world has such an experience been vouchsafed... it took physicists some decades to grasp the full significance of Maxwell's discovery, so bold was the leap that his genius forced upon the conceptions of his fellow-workers."

Other physicists were equally impressed with Maxwell's work, such as Richard Feynman who commented:[5]

"From a long view of the history of the world—seen from, say, ten thousand years from now—there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electromagnetism. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade."

Charles Coulston Gillispie states that the paper introduced the word "field" to the world of physics,[6] but Faraday first coined the term in 1849.[7]

Wikisource has original text related to this article:

On Physical Lines of Force

• A Treatise on Electricity and Magnetism
• Flux tube

• James C. Maxwell (1861). "On Physical Lines of Force" . Philosophical Magazine.
• Basil Mahon (2003). The Man who Changed Everything: The Life of James Clerk Maxwell. Wiley. ISBN 978-0-470-86088-5.
• James Clerk Maxwell (1878). "Ether" . Encyclopædia Britannica Ninth Edition. Vol. 8. pp. 568–572.