Maxwell’s Equations

The “Babbage” science and technology blog at The Economist has an article this week on a truly significant anniversary in the history of the physical sciences, an anniversary marking the publication of one of the great systematizing ideas in physics.  It was 150 years ago, in 1861, that James Clerk Maxwell, a Scottish scientist, published the first part of his paper, “On Physical Lines of Force” [PDF facsimile here], in the London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science.  Maxwell’s objective was to provide a mathematical framework that would accommodate the body of knowledge that had been gained by experimenters like Volta, Ampere, and Faraday.

By the mid-19th century scientists had a fair understanding of each of the three components of electromagnetism, as the phenomenon has come to be called. They knew, for instance, that the distribution of electric charges was linked to the pattern of electric fields and that magnetic poles cannot exist in isolation, in other words that there were no single magnetic charges. They also knew that a moving magnet generates an electric current in a wire coil, as demonstrated by Michael Faraday several decades earlier

As the article points out, getting a better understanding of electricity and magnetism was of some practical importance; the first attempts to lay a trans-Atlantic telegraph cable had been made, and had not been successful, owing to the deterioration and delay of the signal as it crossed (under) the ocean.

Maxwell’s great insight was that electricity and magnetism were closely linked, and that light was a form of electromagnetic wave that could propagate through a vacuum.  He developed four partial differential equations, Maxwell’s Equations, that describe the behavior of electromagnetic fields and forces; these equations are the foundation of classical electrodynamics, and underlie all of our electronic and communications technology.  (They also explain why it is safer to be inside an automobile during a lightning storm; and, no, it has nothing to do with rubber tires.)

Some aspects of Maxwell’s equations may need to be modified, particularly if recent results on magnetic monopoles hold up.  Still, his work is one of the great accomplishments of theoretical physics.

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