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James Clerk Maxwell

Should you wish to pay homage to the great physicist James Clerk Maxwell, you wouldn’t lack for locales in which to do it. There’s a memorial marker in London’s Westminster Abbey, not far from Isaac Newton’s grave. A magnificent statue was recently installed in Edinburgh, near his birthplace. Or you can pay your respects at his final resting place near Castle Douglas, in southwestern Scotland, a short distance from his beloved ancestral estate. They’re fitting monuments to the person who developed the first unified theory of physics, who showed that electricity and magnetism are intimately connected.

But what these landmarks don’t reflect is the fact that, at the time of Maxwell’s death in 1879, his electromagnetic theory—which underpins so much of our modern technological world—was not yet on solid ground.

An extraordinary amount of information about the world—the basic rules by which light behaves, current flows, and magnetism functions—can be boiled down to four elegant equations. Today, these are known collectively as Maxwell’s equations, and they can be found in just about every introductory engineering and physics textbook.

It could be argued that these equations got their start 150 years ago this month, when Maxwell presented his theory uniting electricity and magnetism before the Royal Society of London, publishing a full report the next year, in 1865. It was this work that set the stage for all the great accomplishments in physics, telecommunications, and electrical engineering that were to follow.

But there was a long gap between the presentation and the utilization. The mathematical and conceptual underpinnings of Maxwell’s theory were so complicated and counterintuitive that his theory was largely neglected after it was first introduced.

It took nearly 25 years for a small group of physicists, themselves obsessed with the mysteries of electricity and magnetism, to put Maxwell’s theory on solid footing. They were the ones who gathered the experimental evidence needed to confirm that light is made up of electromagnetic waves. And they were the ones who gave his equations their present form. Without the Herculean efforts of this group of “Maxwellians,” so named by historian Bruce J. Hunt, of the University of Texas at Austin, it might have taken decades more before our modern conception of electricity and magnetism was widely adopted. And that would have delayed all the incredible science and technology that was to follow.

Four Golden Rules

formula for four golden rules

Four Golden Rules

Today, the relationship between electricity and magnetism, along with the wave nature of light and electromagnetic radiation in general, is encoded in the four “Maxwell’s equations” shown above. The equations can be written in different ways. Here, J is the current density. E and B are the electric and magnetic fields, respectively. And there are two other fields, the displacement field D and the magnetic field H. These fields are related to E and B by constants that reflect the nature of the medium that the fields pass through (the values of these constants in vacuum can be combined to give the speed of light). The displacement field D was one of Maxwell’s key contributions, and the last equation describes how both current and changing electric fields can give rise to magnetic fields. The symbols at the beginning of each equation are differential operators. These compactly encode calculus that involves vectors, quantities that have a directionality and thus x, y, and z components. Maxwell’s original formulation of his electromagnetic theory contained 20 equations.


Source : ieee.org


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