**The 19th Century Explanation of the Remarkable Connection Between Electricity And Magnetism**

No explanation I know of in all of recent scientific history is as beautiful or deep, or ultimately as elegant, as the 19th century explanation of the remarkable connection between two familiar, but seemingly distinct forces in nature, electricity and magnetism. It represents to me all that is the best about science: surprising empirical discoveries combined with a convoluted path to a remarkably simple and elegant mathematical framework, which then explained far more than was ever bargained for, and in the process produced the very technology that now powers modern civilization.

It all began with strange experiments with jumping frogs and electric circuits, capped by the serendipitous discovery by the self-schooled, yet greatest experimentalist of his time, Michael Faraday of a very strange connection between magnets and electric currents. It was by then well known that a moving electric charge, i.e. a current, created a magnetic field around the current that could repel or attract other magnets located nearby.

What remained an open question was whether magnets could produce any electric force on charged objects. Faraday discovered, by accident, that when he turned on or off a switch to start or stop a current, creating a magnetic field that grew or decreased with time, during the periods when the magnetic field was changing, a force would suddenly arise in a nearby wire, moving the electric charges within it to create a current.

Faraday's law of induction, as it became known, not only is responsible for the basic principle governing all electric generators, from Niagara falls to nuclear power plants, it produced a theoretical conundrum that required the mind of the greatest theoretical physicist of his time, James Clerk Maxwell to set things straight. Maxwell realized that Faraday's result implied that it was the changing magnetic field (a pictorial concept introduced by Faraday himself because he felt more comfortable with pictures than algebra) that produced an electric field that would push the charges around the wire creating a current.

But in order for mathematical symmetry in the equations governing electric and magnetic fields, this then required that a changing electric field, and not merely moving charges, would produce a magnetic field. This not only produced a set of mathematically consistent equations every physics student knows, and some love, called Maxwell's equations, which can fit on a T-Shirt, but it established the physical reality of what was otherwise a mere figment of Faraday's imagination, a field—some quantity associated with every point in space and time.

But even more than this, Maxwell realized that if a changing electric field produced a magnetic field, then a constantly changing electric field, such as that which occurs when I continue to jiggle a charge up and down, would produce a continuously changing magnetic field. But that in turn would create a continuously changing electric field, which in turn would create a continuously changing magnetic field, and so on. This field 'disturbance' would move out from the original source, the jiggling charge, at a rate that Maxwell could calculate on the basis of his equations. The parameters in these equations came from experiment—measuring the strength of the electric force between two known charges, and the strength of the magnetic force between two known currents.

From these two fundamental properties of nature, Maxwell calculated the speed of the disturbance and found out ... you guessed it, that the speed was precisely the speed that light was measured to have! Maxwell thus discovered that light is indeed a wave ... but a wave of electric and magnetic fields that moved through space at a precise speed determined by two fundamental constants in nature thus laying the basis for Einstein to come along a generation or so later and demonstrate that the constant speed of light required a revision in our notions of space and time.

So, from jumping frogs and differential equations we came up for one of the most beautiful unifications in all of physics, the unification of electricity and magnetism in a single theory of electromagnetism, and that theory explained the existence of that which allows us to observe the universe around us, namely light, and the practical implications of the theory produced the mechanisms that power all of modern civilization and the principles that govern essentially all modern electronic devices, and the nature of the theory itself produced a series of further puzzles that allowed Einstein to yield new insights into space and time!

Not bad for a set of experiments whose worth was questioned by Gladstone (or Queen Victoria—depending upon which apocryphal story one buys)—who came into Faraday's laboratory and wondered what all the fuss was about, and what use all of this experimentation was for. He (or she) was told, either: "Of what use is a newborn baby?"—or in my favorite version of the story—"Use? Why one day this will be so useful you will tax us for it!" Beauty, elegance, depth, utility, adventure, and excitement! Science at its best!