You may have seen this simple electric train

A very simple class of electric motor that operates using one of the four fundamental forces of Nature - electromagnetism.

Electricity was an area of active investigation in the early 19th century when one of the experimenters, a Dane named Hans Øersted, observed that you could make a compass needle jump by making an electric current flow through a nearby wire. A very curious thing - somehow the compass was sensing the current as if it was a magnet. A few years later Michael Faraday discovered the inverse situation - if you move a magnet through a coil of wire, a current flows in the wire. He went on to build the first electric motor and generator. Decades ahead of anything practical, but that wasn't the point. The gauntlet was down - what is going on?

Practical uses were quickly developed with the telegraph being the most important. Telegraphy spread throughout the US and Europe and by the mid 1850s attempts were made to build a transatlantic cable. The planet's first global telecommunication system was under construction. This very technical branch of the Industrial Revolution saw great success, but also dramatic failure. Wires overheated, systems failed without explanation, distortion plagued long range communication. Help was needed and universities built the first formal industrial research labs to solve the problems.

A number of conjectures as to how electromagnetism worked emerged along with a few useful bits of predictive mathematics. A fundamental assumption found in most was an assumption of how electric and magnetic forces were transmitted through space. Newton, in his brilliant theory of gravitation, mathematically assumed 'action at a distance" - namely that gravity acted at a distance instantaneously.^{1} The great predictive success of the theory led people to assume action at a distance would be at the bedrock of a theory of electromagnetism.

Faraday was self-taught and not very skilled in mathematics. But he had fantastic experimental skills and was one of the most intuitive physicists of all time. His extensive experiments led him to the notion that some kind of "field" filled the space around the wires and magnets and it was this field that allowed the forces to move. The physics community thought this crazy - after all Newton had this great theory and it **had** to be the model. Newton was the great mathematician and Faraday was just an amateur.

Nature doesn't care if you're a mathematician or not...

Some of Faraday's experiments involved iron filings to visually show the proposed fields. Objections were raised - the proposed field didn't exist in space .. the paper must have been involved. James Clerk Maxwell agreed with Faraday and set to work developing a mathematical description of the experimental observations. For technical reasons he chose to do his work using a differential calculus in contrast to Newton's techniques. Maxwell had found an approach that allowed him to examine what happens throughout space. It was a natural language for describing fields.

One hundred and fifty years ago this month A Dynamical Theory of the Electromagnetic Field was published. In it Maxwell unified electricity and magnetism as different facets of a more fundamental electromagnetic force. Dramatically he was able to show light was an electromagnetic wave that propagated through space at a finite speed.^{2} Some of the physics of light was known, but that it was an electromagnetic phenomena came out of the blue and laid the bedrock for enormous technical and scientific revolutions.

By the late 1880s Heinrich Hertz had created wireless electromagnetic waves confirming Maxwell's prediction. Manmade radio was invented. The equations are a cornerstone of physics. Much of our current technology rests on them and wouldn't be possible without the deep understanding of Nature they allow.

I've read, or more correctly skimmed, the original paper. The math is old fashioned and a tough slog. Even during the day it was only understand by a handful of physicists and mathematicians. There are about twenty equations rather than the current four. Oliver Heaviside and a few others found a more tractable compact form was possible if you moved to different notation. By the mid 1880s it was boiled down to the four beautiful equations which began to find their way into university physics and electrical engineering courses.

A furious period of invention ensued. As is usually the case much of it was crazy and useless, some was too far ahead of its time, but several threads of innovation emerged that helped define the 20^{th} century.^{3}

Feynman and Einstein are possibly the two most quoted physicists. Quotes are often misattributed - these two are real:

*The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade*. - R. Feynman

*The precise formulation of the time-space laws was the work of Maxwell. Imagine his 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.* - A. Einstein

not bad

Oh - here's what's going on in the toy train. The battery has a strong permanent magnet at each end. The copper wire is uncoated and the battery is able to send a current through a magnet and then to the coil where it then enters the other magnet and goes back into the battery completing the circuit. This current induces a magnetic field down the core of the coil - you've made a solenoid. If you cleverly arrange the small permanent magnets you can get the induced magnetic field to pull one and push the other. It isn't terribly efficient, but fun and insight abound.

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^{1} Gravitational action at a distance was one of the fundamental flaws with Newtonian gravity that Einstein later solved with his theory of Relativity. Special and General Relativity are deeper and more descriptive than Newtonian physics, but for much of the world we live in they reduce to Newtonian physics with great accuracy. It is generally easier to calculate and think in terms of the later, so it is still enormously useful. In physics theories often build on rather than completely replace.

The word theory in science has a different meaning than in popular language. A theory is something that has been observed and verified by the careful work of many. It is predictive rather than merely descriptive.

^{2} As a student this takes your breath away the first time you see it. Ideally an instructor lets you wander in and find the relation yourself. To see it consider the equations in a charge free and current free region - say in a vacuum. You take the curl of the curl equations and use an identity relation to get a pair of wave equations... literally *let there be light*.

^{3} The crazy inventions often the result of lack of clue, but those ahead of their time are waiting for other technologies or conditions. One of my favorite examples is the hybrid electric-internal combustion automobile - where two underlying drivers of the industrial revolution present themselves in one of the important products, namely the automobile. In 1901 Ferdinand Porsche made the Lohner-Porsche hybrid - the first gasoline-electric hybrid. The company he founded is back to making hybrids - this time for different reasons.

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Recipe corner

An out of season lemonade. I had this traveling and though it good in the Winter. Of course it has way to much sugar, so think of it as a desert. It is terrific over ice.

**Ginger Lemonade**

**Ingredients**

° 1 cup fresh squeezed lemon juice

° 4 cups water

° 1/2 cup honey

° 2 inches fresh ginger roughly chopped, you don't need to peel unless you're into that

° 5 cloves

° 2 cardamom pods

° 1 cinnamon stick

**Technique**

° combine the lemon juice, about half the water and everything else in a saucepan. Simmer and stir until the honey is dissolved

° remove from heat, cover and let it steep for 15 to 20 minutes

° pass through a fine mesh stainer into a container you can chill. Add the remaining water

° chill