In Pursuit of the Unknown (36 page)

11
Waves in the ether

Maxwell's Equations

 

 

 

What do they say?

Electricity and magnetism can't just leak away. A spinning region of electric field creates a magnetic field at right angles to the spin. A spinning region of magnetic field creates an electric field at right angles to the spin, but in the opposite direction.

Why is that important?

It was the first major unification of physical forces, showing that electricity and magnetism are intimately interrelated.

What did it lead to?

The prediction that electromagnetic waves exist, travelling at the speed of light, so light itself is such a wave. This motivated the invention of radio, radar, television, wireless connections for computer equipment, and most modern communications.

A
t the start of the nineteenth century most people lit their houses using candles and lanterns. Gas lighting, which dates from 1790, was occasionally used in homes and business premises, mainly by inventors and entrepreneurs. Gas street lighting came into use in Paris in 1820. At that time, the standard way to send messages was to write a letter and send it by horse-drawn carriage; for urgent messages, keep the horse but omit the carriage. The main alternative, mostly restricted to military and official communications, was the optical telegraph. This used semaphore: mechanical devices placed on towers, which could represent letters or words in code by arranging rigid arms at various angles. These configurations could be seen through a telescope and relayed to the next tower in line. The first extensive system of this kind dates from 1792, when the French engineer Claude Chappe built 556 towers to create a 4800 kilometre network across most of France. It remained in use for sixty years.

Within a hundred years, homes and streets had electric lighting, electric telegraphy had come and gone, and people could talk to each other by telephone. Physicists had demonstrated radio communications in their laboratories, and one entrepreneur had already set up a factory selling ‘wirelesses' – radio sets – to the public. Two scientists made the main discoveries that triggered this social and technological revolution. One was the Englishman Michael Faraday, who established the basic physics of electromagnetism – a tightly-knit combination of the previously separate phenomena of electricity and magnetism. The other was a Scotsman, James Clerk Maxwell, who turned Faraday's mechanical theories into mathematical equations and used them to predict the existence of radio waves travelling at the speed of light.

The Royal Institution in London is an imposing building, fronted by classical columns, tucked away on a side street near Piccadilly Circus. Today its main activity is to host popular science events for the public, but when it was founded in 1799 its brief also included ‘diffusing the knowledge, and facilitating the general introduction, of useful
mechanical inventions'. When John ‘Mad Jack' Fuller established a Chair in Chemistry at the Royal Institution, its first incumbent was not an academic. He was the son of a would-be blacksmith, and he had trained as a bookseller's apprentice. The position allowed him to read voraciously, despite his family's lack of cash, and Jane Marcet's
Conversations on Chemistry
and Isaac Watts's
The Improvement of the Mind
inspired a deep interest in science in general and electricity in particular.

The young man was Michael Faraday. He had attended lectures at the Royal Institution given by the eminent chemist Humphry Davy, and he sent the lecturer 300 pages of notes. Shortly afterwards Davy had an accident that damaged his eyesight, and asked Faraday to become his secretary. Then an assistant at the Royal Institution got the sack, and Davy suggested Faraday as a replacement, setting him to work on the chemistry of chlorine.

The Royal Institution allowed Faraday to pursue his own scientific interests as well, and he carried out innumerable experiments on the newly discovered topic of electricity. In 1821 he learned of the work of the Danish scientist Hans Christian Ørsted, linking electricity to the much older phenomenon of magnetism. Faraday exploited this link to invent an electric motor, but Davy got upset when he didn't get any credit, and told Faraday to work on other things. Davy died in 1831, and two years later Faraday began a series of experiments on electricity and magnetism that sealed his reputation as one of the greatest scientists ever to have lived. His extensive investigations were partly motivated by the need to come up with large numbers of novel experiments to edify the man in the street and entertain the great and the good, as part of the Royal Institution's brief to encourage the public understanding of science.

Among Faraday's inventions were methods for turning electricity into magnetism and both into motion (a motor) and for turning motion into electricity (a generator). These exploited his greatest discovery, electromagnetic induction. If material that can conduct electricity moves through a magnetic field, an electrical current will flow through it. Faraday discovered this in 1831. Francesco Zantedeschi had already noticed the effect in 1829, and Joseph Henry also spotted it a little later. But Henry delayed publishing his discovery, and Faraday took the idea much further than Zantedeschi had done. Faraday's work went far beyond the Royal Institution's brief to facilitate useful mechanical inventions, by creating innovative machines that exploited frontier physics. This led, fairly directly, to electric power, lighting, and a thousand other gadgets. When others took up the baton, the whole panoply of modern electrical and
electronic equipment burst upon the scene, starting with radio, moving on to television, radar, and long-distance communications. It was Faraday, more than any other single individual, who created the modern technological world, with the help of vital new ideas from hundreds of gifted engineers, scientists, and businessmen.

Being working class and lacking the normal education of a gentleman, Faraday taught himself science but not mathematics. He developed his own theories to explain and guide his experiments, but they rested on mechanical analogies and conceptual machines, not on formulas and equations. His work took its deserved place in basic physics through the intervention of one of Scotland's greatest scientific intellects, James Clerk Maxwell.

Maxwell was born the same year that Faraday announced the discovery of electromagnetic induction. One application, the electromagnetic telegraph, quickly followed, thanks to Gauss and his assistant Wilhelm Weber. Gauss wanted to use wires to carry electrical signals between Göttingen Observatory, where he hung out, to the Institute of Physics a kilometre away, where Weber worked. Presciently, Gauss simplified the previous technique for distinguishing letters of the alphabet – one wire per letter – by introducing a binary code using positive and negative current, see
Chapter 15
. By 1839 the Great Western Railway company was sending messages by telegraph from Paddington to West Drayton, a distance of 21 kilometres. In the same year Samuel Morse independently invented his own electric telegraph in the USA, employing Morse code (invented by his assistant Alfred Vail) and sending its first message in 1838.

In 1876, three years before Maxwell died, Alexander Graham Bell took out the first patent on a new gadget, the acoustic telegraph. It was a device that turned sound, especially speech, into electrical impulses, and transmitted them along a wire to a receiver, which turned them back into sound. We now know it as the telephone. He wasn't the first person to conceive of such a thing, or even to build one, but he held the master patent. Thomas Edison improved the design with his carbon microphone of 1878. A year later, Edison developed the carbon filament electric light bulb, and cemented himself in the popular mind as the inventor of electric lighting. In point of fact, he was preceded by at least 23 inventors, the best known being Joseph Swan, who had patented his version in 1878. In 1880, one year after Maxwell's death, the city of Wabash, Illinois became the first to use electric lighting for its streets.

These revolutions in communication and lighting owed a lot to Faraday; electrical power generation also owed a lot to Maxwell. But Maxwell's most far-reaching legacy was to make the telephone seem like a child's toy. And it stemmed, directly and inevitably, from his equations for electromagnetism.

Maxwell was born into a talented but eccentric Edinburgh family, which included lawyers, judges, musicians, politicians, poets, mining speculators, and businessmen. As a teenager he began to succumb to the charms of mathematics, winning a school competition with an essay on how to construct oval curves using pins and thread. At 16 he went to Edinburgh University, where he studied mathematics and experimented in chemistry, magnetism, and optics. He published papers in pure and applied mathematics in the Royal Society of Edinburgh's journal. In 1850 his mathematical career took a more serious turn and he moved to Cambridge University, where he was privately coached for the mathematical tripos examination by William Hopkins. The tripos in those days consisted of solving complicated problems, often involving clever tricks and extensive calculations, against the clock. Later Godfrey Harold Hardy, one of England's best mathematicians and a Cambridge professor, would have strong views about how to do creative mathematics, and cramming for a tricky examination wasn't it. In 1926 he remarked that his aim was ‘not. . . to reform the tripos, but to destroy it'. But Maxwell crammed, and thrived, in the competitive atmosphere, probably because he had that sort of mind.

He also continued his weird experiments, among other things trying to work out how a cat always lands on its feet, even when it is held upside down only a few centimetres above a bed. The difficulty is that this appears to violate Newtonian mechanics; the cat has to rotate through 180 degrees, but has nothing to push against. The precise mechanism eluded him, and was not worked out until the French doctor Jules Marey made a series of photographs of a falling cat in 1894. The secret is that the cat is not rigid: it twists its front and back in opposite directions and back again, while extending and retracting its paws to stop these motions cancelling out.
1

Maxwell got his mathematics degree, and continued as a postgraduate at Trinity College. There he read Faraday's
Experimental Researches
and worked on electricity and magnetism. He took up a chair of Natural Philosophy in Aberdeen, investigating Saturn's rings and the dynamics of the molecules in gases. In 1860 he moved to King's College London, and here he could sometimes meet with Faraday. Now Maxwell embarked on
his most influential quest: to formulate a mathematical basis for Faraday's experiments and theories.

At the time, most physicists working on electricity and magnetism were looking for analogies with gravity. It seemed sensible: opposite electrical charges attract each other with a force which, like gravity, is proportional to the inverse square of the distance separating them. Like charges repel each other with a similarly varying force, and the same goes for magnetism, where charges are replaced by magnetic poles. The standard way of thinking was that gravity was a force whereby one body mysteriously acted on another distant body, without anything passing between the two; electricity and magnetism were assumed to act in the same manner. Faraday had a different idea: they are both ‘fields', phenomena that pervade space and can be detected by the forces they produce.

What is a field? Maxwell could make little progress until he could describe the concept mathematically. But Faraday, lacking mathematical training, had posed his theories in terms of geometric structures, such as ‘lines of force' along which the fields pulled and pushed. Maxwell's first great breakthrough was to reformulate these ideas by analogy with the mathematics of fluid flow, where the field in effect
is
the fluid. Lines of force were then analogous to the paths followed by the molecules of the fluid; the strength of the electric or magnetic field was analogous to the velocity of the fluid. Informally, a field was an invisible fluid; mathematically, it behaved exactly like that, whatever it really was. Maxwell borrowed ideas from the mathematics of fluids and modified them to describe magnetism. His model accounted for the main properties observed in electricity.

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