Faraday, Maxwell, and the Electromagnetic Field Read online

  Is it not wonderful that views differ at first? Time will gradually sift and shape them. And I believe that we have little idea at present of the importance they may have ten or twenty years hence.8

  Faraday had so far failed to detect magnetic properties in gases, but in 1847 he had news from Italy: Professor Michele Bancalari of Genoa University had shown that magnetism affected the behavior of flames. Faraday, as always, checked the result for himself. He expressed surprise that he had “failed to observe the effect years ago,”9 and, within a few weeks, he had experimented with many gases and shown not only that they all possessed magnetic properties but also that they differed considerably, one from the other—most were diamagnetic, but oxygen was paramagnetic.

  Part of Faraday's investigation was to study the magnetic properties of empty space, using the best vacuum pumps available. Two questions arose. First: Why did a vacuum conduct the lines of force better than diamagnetic substances did? He couldn't answer, and neither could anyone else before the development of quantum mechanics in the twentieth century. Second: How did a vacuum conduct lines of force? His answer was enigmatic:

  Mere space cannot act as matter acts, even though the utmost latitude be allowed to the hypothesis of an aether.10

  In his “Ray-vibrations” talk, he had dismissed the aether outright. Had the hard line softened? He clarified his views a little in subsequent papers: The aether was probably an unnecessary contrivance, but if it did exist, it would serve to transmit magnetic lines of force as well as light.

  For years, Faraday had been thinking heresies but, aside from his off-guard outburst in the impromptu “Ray-vibrations” lecture, he had largely kept them to himself. His reasons were clear. Even though he was recognized as a great experimental scientist—the Royal Society had awarded him three medals, including its top one, the Copley Medal—Faraday knew that his lack of mathematics was a bar to similar recognition as a theorist. The mathematically based Newtonian tradition, with its theories of action at a distance along straight lines between electric charges or magnetic poles, still held sway, and almost nobody thought that the beautiful mathematical theories of Coulomb and Ampère might be wrong. Even Faraday's brief and guarded references to the possible existence of lines of force had generally been greeted with derision. The results that came from his laboratory were, in truth, becoming harder and harder for the mathematicians to explain in Newtonian terms, but Weber had taken on Ampère's mantle, and he and others were producing ever more ingenious mathematical models to account for everything by action at a distance. By comparison, Faraday's theories seemed like a child's fantasy. The prevailing view was cogently expressed by the British Astronomer Royal, Sir George Biddell Airy:

  I can hardly imagine anyone who practically and numerically knows the agreement [between calculations based on action at a distance and experimental results] to hesitate an instant between this simple and precise action on the one hand and anything so vague and varying as lines of force on the other.11

  But to Faraday, experimental results were the only truth. He had always been prepared to abandon any line of inquiry the moment his results showed it to be false. Yet his idea of lines of force had withstood every test. In the course of hundreds of experiments over the years, culminating with those on diamagnetism, he had come to believe that lines of force were not simply an indication of the presence and pattern of electric and magnetic forces and of the accompanying strains in matter, they were the vehicle that conveyed the forces and were physically present in space. Though nothing could be proved beyond doubt, the evidence from experiment after experiment overwhelmingly favored them over the rival hypothesis of action at a distance. All his results suggested that nothing happened at a distance, that all forces and all induction acted through some kind of strain in the intervening medium, and that the strain acted along paths that were rarely straight. After his success in discovering diamagnetism, Faraday became bolder and began to mount an open challenge to orthodox views. The term magnetic field now cropped up regularly in his writings and he tried to convey his ideas in one of the reports in his Experimental Researches in Electricity:

  From my earliest experiments on the relation of electricity and magnetism, I have had to think and speak of lines of magnetic force as representations of magnetic power—not merely in the points of quality and direction but also in quantity.12

  This is a little disingenuous—his thinking and speaking on this controversial topic had been largely private. But he goes on:

  Important to the definition of these lines is that they represent a determinate and unchanging amount of force. Though, therefore, their forms, as they exist between two or more centers or sources of power, may vary greatly, and also the space through which they may be traced, yet the sum of power contained in any one section of a given portion of the lines is exactly equal to the sum of power in any other section of the same lines, however altered in form or however convergent or divergent they may be at the second place.13

  Faraday, the nonmathematician, was here describing precisely a property of the magnetic field that was later given mathematical form in one of the four famous “Maxwell's equations.”

  In further experiments he quantified his result of 1831 that a current was induced in a wire when it “cut” magnetic lines of force, and he summed up the findings in a deceptively profound statement. The “quantity of electricity thrown into a current” was “directly as the amount of curves intersected.”14 This statement was true whether the curves were dense or sparse, converging or diverging, and neither the shape of the wire nor its mode of motion made any difference, except that the direction of the current depended on what became known as the right-hand rule.15 It was the original statement of one of the most fundamental laws of electromagnetism—now called simply Faraday's law of induction.

  One of Faraday's heresies was to question the existence of magnetic poles. He had three good reasons. Two of these were acknowledged by everyone, though only Faraday seems to have pursued their consequences. First, why should arbitrary points at the end of magnets act as centers of force? Second, nobody had ever found a single pole; they always occurred in north–south pairs. If you sliced up a magnet, every sliver, no matter how thin, would have a north face and a south face, and this suggested that the power of the original magnet was distributed along its length rather than concentrated at the ends.

  The third reason was Faraday's own. Unlike lines of electric force, which ran between oppositely charged objects, lines of magnetic force didn't start or stop anywhere—they were continuous loops. His floating-needle experiment of 1831 had shown that each loop of magnetic force around a current-carrying coil ran all the way through the coil. If an iron bar magnet of the same size and strength were substituted, the magnetic effect would be exactly the same—the pattern of loops of force would be unchanged. It seemed that the loops of force must run along the length of the iron magnet just as they did through the coil. The ends of the bar magnet were simply the surfaces where the looping lines of force entered and left; there were no poles.16

  Faraday chose not to offer any explanation of the source of the lines of force inside a permanent magnet. One may wonder why he didn't accept Ampère's and Fresnel's hypothesis of tiny currents that circulated around the iron particles in a magnet, as this would have fit in so well—each little loop of current would have a line of force running through it. Perhaps he didn't want to sully the concept of lines of force, perfect in itself and supported by hard-won experimental evidence, by adding on something as speculative as Ampère's and Fresnel's currents. Moreover, he was a chemist and perhaps something about the idea of electric currents circulating around particles of matter didn't seem right to him.

  Along with magnetic lines of force went another notion. Faraday wrote, “Again and again the idea of an electrotonic state has been forced on my mind.”17 He could explain all the known interactions of magnetic fields with electrical circuits very well in terms of lines of force but co
uldn't shake off the idea that some kind of state of strain or tension was involved in the process. Time and again, he observed something first shown in his iron-ring experiment of 1831. When a magnetic field was suddenly removed from the neighborhood of a wire loop, a brief current flowed in the loop. This could be explained by lines of force collapsing and “cutting” the wire, but it also seemed to Faraday that a state of strain existed in and around the wire loop, and that the release of this strain took the form of a current. Similarly, the brief current that accompanied the discharge of a storage device like a Leyden jar seemed to come from the release of a strain in the insulating material between the charged metal surfaces—the electrical version of the electrotonic state.

  In 1855, Faraday completed the third and last volume of his Experimental Researches in Electricity.18 These volumes were a faithful account of hundreds of investigations, both successful and unsuccessful; of his many bold hypotheses, most discarded or modified after rigorous testing; and of his chains of reasoning—all pervaded by a spirit of relentless inquiry. The work had been accomplished despite an increasingly failing memory—he once found when looking back at his notes that he had repeated a long series of experiments done only six months earlier—and a dwindling stock of the mental energy that had been so abundant in his youth. He had coped by placing bounds on his life, taking frequent breaks from laboratory work and turning down almost all invitations to dinners and other functions, yet he managed to take up social causes with all his old passion, for example, campaigning to rid the River Thames of pollution.

  He also did his best to expose charlatans who promoted the mystic nonsense of table-turning that gripped fashionable London in the 1850s—when several people placed their hands on a table it would move, as though propelled by ghostly powers. Faraday personally investigated three séances where the participants sat in the dark with their hands palms down on the table top and mystic forces supposedly turned the table. When the experiments were tried again after Faraday had placed hidden rollers to detect pushing, the table, unsurprisingly, remained immovable. Equally unsurprisingly, the fraudsters conducting the séances shrugged off this outcome, claiming that one could hardly expect spirits to perform while under close surveillance. In July 1853, Faraday wrote a long letter to the Athenaeum magazine debunking the fad, causing the spiritists and their disturbingly large body of sympathizers to rail bitterly against him. He wrote to a friend:

  I have not been at work except in turning the tables upon the table turners nor should I have done that, but that so many inquiries poured in upon me, that I thought it better to stop the inpouring flood by letting all know at once what my thoughts and views were. What a weak, credulous, unbelieving, superstitious, bold, frightened, what a ridiculous world ours is, as far as concerns the minds of men. How full of inconsistencies, contradictions and absurdities it is.19

  Despite the efforts of Faraday and others, the superstition persisted. Nine years later, he turned down an invitation to a séance, saying, “I will leave the spirits to find out for themselves how they can move my attention. I am tired of them.”20

  Faraday had made great discoveries, but in the 1850s it was by no means apparent where they would lead. He had demonstrated the principles of the electric motor, the electric generator, and also, by his iron ring, the transformer—a device now indispensable in electrical power systems—but they had so far not yielded much. Inventors had produced electromagnetic machines, but they were largely curiosities, of little practical use. What eventually opened up the field was, curiously, the development in the 1870s by Heinrich Geissler and others of effective vacuum pumps. This made possible the filament light bulb, which, in turn, led to investment in power-distribution systems requiring efficient generators. It then became practicable to develop electric motors for all manner of purposes, fed from the grid. And in the late 1800s, Nikola Tesla demonstrated the advantages of high-voltage, alternating-current power-distribution systems, which required transformers.

  Electric lighting may have been some way off, but another application of electricity was the wonder of the age. Pioneered by Charles Wheatstone and his partner William Fothergill Cooke in Britain and by Samuel Morse in America, the telegraph was making spectacular progress. By the late 1840s, many cities were already connected by landlines, but telegraphers couldn't get lines to work reliably under water. Among his many other activities, Faraday played a part in making undersea telegraphy possible. The problem had been to find a satisfactory material to use as an insulator between the metal cable core and its outer sheath, which was in contact with the seawater. Telegraphers had tried everything they could think of—cotton, rubber, rope soaked in boiled tar—but the insulation always broke down. Then, in 1848, somebody sent a sample of a Malayan tree gum called gutta percha to Faraday, who tested it and found it to be not only an excellent insulator but also water-resistant, flexible, resilient, and easily molded to shape when warm. Such was Faraday's reputation that his recommendation quickly led to a huge demand for gutta percha. The material met every demand placed on it, and cables soon ran across the English Channel and the Irish Sea.

  The next challenge was both obvious and daunting—to lay a cable under the Atlantic Ocean. The task presented many problems, one of which was that the signal pulses became blurred when sent along undersea cables; signals had to be sent slowly so that each pulse could be distinguished from the next. The longer the cable, the worse the problem, so before investing a huge sum in its cable project, the Atlantic Telegraph Company needed to know whether it would be able to send signals at a fast-enough rate to be profitable.

  At first, telegraphers had no idea why the blurring happened, but Faraday soon supplied the answer. A cable, with its copper core surrounded by insulating material and an outer sheath, was rather like a hugely extended Leyden jar. He had found in the laboratory that all electrical induction takes time to act through the insulating medium. Hence a device like a Leyden jar takes time to charge and to discharge; and this was exactly what was happening in the cable. When the telegraph operator pressed his key at the sending end, the current at the receiving end grew only gradually and didn't reach full value until the cable was fully charged. And when the key was released, the current at the receiver similarly took time to fall to zero. So what should have been a sharp pulse turned into a smeared-out blob.

  But Faraday couldn't quantify the charging time, and the Atlantic Telegraph Company turned to William Thomson, the young Scot who had earlier worked out an equation for Faraday's lines of electric force. He had then used the analogy of heat flow and now did so again, reasoning that electrical induction would diffuse through the insulating material like heat through a metal bar. This way, he worked out an equation for undersea cables and gave the company the bad news that the charging time increased proportionally with the square of the distance—even using an expensive, low-resistance cable, it would take far longer to send a message across the Atlantic than across, say, the Irish Sea. They went ahead anyway and, after many setbacks, laid a cable in 1858, only for it to fail shortly after transmitting messages between Queen Victoria and President Buchanan at a rate of two seconds per character. Later attempts were more successful: the company eventually made a profit for its staunch shareholders, and Thomson earned a knighthood.

  The mercurial Thomson rarely worked on any topic for more than a few weeks before his mind was captured by a new idea, often in a completely different area of science. His early study of Faraday's electric lines of force had been a typical inspired burst. From time to time he returned to electricity; he gave mathematical expression to Faraday's idea that each material had its own specific inductive capacity for electricity and another for magnetism, and he derived a formula for the total energy of a magnetic system. But, as we'll soon see, his greatest contribution was to give some good advice to another young Scot who wanted to study electricity.

  Faraday was a lone worker. He had no close colleagues after Davy and, although he had been Davy's p
rotégé, he never took on a pupil of his own. In part-explanation, Faraday wrote:

  I have looked long and often for a genius for our laboratory, but have never found one. But I have seen many who would, I think, if they had submitted themselves to a sound self-applied discipline of mind, have become successful experimental philosophers.21

  He had nevertheless turned down an ardent request from Lord Byron's daughter Ada Lovelace, who wanted to join him and become, in her words, a bride to science. Perhaps he was not prepared for Lovelace's particular brand of dedication. Or perhaps his intensely personal style of working made it impossible for him to take on the role of mentor.

  Whatever the reasons, it seemed that Faraday's radical ideas about physical lines of force in space might wither on the vine. No one but Thomson had shown any interest, and he regarded lines of electric force principally as an interesting aspect of the mathematics. Nevertheless, Thomson made a vital contribution: When a young friend asked for advice on how best to start studying electricity, he told him to be sure to read Faraday's Experimental Researches in Electricity.

  Early in 1857, Faraday received in his post a copy of a paper with the title “On Faraday's Lines of Force.” The author was James Clerk Maxwell, a young professor of natural philosophy at Marischal College, Aberdeen, who had written the paper while still a student at Cambridge. It began:

  The present state of electrical science seems peculiarly unfavorable to speculation.22

  Faraday must have feared for what was to come, but this was Maxwell's way of introducing his use of an analogy from another branch of physics. The analogy he presented for lines of force was the flow of an incompressible fluid. The streamlines of flow represented lines of force, either electric or magnetic, while the speed and direction of fluid flow at any point represented the density and direction of the lines of force there. He was able to extend the analogy to cover all static electrical and magnetic effects, including the magnetic force between two current-carrying circuits. The mathematics of fluid flow were indisputable, and he set them out in words with a few equations by way of summary. In the final sentence of part 1 of the paper, Maxwell signaled his intention to take Faraday's guidance on electromagnetism: