Faraday, Maxwell, and the Electromagnetic Field

by Nancy Forbes

  Back at work after the marriage, Faraday had a request from one of his friends at the City Philosophical Society. Richard Phillips had been appointed editor of the journal Annals of Philosophy, and he asked Faraday to write a historical account of electromagnetism. Faraday had, so far, only dabbled in the subject, but this was an important commission and he brought all his faculties to bear. He read everything he could find, repeated the experiments, and did his best to follow the reasoning of Oersted and Ampère.

  As we now know, Oersted's view, derived from Kant, that all space was crisscrossed by forces of one kind or another, turned out to be somewhere near the truth. It was also close to the view that Faraday eventually came to. In all likelihood, he had also been indirectly influenced by Kant, Schelling, and Naturphilosophie. Davy's poetical and philosophical friend Samuel Taylor Coleridge had become an evangelist for Naturphilosophie after visiting Germany in 1798, and some of his enthusiasm had rubbed off on Davy, in particular the notion of the unity of all nature's forces. Faraday, in his formative years, had thus been exposed to the ideas of the German school. But, try as he might, he couldn't make heads or tails of Oersted's vague theory of “conflicts,” nor of his proposition that an electric current was a wave of chemical disruption and reconstitution. Ampère's work was much more to the point. It was precise and elegant, and the mathematically based theory was backed by experiment. But Faraday's self-education was deficient in one significant respect: he had learned no mathematics. For him, Ampère's equations might as well have been written in Egyptian hieroglyphics.

  We shall never know what Faraday would have achieved had he mastered mathematics, but, paradoxically, his ignorance may have been an advantage. It led him to derive his theories entirely from experimental observation rather than to deduce them from mathematical models. Over time, this approach gave him a deep-seated intuition into electromagnetic phenomena. It enabled him to ask questions that had not occurred to others, to devise experiments that no one else had thought of, and to see possibilities that others had missed. He thought boldly but would never commit himself to an opinion until it had withstood the most rigorous experimental testing. As he explained in a letter to Ampère:

  I am unfortunate in a want to mathematical knowledge and the power of entering with facility any abstract reasoning. I am obliged to feel my way by facts placed closely together.5

  For Ampère, on the other hand, mathematics was the language of nature. As we've seen, his views on electricity and magnetism were derived mostly by mathematical analogy with the theory of gravitation. He did carry out some fine experiments, but these were largely to confirm theories he had already developed by abstract reasoning. The stark difference between the two great scientists stemmed from their backgrounds. Ampère was a product, and now a leading member, of the well-established French Newtonian school of mathematical physicists, whereas Faraday, although nurtured under Davy's patronage, was very much his own man—the outsider who eventually came to take center stage. Despite their differences, the two men were drawn together by a mutual passion for science, and they enjoyed many years of friendly correspondence. Faraday believed that differences of opinion served to ferret out the truth.

  Much as he admired Ampère's work, Faraday began to develop his own views on the nature of the force between a current-carrying wire and the magnetic needle it deflected. Ampère's mathematics (which he had no reason to doubt) showed that the motion of the magnetic needle was the result of repulsions and attractions between it and the wire. But, to Faraday, this seemed wrong, or, at least, the wrong way around. What happened, he felt, was that the wire induced a circular force in the space around itself, and that everything else followed from this.

  The next step beautifully illustrates Faraday's genius. Taking Sarah's fourteen-year-old brother George with him down to the laboratory, he stuck an iron bar magnet into hot wax in the bottom of a basin and, when the wax had hardened, filled the basin with mercury until only the top of the magnet was exposed. He dangled a short length of wire from an insulated stand so that its bottom end dipped in the mercury, and then he connected one terminal of a battery to the top end of the wire and the other to the mercury. The wire and the mercury now formed part of a circuit that would remain unbroken even if the bottom end of the wire moved. And move it did—in rapid circles around the magnet!

  Fig. 4.1. Faraday's first electric motor apparatus. (Used with permission from Lee Bartrop.)

  Not done yet, he modified the apparatus slightly, freeing the magnet and letting it float in the mercury, but with one end tethered to a fixed point in the base of the basin. About a quarter of the magnet was now exposed above the surface of the mercury. He replaced the dangling wire with a fixed one that dipped into the mercury at the center of its surface, and then he reconnected the battery. This time, the magnet revolved around the wire! Faraday had become a discoverer: he had made the world's first electric motor. He and George danced around the table and went off to the circus to celebrate. George later recalled the moment: “I shall never forget the enthusiasm expressed in his face and the sparkling in his eyes.”6 We can imagine the joy with which Faraday wrote the simple words in his journal: “Very satisfactory, but make a more sensible apparatus.”7

  He might have added: Get it published—tell the world about it. (Faraday's constant motto was Work, Finish, Publish.) With that thought in mind, he dashed off a paper called “On Some New Electromagnetic Motions and the Theory of Electromagnetism” in time to catch the next edition of the Quarterly Journal of Science. Within a month, his discovery was in print; but within another week, his elation vanished. In his haste, he had neglected to pay the customary compliments to his mentor and senior colleague Davy. Worse than that, he had failed to mention the work of Davy's close friend, Wollaston, who had been trying for a year to produce rotary motion with currents and magnets. Though Faraday had not worked with Davy on electromagnetism since Wollaston came on the scene, he had overheard the two in conversation and had a rough idea of what Wollaston was doing. In fact, Wollaston was on another track—trying in vain to get a wire coil to spin around its own axis in response to a magnet—but the difference between that kind of rotation and Faraday's was too subtle for the casual observer to recognize. Faraday was accused of plagiarism, not by Wollaston directly, but by others, including Davy.

  To be suspected of such a dishonorable act was a sickening blow, made worse by knowing that Davy, the man he most admired in the world, was his leading accuser. We can only guess at Davy's motives. A complex character, he was both generous and vain. Perhaps the best, simple explanation is that generosity prevailed while Faraday was a protégé whose achievements boosted his own public standing, but vanity took over when the protégé appeared in the character of a rival. And Faraday's ill-mannered oversight in not sharing some of the credit with his guide and mentor was an affront to Davy's dignity.

  Desperate to clear himself of the slur, Faraday wrote to Wollaston to apologize. He received a somewhat dismissive reply:

  You seem to me to labor under some misapprehension of the strength of my feelings on the subject to which you allude. As to the opinions which others have of your conduct, that is your concern and not mine; and if you acquit yourself fully of making any incorrect use of the suggestions of others, it seems to me that you have no occasion to concern yourself much about the matter.

  Faraday battled alone to rebut the plagiarism charge and, for the most part, succeeded. Even so, he was still out of favor with the old guard of the British scientific establishment who set great store by protocol and expected deference from their juniors.

  But the wider world cared little for such things, and his discovery took on a life of its own. Within a few months, the Royal Institution had a large rotator in its lecture hall for all to see and had sent pocket-sized versions to scientists around Europe. Electromagnetism was now a hot topic. Many people wanted to find out more about it and turned gratefully to a series of articles in the Annals of Philosop
hy that set out everything for them. The author had modestly called himself “M.” Rumors spread, and they pointed overwhelmingly to Faraday. This was, indeed, the historical review he had written at Richard Phillips's request, and he was obliged to acknowledge authorship. He was famous.

  The next step in his career was to become a fellow of the Royal Society, and a band of current fellows, including Wollaston, put him up for election. Things seemed to be going well, but the prelude to the election turned out to be one of the most unpleasant episodes in his life. The accusations of ungentlemanly conduct had not gone away, and there was opposition from a small group headed by the president, Sir Humphry Davy. Faraday was in a corner. To overcome the injustice, he was forced to put aside all the rules of his Sandemanian upbringing and press for his own advancement by appealing to those who stood in his way. This was a hateful task, but he carried it out, and in January 1824, he was elected F. R. S., with one dissenting vote. It is a measure of Faraday's character that he never harbored rancor about this incident, although he did confess to a friend that his relationship with Davy was never the same afterward.

  The following year, Davy nevertheless instigated Faraday's promotion to director of the Royal Institution—perhaps it was a case of force majeure. Faraday's immediate task was to rescue the Institution from a precarious financial state, and he did it with panache rivaling that of Davy twenty years before. On Davy's home turf, too—the lecture hall. He started by inviting the Institution members to talks in the laboratory on Friday evenings, but these soon became so popular that he moved them to the grand lecture theater upstairs. So began the tradition of Friday Evening Discourses at the Royal Institution that continues today. Even the format is unchanged, theatrical in its simplicity—at precisely the appointed time, the speaker enters unannounced, speaks for exactly one hour, takes his bow, and leaves the stage. The early talks went so well that Faraday decided to put on a special set of lectures for children at Christmas. These, too, have run ever since; the television audience for them now is huge. Faraday's immediate purpose was served, too: the Institution's membership, and its income, swelled as people were drawn to the lectures. Though by no means prosperous, the Institution now at least had its head above water.

  The success of the talks didn't happen by chance. As we've seen, Faraday had early on begun to form his own ideas on the art of the scientific lecture, and had, by now, built up an unrivaled body of expertise: had he written a book on the topic, it would have become the standard work. His various notes contain guidance on everything from the layout of the seating to the ventilation and lighting in the hall, and copious advice to the lecturer, beginning: “A flame should be lighted at the commencement and kept alive with unremitting splendour to the end.”8 Faraday gave many of the lectures himself and drew devoted audiences just as Davy had done, though with quite a different style. In place of Davy's flamboyance and flashes of brilliant improvisation there was simple charm, as he conveyed the wonder of science with consummate phrasing and timing. He soon became the foremost public lecturer on science in England in a career lasting from 1823, when he was called in unexpectedly to substitute for William Brande, to his final appearance in 1862.

  The nature of Faraday's genius is hard to pin down, but his mastery of the lecture offers some clues: his knowledge of the subject came not from what he had read or been told but from personal observation; he looked and listened with rare intensity and was able to capture subtle effects and nuances that passed other people by. By the same token, he took pains to identify all the factors that contributed to an audience's enjoyment and evaluated their effects, both singly and in combination. Perhaps the most revealing aspect is that he never demonstrated an experiment on stage, no matter how spectacular, unless he could also present the audience with the theory behind it. His scientific genius lay not simply in producing experimental results that had eluded everyone else but in explaining them, too.

  Faraday's elevation to the scientific establishment led to new demands on his time. While coping with the day-to-day business of the Royal Institution, he had to fend off requests to take on other administrative work, for example secretaryship of the new Athenaeum Club. But there was one request he couldn't refuse. In the early 1700s, Britain had led the world in the manufacture of high-quality glass for optical instruments, but in 1746, the government decided to raise money by levying a heavy tax on all glass. The goose that had laid the golden eggs slowly died from suffocation—by the 1820s, the French and the Germans were making superb lenses, but British manufacturers had forgotten how to do it. The government couldn't bring itself to drop the tax, but in 1825, the Royal Society set up the Committee for the Improvement of Glass for Optical Purposes to try to rescue the situation. Faraday was invited to join—in effect to run the project—and it was his patriotic duty to accept.

  In a backbreaking series of experiments—first at the nearby Falcon Glass Works, then in his own laboratory using a freshly installed glass furnace—Faraday examined all possible causes of imperfections in the glass, eliminating them one by one, at the same testing new methods and ingredients. It was tiresome work that dragged on and on; after each failure, the process of finding the cause and putting it right took weeks. All this was fitted in with Faraday's other duties, and whatever he could squeeze in of his own research. After three years, he succumbed to what he described as “nervous headaches and weakness”9 and Sarah took him off to the country for two months to recover. This sequence of hard work, mental exhaustion, and enforced relaxation was one that was to repeat itself several times during his career.

  Possibly nobody but Faraday could have wrought any success from this thankless task, but in 1830, he delivered a modest-sized sample of acceptable glass, in which he had used a silicated borate of lead in place of the more traditional lead oxide. It worked well when used in a telescope lens, and what the committee wanted now was more of it, to make bigger lenses. Faraday felt himself being sucked into a morass. If he didn't wrench himself free now, he would spend much of the rest of his life working for committees. In 1831, he parceled up six volumes of experimental notes, sent them to the Royal Society, and resigned from the optical glass committee.

  Thirty-nine-year-old Faraday had done his duty. After years of frustration through having too little time to devote to his own research, he took matters into his own hands. He had already turned down the offer of a professorship at the new London University but accepted a part-time post at the Royal Military Academy at Woolwich—he enjoyed teaching, and the £200 annual salary was a useful boost to his modest pay from the Royal Institution. But now there would be no more work for committees, no more hack analysis work for commercial companies even though that could have made him a rich man. And no striving for high office. The Royal Institution was both his home and his professional stage; he would stay there and follow his scientific muse. There was one good legacy from the wearisome glass project. Faraday had acquired an assistant—Sergeant Anderson, newly retired from the Royal Artillery—who remained in post until he died in 1866. Faraday's successor at the Royal Institution, John Tyndall, who had a great admiration for Anderson, summed up his merits in two words: “blind obedience.”10 Faraday's friend Ben Abbott was fond of telling a story that one night Faraday forgot to tell Anderson he could go home and came in the following morning to find him still stoking the furnace.

  Ten years had passed since Faraday had produced rotary motion with an electric current and a magnet, but the mystery of it had been a constant backdrop to his thoughts. He now had no close colleagues in England, but he enjoyed a lively and friendly correspondence with Ampère. They liked each other and had huge mutual respect even though they disagreed fundamentally about nature's mechanism for electromagnetism. In fact, Faraday was beginning to realize how sharply his own ideas diverged from the mainstream. Ampère's highly mathematical theory of action at a distance, set in the French Newtonian tradition, seemed to give leading scientists all they needed and was almost universally
accepted. Faraday acknowledged this in his own writings, where any contradictory suggestions were very cautiously expressed. The reason he had uncharacteristically used a pseudonym in his review of electromagnetism for the Annals of Philosophy was probably that he didn't want to be characterized as a bumptious upstart. His letters to Ampère, though, were free and frank; for example:

  I am naturally sceptical in the matter of theories and therefore you must not be angry with me for not admitting the one you have advanced immediately. Its ingenuity and applications are astonishing and exact but I cannot comprehend how the currents are produced and particularly if they be supposed to exist round each particle and I wait for further proofs of their existence before I finally admit them.11

  Ampère had become a trusted confidant, as is evident from another letter, in which Faraday contrasts their working lives:

  Every letter you write me states how busily you are engaged and I cannot wish it otherwise knowing how well your time is spent. Much of mine is unfortunately occupied in very common place employment and I may offer this as an excuse (for want of a better) for the little I do in original research.12

  There were, indeed, many distractions from the work he really wanted to do. Once, when immersed in investigations into electromagnetism, he had to put everything aside to test thirty-two samples of the Royal Navy's oatmeal to determine whether they were contaminated. Nevertheless, in whatever time he could spare from other duties, Faraday had got on with exploring electricity and magnetism by experiment. It was probably through testing out Ampère's ideas that his own began to develop. He started by bending a current-carrying wire into a circular loop and found, as Ampère had done, that the loop of current behaved exactly like a magnet—its south pole was on the side from which the current appeared to flow clockwise, and its north pole was on the other. With a single loop, the force was feeble; but by winding the wire into a helix with many turns, he made a powerful magnet. By Ampère's theory, the magnetic force was simply what you got when you added all the straight-line forces between pairs of current elements mathematically. Faraday saw things differently—to him, the magnetic force that curved around any current-carrying wire was not an indirect, mathematically derived effect of straight-line forces, it was something primal, a circular force in its own right. The idea of a circular force was quite beyond the generally accepted doctrine of Newtonian forces, and Faraday's lack of a traditional scientific education probably made it easier for him to accept it. His thinking ran on in a way even further removed from the Newtonian model—he reasoned that by winding the wire into a helix, he had squashed parts of the circular force into a tube that ran through the helix and allowed the other parts of the force to spread out into space.