Faraday, Maxwell, and the Electromagnetic Field

by Nancy Forbes

  Joseph Louis Lagrange produced the definitive work on dynamics, his Mécanique analytique, which didn't contain a single diagram; Pierre Simon Laplace wrote his masterly, five-volume Mécanique céleste; and Siméon Denis Poisson worked out the exact distribution of charge on the surfaces of two spherical conductors a given distance apart. Newton's warning about the “absurdity” of supposing gravity to act instantaneously at a distance without any kind of medium was not entirely forgotten. Supposing the medium to be fluid, Laplace calculated that gravitational forces would be transmitted at least seven million times faster than light, and this result seems to have reassured others that any difference from instantaneous action, both for gravity and for electrical and magnetic forces, could be safely ignored. With electricity and magnetism, it seemed that Newton's gravitational model had provided a royal road, but it eventually turned out to be a cul-de-sac.

  Before 1800, all man-made electricity was static. The discovery of continuous currents came as a complete surprise and was in the best tradition of scientific serendipity. Luigi Galvani, an anatomist in Bologna, used to hang dead frogs’ legs on a row of brass hooks to dry. When, around 1780, he touched one of the legs with a piece of iron that happened to be in contact with the brass hook, the leg twitched! The muscle tissue in the frog's leg was producing electricity, or so Galvani thought. His friend Alessandro Volta disagreed and set out to test an alternative theory that the electricity was being generated by chemical action between the different metals in contact with the frogs’ legs. The result, a decade or so later, was the voltaic pile, or battery. His first battery was a pile of alternate discs of silver and zinc interleaved with layers of brine-soaked pasteboard. Amazingly, this simple assembly of seemingly inert components produced a continuous electric current when the silver disc at one end was connected through a metal circuit to the zinc disc at the other. The more discs in the pile, the greater was the electric effect, and it turned out that there was no need for expensive silver. Any two metals would do; copper and zinc worked very well.

  Volta had never intended to invent the battery, but it soon took on a life of its own. Experimenters discovered that interesting things happened when you connected a wire to each of the terminals of a battery and dipped the two wire ends in a chemical solution. Up to now, the only way chemists could investigate the constituents of matter was to mix substances together and watch what happened. Now a new technique called electrochemistry opened up the field. You could make a solution of the substance under investigation, dip the two wires from a battery into it, and let the electrical force do the work; sometimes it would separate the constituent parts of the substance, each part being drawn toward one of the wire ends. As we have seen, news of this eventually reached the young enthusiasts at the City Philosophical Society, and Faraday, using his seven-halfpenny battery, joyfully watched as bubbles of gas appeared and his solution of magnesium sulfate turned murky as it decomposed.

  At the other end of the size scale, Humphry Davy was using his huge battery, formed of 2,000 voltaic cells, at the Royal Institution to break new ground in chemistry. By bold and sometimes-dangerous experiments, he isolated a string of new elements: barium, calcium, sodium, potassium, magnesium, and boron (the last-named together with the Frenchmen Joseph Louis Gay-Lussac and Louis-Jacques Thénard). In the course of this work, Davy became more and more convinced that all chemical reactions were the result of electrical action. His views certainly influenced those of his protégé, though Faraday took nobody's word, even Davy's, for granted and always had to work out everything for himself.

  Electricity was shaking up chemistry, but a new wind was coming in from a surprising direction. Immanuel Kant had published his Critique of Pure Reason in 1781, and it became a preamble to a German school of scientific thought called Naturphilosophie, advanced principally by Friedrich von Schelling. Hans Christian Oersted, professor of physics at the University of Copenhagen, was an adherent of both science and philosophy. The son of an apothecary, Oersted was a close friend of his near-namesake Hans Christian Andersen and brother to Anders Oersted, who became prime minister of Denmark. He was a man of many parts—among other things, he wrote poetry—but he was drawn early on to science, especially chemistry, and to German philosophy.

  In his 1786 work, Metaphysical Foundations of Natural Science, Kant put forward a dynamical theory of matter—matter as made up of fundamental forces of repulsion and attraction—and thus opened up the possibility of a unified treatment of all forces, including electricity and magnetism. In this theory, all reality was reduced to the two opposing forces of attraction and repulsion. The two forces were diffused throughout all of space and propagated through a medium: by Kant's theory, a medium of some kind was needed to transmit all physical forces—light, gravity, electricity, and magnetism.

  Schelling believed, like Kant, that all phenomena could be reduced to the effects of attractive and repulsive forces, but he went further by suggesting that the fundamental forces became manifest in different forms in different circumstances. Electricity, for example, was the manifestation of attraction and repulsion under given physical conditions. According to Naturphilosophie, all space was filled by a web of forces that manifested themselves in various forms according to the conditions that existed locally. And along with the unity of all forces went the idea that each form of the force—light, heat, electricity, magnetism, gravitation—could be converted into any of the others under the proper experimental conditions. This was the first step toward the realization of a field theory—one in which the energy associated with physical phenomena lies in a continuous medium surrounding bodies rather than in the bodies themselves.

  Coulomb, a good Newtonian, argued that material bodies acted on one another at a distance, along a straight line between them, with the intervening space playing no part at all. Unlike Kant and Schelling, Coulomb believed that each type of force was distinct: for example, electrical forces required a different type of fluid from magnetic forces, so it was impossible that one could be converted to the other.

  From our distant and privileged viewpoint, it is evident that Kant and Schelling were right, at least in broad terms, and that Coulomb was wrong. But things looked different in the early 1800s. Coulomb's equations were clear, elegant, and gave exact answers, while the ideas of Kant and Schelling were speculative and vague, even metaphysical. After being taken aback by Oersted's discovery in 1820 of the connection between electricity and magnetism, André Marie Ampère, the French mathematical physicist whom Davy and Faraday had met in Paris, explained in a letter to a friend why none of his countrymen had thought of placing a compass near a current-carrying wire, as Oersted had done:

  You certainly have a right to ask why it is inconceivable that no one tried the action of the voltaic pile on a magnet for twenty years. However, I believe that the cause of this is easily discovered: it simply existed in Coulomb's hypothesis on the nature of magnetic action; everyone believed this hypothesis as though it were a fact; it simply discarded any possibility of the action between electricity and so-called magnetic wires…. Everyone resists changing ideas to which he is accustomed.4

  Oersted approached electricity and magnetism from quite a different angle. He had been strongly influenced by Naturphilosophie, along with its tenet of the unity of all nature's forces. In principle, he took the Kantian view that all matter was made up of two forces, one that attracted and one that repelled, but he interpreted these as combustion and combustibility. When latent, these forces constituted the chemical properties of bodies, and when conditions allowed them to act freely they produced electricity. An idea formed for exploring how electricity and magnetism might be connected. He would use a battery to send an electric current through a thin wire filament that would grow hot and glow—he thought that magnetic effects might eradiate from the wire along with heat and light. Near the wire would be a compass; perhaps its needle would be deflected. He built the apparatus and tentatively tried it during a lecture. When he c
onnected the battery, the needle twitched, but very feebly, and the experiment made little impression on the audience. Nor can it have done on Oersted because three months passed before he tried it again. Once more, just a feeble twitch. Only when he used a thick wire in place of the filament, thereby greatly increasing the current, did the needle take up a new fixed position. It set itself at right angles to the wire! This time there was no heat and no glow: the connection was directly between electricity and magnetism. The electric current set up a “conflict” that acted in a circle around the wire and gave rise to a force when it encountered magnetic materials.

  This effect was like nothing seen before, and it sent shock waves through the scientific community. Oersted's own explanation of it, though understandably somewhat tentative and vague, ran completely counter to the accepted Newtonian doctrine of push-pull forces acting at a distance in a straight line, and so added to the shock. He wrote:

  We may now make a few observations towards explaining these phenomena. The electrical conflict acts only on the magnetic particles of matter…their magnetic particles resist the passage of this conflict. Hence they can be moved by the impetus of the contending powers.

  It is sufficiently evident from the preceding facts that the electrical conflict is not confined to the conductor, but dispersed pretty widely in the circumjacent space…we may likewise collect that this conflict performs circles; for without this condition it seems impossible that the one part of the uniting wire, when placed below the magnetic pole, should drive it towards the east and when placed above it towards the west; for it is the nature of a circle that the motions in opposite parts should have an opposite direction. Besides, a motion in circles, joined with progressive motion according to the length of the conductor, ought to form a conchoidal or spiral line, but this, unless I am mistaken, contributes nothing to explain the phenomena observed.5

  Oersted had jolted physical science on to a new track. Everyone now knew that electricity and magnetism were inextricably linked. But the exact nature of the linkage was to prove elusive. Finding it would take boldness, tenacity, and genius.

  Davy and Faraday lost no time in repeating Oersted's experiment. They watched the magnetic needle set itself at right angles to the current-carrying wire and, by setting the wire vertical and moving the needle around it, found that the force did, indeed, act in a circle. Seeing is believing, but there must have been a moment when they doubted their senses. Nature's three known primary forces—gravity, electricity, and magnetism—either pulled directly toward the source or pushed directly away from it, in accordance with Newtonian principles. This new force acted sideways.

  At this time, Faraday was immersed in laborious experiments on alloys of steel—bringing in much-needed income for the Royal Institution—and had another serious distraction that we'll come to shortly, so Davy turned to his friend William Hyde Wollaston for help. Wollaston was a distinguished scientist who, among many achievements, had demonstrated that electricity produced by friction, for example by rubbing glass with silk, is the same as that produced by a battery. Together, they quickly dismissed Davy's original guess that the current-carrying wire itself became magnetized, and Wollaston began to carry out some promising experiments.

  Meanwhile, someone else was blazing a trail in Paris. André Marie Ampère latched onto Oersted's discovery with astonishing speed. In an unmatched display of scientific virtuosity, he produced a theory of electromagnetism in only a few months that went on to win almost universal acceptance. And it wasn't just a paper theory; he backed it up with exquisitely elegant experiments. Ampère had overcome personal tragedy to become a popular professor at the École Polytechnique—his father had been a victim of the terror inflicted by the Jacobins in the wake of the Revolution and his wife had died after only four years of marriage. A staunch member of the French Newtonian school, he sought a way to explain Oersted's discovery in terms of straight-line forces and action at a distance, and, with wonderful ingenuity, he found one.

  His inspiration was to test whether two parallel current-carrying wires exerted a force on one another. To his, delight they did—the wires were attracted to one another when the currents ran in the same direction and repelled when the currents ran in opposite directions. The momentous idea came to him that electric currents might be the source of all magnetism. How, then, did permanent iron magnets work? His first idea was that cylindrical currents whirled around an axis that ran between the north and south poles of the magnet, but, if so, where did the currents come from and why had nobody noticed them? In the course of trying to detect these currents, Ampère's friend Augustin Fresnel made the astonishingly prescient conjecture that magnetism in iron was produced by currents circulating around each minute particle of metal, each loop of current acting as a tiny magnet. In a permanent magnet, these circulating currents became aligned with one another and so acted cumulatively to produce a strong magnetic effect.

  Ampère conjectured that the total effect of all these little internal currents in a cylindrical-shaped permanent magnet would be the same as that of a single current circulating only on the surface of the cylinder. The idea was easily tested. He wound a wire in the form of a helix and passed a current through it. His helical coil—the world's first solenoid—was, in effect, carrying a cylindrical current and it behaved exactly like a permanent magnet of the same size and strength. When carefully suspended, it aligned itself with Earth's magnetic field, just like a compass needle.

  Like almost all scientists of the time, Ampère, was steeped in the Newtonian tradition. As he saw it, the pressing question was how to explain his newly discovered force between current-carrying wires in Newtonian terms. His mathematical skill now came to the fore.

  An electrical circuit could be treated mathematically as a string of infinitesimal current elements, each with its own strength and direction. Any two of these elements would exert a mutual force of attraction or repulsion that would depend on their strength and direction and could be assumed to act along the straight line joining them. Moreover, true to Newton's precepts, the force would be inversely proportional to the square of their distance apart. (Ampère had shown by experiment that such a law applied to two current-carrying circuits in parallel planes, and it was reasonable to assume that all elements of the wires behaved in the same way.) By this means, Ampère produced a formula for the mutual force between any two current elements, no matter what their strength and direction or their spatial separation The total force between two complete current-carrying circuits could then, in principle, be worked out by summing the forces between every pair of elements mathematically.

  Ampère's work was a tour de force. Faraday would soon form his own ideas on the subject, but in the winter of 1820 and 1821, he had other things on his mind. One of his friends at the City Philosophical Society was a fellow Sandemanian Edward Barnard. When Faraday met Edward's nineteen-year-old sister Sarah, he was smitten. A few years earlier, he would have claimed that his single-minded pursuit of scientific truth left little room for the fair sex and that love was something to be avoided. In fact, he had jotted a poem in his commonplace book that began:

  What is the pest and plague of human life?

  And what is the curse that often brings a wife?

  ’tis love.1

  How empty and foolish those words seemed now. He had found his life's companion, and he opened his heart to her in a letter:

  You know my former prejudices and my present thoughts—you know my weaknesses, my vanity, my whole mind; you have converted me from one erroneous way, let me hope you will attempt to correct what others are wrong…. In whatever way I can best minister to your happiness, either by assiduity or by absence, it shall be done. Do not injure me by withdrawing your friendship, or punish me for aiming to be more than a friend by making me less; and if you cannot grant me more, leave me what I possess, but hear me.2

  When Sarah showed the letter to her father, he straightaway packed her off to stay with her sister on
the Kent coast. Disconsolate but undeterred, Faraday left his work and followed. For a while he made no headway in his quest, but then came a wonderful day when he and Sarah took a tour of the cliffs of Dover. His journal entry brims with joy.

  The cliffs rose like mountains…. At the foot of these cliffs was the brilliant sparkling ocean, stirred with life by a fresh and refreshing wind, and illuminated by a sun which made the waters themselves seem inflamed…. I can never forget this day. Though I had ventured to plan it, I had little hope of succeeding. But, when the day came, from the first waking moment in it to the last it was full of interest to me; every circumstance bore so strongly on my hopes and fears that I seemed to live with thrice the energy I had ever done before.3

  Sarah had accepted his proposal. They were married in June 1821 and remained devoted to one another all their lives. Though Sarah knew nothing of science, she understood very well how important her husband's work was to him and to the wider world. She made sure that he ate nourishing food and did her best to see that the long hours in the laboratory were balanced by adequate relaxation. She was, as Faraday put it, “a pillow to his mind.”4 They had no children of their own, but their apartment at the Royal Institution was a vibrant, happy home, often the scene of family celebrations at birthdays or after weddings. It was always a treat for young relations to visit Uncle Michael and Aunt Sarah: There were lively games and a never-ending supply of soda, ginger wine, and lozenges that Faraday made in the laboratory downstairs. Even there, he would let the children sit and watch him work. Sometimes he would put on a little show for them—tossing some potassium into water so it would fizz and dart around amid lilac-colored flames, or sealing up some mercury in a glass tube so they could feel its weight and watch it roll around.