Faraday, Maxwell, and the Electromagnetic Field

by Nancy Forbes

  Fig. 5.6. Magnetic lines of force shown by iron filings sprinkled on paper over a magnet. (Courtesy of Windell H. Oksay / www.evilmadscientist.com.)

  The iron filings showed a cross section of a three-dimensional pattern that Faraday saw in his mind's eye, not only around every iron magnet but also around every current-carrying wire coil. (Such coils acted as magnets, as Ampère had shown.)

  Fig. 5.7. Magnetic lines of force around a current-carrying coil. (Used with permission from Lee Bartrop.)

  The pattern changed when a second magnet was brought in, and one of its poles placed near a pole of the first magnet. He explained the notion in his Experimental Researches in Electricity: “By magnetic curves, I mean the lines of magnetic forces, however modified by the juxtaposition of poles, which would be depicted by iron filings.”3

  This was the first public appearance of the term “lines of force”—a concept central to the development of field theory. Along with the electrotonic state, it helped explain what he had discovered in the laboratory. A current was created in a wire circuit when the wire moved near a magnet, or vice versa; that is, when the wire cut across the magnet's lines of force. This act of “cutting” magnetic lines of force, Faraday surmised, was what produced an electrical force in the wire. If the wire was part of a complete circuit, a current then flowed. For example, by pushing a magnet into the cavity of a coil, Faraday had caused its lines of force to be “cut” (in the sense of crossed, not severed) by all the turns of wire in the coil, and thus he generated a current. The same happened in reverse when he pulled the magnet away, and a current flowed in the other direction.

  What about his dynamo? At any instant, a part of the copper disc was moving between the poles of the magnet and cutting its lines of force, hence the steady current across the disc. The same principle held in the iron-ring experiment, though in a less obvious way. When the primary current was first switched on, a wave of lines of magnetic force spread out from the primary coil around the iron ring and into the surrounding space, and as they spread through the secondary coil, they were cut by all the turns of wire there, causing a current to flow. Once the lines of force had settled to a fixed pattern, they were no longer being cut and the secondary current stopped. But when the primary current was turned off, the process was reversed; the lines of force were cut again while they receded, and a current flowed in the opposite direction in the secondary circuit.

  By his unique combination of faculties, complementing supreme experimental skill with sustained imaginative thought, Faraday had produced two entirely new concepts: (1) the electrotonic state and (2) lines of magnetic force. He felt sure they both fit into a larger picture, but at this stage the picture was still a hazy one. Meanwhile, he had an unwelcome taste of déjà vu.

  As we have seen, Faraday had reported his discovery of electromagnetic induction to the Royal Society on November 24, 1831. Around this time, he had also sent word of it to Paris, and his correspondent, J. N. P. Hachette, read out his letter at the December meeting of the Académie des Sciences. So far, so good, but a garbled account of the meeting got to the magazine Le Lycée, which published it and followed up with an article that attributed the discovery to two French scientists. Meanwhile, two Italians, Leopoldo Nobili and Vincenzo Antinori, who had seen the first Lycée article, repeated the experiments and published their own findings. They acknowledged Faraday but, by some mischance, the journal in which their article appeared carried the false date November 1831, whereas Faraday's paper didn't appear in print until early 1832. Back in London, things went from bad to worse: William Jerden of the Literary Gazette spotted the difference in dates and told his readers that two Italians had just beaten Michael Faraday to a great discovery.

  A decade after being falsely accused of plagiarizing Wollaston's ideas on electromagnetic rotations, Faraday was once again innocently embroiled in controversy. All his Sandemanian self-control couldn't contain his fury. He wrote to Jerden:

  I never took more pains to be quite independent of other persons than in the present investigation; and I have never been more annoyed about any paper than the present by the variety of circumstances which have arisen seeming to imply that I had been anticipated.4

  Hachette and Jerden made private and public apologies; and the English translation of Nobili's and Antinori's article carried a prominent acknowledgement of Faraday's prior claim. But this was the last time Faraday freely announced his results before publication.

  His distress from this episode was balanced by the joy of having discovered, by simple experiment and plain reasoning, facts that had eluded all the mathematical physicists. His Sandemanian conscience was put to the test again. This time he succumbed, if only for an instant, to the sin of pride, writing to Richard Phillips:

  It is quite comfortable to me to find that experiment need not quail before mathematics but is quite competent to rival it in discovery and I am amused to find that what high mathematicians have announced…has so little foundation…. Excuse this egotistical letter.5

  Faraday's thoughts on electricity and magnetism ran on—his conjecturing stretched the imagination but was always based on what he had observed in experiments. While carrying out his experiments on acoustic vibrations and waves, he had begun to wonder whether he was watching a relatively slow-motion version of what happened with electricity and magnetism, and his new results with magnets and electric circuits had hardened that thought almost into a conviction. The establishment of magnetic lines of force around the wire when a battery was connected to its circuit must, he thought, take time, and magnetic and electric forces must be transmitted over time by vibrations or waves in the intervening medium, rather like acoustic pressure in air. Such thoughts ran completely counter to the prevailing theory of instantaneous action at a distance, but he had no direct evidence to support them and so held back from mentioning them in his published papers. There was, however, a way to register these radical thoughts formally while still keeping them private. In March 1832, he asked the secretary of the Royal Society to deposit a note in his safe. It read:

  Certain of the results embodied in the two papers Experimental Researches in Electricity and Magnetism…led me to believe that magnetic action is progressive and requires time, i.e. that when a magnet acts on a distant magnet…the influencing cause…proceeds gradually from the magnetic bodies and requires time for its transmission which will probably be found to be very sensible. I think also that electrical induction (of tension) is also performed in a similarly progressive time.

  I am inclined to compare the diffusion of magnetic forces from a magnetic pole to the vibrations upon the surface of disturbed water or those of air in the phenomenon of sound; i.e. I am inclined to think the vibratory theory will apply to these phenomena, as it does to sound and, most probably, to light.6

  Having twice been wrongly accused of plagiarism, Faraday was probably taking a precaution against the same thing happening again.

  There were now several known sources of electricity. Some fish, like electric eels, generated their own; friction produced static electricity, which could be stored in devices like the Leyden jar that released all their charge in one burst; voltaic batteries produced a steady electric current from chemical action between two different metals; and there were Faraday's new magneto-electric currents. Were all the types of electricity identical? Wollaston and others had shown that static and voltaic electricity produced similar electrochemical effects, but, as always, Faraday had to see things for himself, and now he decided to carry out a thorough investigation. He first identified six different types of electrical effect: the attraction and repulsion of electric charges; the heating effect of a current; the production of magnetic forces; chemical decomposition; physiological effects; and, lastly, the spark. He then worked through these effects systematically and demonstrated to his own satisfaction that they were the same whatever the source of the electricity, not neglecting electric fish. As to what electricity actually was—one fluid, two
fluids, or something else—he kept an open mind. This agnosticism is evident from the description of an electric current that he gave in his Experimental Researches in Electricity in 1833.

  By current, I mean anything progressive, whether it be a fluid of electricity, or two fluids moving in opposite directions, or merely vibrations, or, speaking still more generally, progressive forces.7

  Currents didn't exist just in wires; they also flowed in chemical solutions, and there, Faraday thought, he might discover more about them. In the course of yet another historic series of experiments, he established the two fundamental laws of electrolysis: the mass of a substance in a chemical solution that is decomposed when a current is passed through it is proportional to the total amount of electricity passed; and the masses of different substances produced by a given amount of electricity are proportional to what is called their “equivalent masses.” The equivalent mass of an element is now defined in terms of its atomic structure. We can only wonder at the genius of a man who was able to establish this law seventy years before the existence of atoms was proved, especially since Faraday held similar agnostic views about atoms to those that he held about electricity. He wrote:

  The equivalent weights of bodies are simply those quantities of them which contain equal quantities of electricity, or have naturally equal electric powers; it being the ELECTRICITY which determines the equivalent number, because it determines the combining force. Or, if we adopt the atomic theory or phraseology, then the atoms of bodies which are equivalents to each other in their ordinary chemical action, have equal quantities of electricity naturally associated with them. But I must confess I am jealous of the term atom, for though it is very easy to talk of atoms it is very difficult to form a clear idea of their nature, especially when compound bodies are under consideration.8

  When giving a lecture in memory of Faraday almost half a century later, the great German physicist Hermann von Helmholtz shone a light on Faraday's extraordinary prescience. He said:

  The most startling result of Faraday's law is perhaps this. If we accept the hypothesis that the elementary substances are composed of atoms, we cannot avoid concluding that electricity also, positive as well as negative, is divided into elementary portions, which behave like atoms of electricity.9

  The fact that Helmholtz was speaking a decade before the electron was discovered makes his words still more potent. Today we may wonder why Faraday didn't pursue the possibility that each atom has a positively charged part and a negatively charged one. A clue lies in his strange use of the word jealous to describe his opinion of atoms. Like his mentor Davy, Faraday distrusted John Dalton's theory that all matter was composed of atoms, even though it offered a simple explanation for the proportional weights of elements in chemical reactions. Both Davy and Faraday sought unifying theories and didn't like the way that Dalton had apparently divided chemical substances into many unrelated types, each with its own kind of atom. Yet Dalton's simple theory turned out to be fundamentally correct—in this rare case we might say that Faraday threw the baby out with the bath water.

  Meanwhile, Faraday faced the question, how does a current flow in a chemical solution? The prevailing view was analogous to the action-at-a-distance theories of forces between charged objects and between magnetic poles: When the ends of wires connected to a battery were dipped in the liquid, the wire ends became centers of forces that acted along a straight line between them and tore apart the particles of the substance in the solution. The two parts of each torn-apart particle were oppositely charged, so one was drawn toward the negative wire end; the other was drawn to the positive; and the movement of all the free fragments, constituted the current. So prominent was this view that the wire ends were called poles, by analogy with magnetic poles.

  Faraday's mentor Davy, along with Theodor Grothuss from Leipzig, thought the process was rather more complex. In their interpretation, forces from the positive and negative poles did not simply tear the particles apart; they set up a chain of chemical exchanges in the solution, in the course of which the charged fragments continually changed partners in such a way that the positively charged parts moved one step at a time toward the negative pole and the negatively charged ones moved the other way—rather like buckets in a two-way human bucket chain. When the positively or negatively charged fragments reached their respective wire ends, they forsook their last temporary partners, donated their charges to the wire, and emerged free.10

  Fig. 5.8. Moving chain of charged particles in electrolysis. (Used with permission from Lee Bartrop.)

  In one of his brilliant flashes of insight, Davy had taken a further step by saying that electricity was the force that bound different elements together into compounds, implying that it was an inherent property of matter. No need for two fluids, or even one. He was, of course, right, but the notion of fluids had taken such a firm hold that many years passed before they were finally abandoned.

  Faraday sided with Davy and Grothuss but went still further by refuting the role of poles altogether. Whereas they thought that it was the forces from the poles that caused the chemical exchanges, and that these forces diminished with distance, Faraday believed that the poles exerted no force at all—they were simply the entry and exit ports for the electric current that flowed through the solution, powered by the battery. He was right.

  When writing up his researches on electrochemistry, Faraday was faced with a difficulty: he was trying to describe physical processes that nobody had described, or perhaps even thought of, before. This was not a new problem; he had already, with the help of friends, invented the term electrotonic state. As his ideas grew, language itself became part of his thinking. Each new word and each new phrase helped to clarify, even define, the underlying concept, even if that itself was not fully formed. He sought precision and faced a particular problem with words that were in common use but had misleading theoretical connotations. The prime example was current, which implied that electricity was a fluid. Here he never found a useful alternative—nor has anybody since—but elsewhere he coined new words that eventually became the standard ones. By careful and creative attention to language in his writings, he often made it possible for others to grasp and accept new ideas, even when they ran completely counter to prevailing theories. There were exceptions; some of his concepts were so different from anything seen before that none of his contemporaries understood them, especially as he was unable to express them in mathematical terms. His successor at the Royal Institution, John Tyndall, explained the difficulty:

  It sometimes strikes me that Faraday saw the play of fluids and ethers and atoms though his previous training did not let him resolve what he saw into constituents or describe it in a way satisfactory to a mind versed in mechanics…. It must, however, always be remembered that he works at the very boundaries of knowledge and that his mind habitually dwells in the “boundless contiguity of shade” by which that knowledge is surrounded.11

  As we'll see, it took James Clerk Maxwell to understand how Faraday “saw the play” and to translate Faraday's ideas into the kind of mathematical language that others could understand.

  When he needed a new word, Faraday took care to draw on the best advice. He now consulted his friend Dr. Whitlock Nicholl. With Nicholl's help, Faraday now proposed to do away with the misleading term pole for the circuit terminals that dipped into the solution and to replace it with electrode. Hence, also, came electrolysis for the process of separating the components of a solution by passing an electric current through it, and electrolyte for the solution so treated. For further advice, Faraday turned to the Cambridge polymath William Whewell, who proposed anode for the positive electrode, cathode for the negative one, anion, cation, and more generally ion. Like many innovations, the new words met sharp resistance at first, but Faraday was, by now, worldly wise and he countered it by making full use of Whewell's formidable reputation. He acknowledged the debt in a letter to Whewell:

  I had some hot objections made to them here an
d found myself very much in the condition of the man with his son and Ass, who tried to please every body; but when I held up the shield of your authority it was wonderful to observe how the tone of objection melted away.12

  Remarkably, all the common terms now used in electrolysis, except for the stubborn old survivor, current, are the ones that Faraday created in the 1830s with the help of his learned friends. They are testament to the immense care he always took to describe his findings in accurate language, and to his skill in communication. New words were needed not for their own sake but because existing ones carried theoretical baggage that could constrain one's thinking. He may not have known classical Greek, but he had the savoir faire to consult scholars who did, and to choose the right words when they were offered—words that conveyed their meanings clearly, memorably, and with no prior theoretical connotations.

  From his early days with Davy, Faraday had been exposed to the idea that electricity was an inherent power of matter. Now he knew it for a fact. His investigations had also shown beyond doubt that, in electrochemistry at least, electrical force was transmitted not at a distance but locally from particle to particle. Moreover, the force did not act in straight lines but in curves. For example, when two wire terminals from a battery were dipped in a solution of copper chloride, copper was deposited not just on the side of the cathode that directly faced the anode but all around; if the cathode was in the shape of a blade, it became copper-plated at the back as well as the front, showing that the chains of chemical exchanges, and hence the forces, must follow curved paths.

  These were remarkable results, but mathematical physicists, whether in Britain, in France, or elsewhere paid them little attention. Messy, smelly chemistry was outside their province, and they cared little for it. Things were different, however, when Faraday ventured into their heartland of electrostatics, where Coulomb's law, with all its connotations of straight-line action at a distance, was sacrosanct. How dare a mathematical illiterate like Faraday poke his nose in their domain?