Maxwell + faraday

Part 3. The Electromagnetic Field 

by Keith J. Laidler, 

Department of Chemistry, 

University of Ottawa, 

Maxwell's theory of electromagnetic radiation alone places him among the great scientists of all time. It is contained in three substantial papers, and his Treatise on Electricity and Magnetism. The first of the papers appeared in 1856 when he was aged 25 and had the previous year been elected a Fellow of Trinity College, Cambridge. In this paper he gave a mathematical treatment of Faraday's unconventional ideas about electricity and magnetism. The second paper appeared in 1861-62, and suggested a rather complex and artificial model for the ether. In the third paper, published in 1864, Maxwell dispensed with the model and relied entirely on mathematical equations for the electromagnetic field. His book, published in 1873, was to some extent a survey of the whole field, but it raised a number of questions for further treatment. Perhaps if he had lived longer he would have answered many of them. In all his publications Maxwell emphasized his great debt to Michael Faraday. In the preface to his book he said that his main task had been to convert Faraday's physical and qualitative ideas into mathematical form. To understand Maxwell's theory of electromagnetic radiation it is therefore important to have a clear idea of Faraday's experimental results and of his conclusions. It is useful to start with Oersted's discovery of electromagnetism, and its interpretation by Amp�re, as it was this interpretation that led Faraday to think along different lines. 

Oersted: Electromagnetism (1820) 

In l820 Hans Christian Oersted (1777- l851), professor of physics at the University of Copenhagen, brought a compass needle near to a wire through which an electric current was passing. He found that the needle tended to turn towards a direction at right angles to the wire. When the direction of the current was reversed, the needle turned in the opposite direction. A remarkable feature of this famous discovery is that it was made in front of a class of students. Oersted and his assistant had set up the experiment but had not had time to try it out before the students arrived. Oersted first decided to defer the experiment until later, but during the lecture began to feel confident that it would work, and performed it successfully. Another remarkable feature is that, since the deflection of the needle had been small, Oersted was so little impressed by the result that he performed no further experiments on the subject for three months. Then having confirmed the effect, he sent a four-page announcement of it, in Latin, to many leading scientific journals, and to a number of scientists. The announcement appeared, in various languages, in a considerable number of journals, such as the Annals of Philosophy, Gilbert's Annalen der Physik und physikalische Chemie, and the Annales de chimie et de physique. Further publicity was given to the discovery by the fact that the distinguished scientific statesman Fran�ois Arago (1786-1853) called attention to the discovery at a meeting of the Acad�mie des Sciences in Paris in September, 1820. Oersted's experiment was the first to show a connection between electricity and magnetism, and can be called the birth of electromagnetism. At the time, in the scientific tradition established in particular by Newton, theories were formulated in terms of forces acting in straight lines between points; these were known as central forces. In 1767 the English chemist Joseph Priestly (1733-1804) showed that the forces followed the inverse square law. Later the French military engineer Charles Augustin de Coulomb (1736-1806) carried out careful experiments on bodies charged with static electricity, and on magnets, and in 1794 confirmed that the attractions and repulsions followed the inverse square law. The fact that the magnetized needle moved towards a position at right angles to the wire, rather than parallel to it, was therefore particularly surprising. It suggested a force not acting in a straight line but circularly, which most scientists thought to be unreasonable. However, within a short time many scientific investigators had confirmed the result. During the next six years much progress, along both experimental and theoretical lines, was made by the French physicist Andr� Marie Amp�re (1775-1836), who had been in the audience when Arago announced Oersted's discovery in Paris. Besides confirming Oersted's results, Amp�re made careful studies of the effects of electric currents on one another. He found that if currents travelled in the same direction along two parallel wires, there was attraction between them; if the currents travelled in the opposite directions there was repulsion. He also worked out a detailed mathematical treatment of the interactions, on the basis of the assumption that current-carrying elements of the wire interacted with one another according to the inverse square law. By integrating the effects of all the elements he arrived at expressions that were consistent with the experimental results. This was a very impressive treatment, and because of it Maxwell in his Treatise (1873) referred to Amp�re as the "Newton of electricity". To explain the effect on an electric current on a magnet, Amp�re supposed that magnetism arises from electricity moving in circular orbits around the axis of the magnet. He carried out experiments with wires wound around glass tubes, and confirmed that when a current passed, a magnetic effect was obtained. He then developed an elegant mathematical treatment of the interactions between electric currents and the circular currents around the magnets, and was able to explain Oersted's results in terms of central forces. Amp�re's work was at once recognized by most investigators as an achievement of great significance, but some objections were raised. It was pointed out that there was no experimental evidence for a flow of electricity around magnets, and no suggestion as to how it might arise. Volta had found that a current results when two dissimilar metals are present, but not if only one metal is present. Amp�re's later modified his theory to relate to the molecules in the magnets, suggesting that perpetual electric currents moved in orbits around them. It must be remembered that at the time there was no understanding of the nature of electricity; the electron was not to be discovered until over half a century later. Michael Faraday (1791-1867) was particularly unhappy with Amp�re's treatment. Since he knew little mathematics, and was ill-versed in physical theories, he simply could not understand it. He was quite content to think of a circular force arising from a current flowing in a wire. Hardly anyone brought up on the physics of the time could accept such an idea, and yet it was the origin of the important concept of the electromagnetic field, which was to be the core of the later ideas of Faraday and Maxwell. 

Faraday: Fields of Force (1821-1860) 

Michael Faraday's background was very different from Maxwell's, but they grew up to be very alike in many ways; both were men of the utmost kindness and simplicity of character. Faraday was the son of a blacksmith who could do little more than provide the bare necessities of life to his wife aid many children. At the age of 14 Michael left school and was apprenticed to a good natured bookbinder who encouraged him to read the books he was binding. One particular book, Jane Marcet's Conversations on Chemistry, made a particular impression on Faraday, and perhaps did more than anything else to arouse his interest in science. He attended some of Sir Humphry Davy's lectures at the Royal Institution, and by a fortunate chance managed in 1813 to obtain a position as Davy's assistant. He was so successful in the research that he did there that only twelve years later he succeeded Davy as Director of the Royal Institution laboratories. In 1821, soon after Amp�re had presented his interpretation of Oersted's result, Faraday's friend Richard Phillips, an editor of the Philosophical Magazine, persuaded Faraday to look into the subject of electromagnetism. Like other editors of scientific journals, Phillips had been inundated with papers on the subject The situation is a little like that in 1989, when the submission of the original paper on "cold fusion" (Chem 13 News, October 1984, pp 6-7) produced an avalanche of submitted papers, in some of which the authors made claims that they hoped would bring them fame and fortune. Happily, Oersted's announcement was more fruitful. Faraday accepted Phillips's suggestion rather reluctantly, as previously his work had been on chemistry and rather far from electromagnetism. Posterity must be grateful to Phillips for his gentle prodding. Faraday at once repeated Oersted's experiments, and he noted that when a small magnetic needle was moved around a wire carrying a current, one of the poles turned in a circle. He then speculated that a single magnetic pole, if it could exist, would move continuously around a wire as long as the current flowed. This led him to perform an experiment of great simplicity and also of great importance. In 1821 he attached a magnet upright to the bottom of a deep basin, and then filled the basin with mercury so that only the pole of the magnet was above the surface. A wire free to move was attached above the bowl and dipped into the mercury. When Faraday passed a current through the wire and the magnet, the wire continuously rotated around the magnet. In an adaptation of the experiment, he made the magnet rotate around the wire. The great significance of these simple demonstrations is that electrical energy was being converted into mechanical energy for the first time. To Faraday the results implied that there were circular "lines of force" around the current-carrying wire, and he accepted this as a simple experimental fact. Almost everyone else concluded that the force could not be simple, but must be explained in some way in terms of central forces. For the next ten years Faraday worked only sporadically on electricity. In 1831 he learned of the experiments of Joseph Henry (1797-1878) in Albany, New York. The first electromagnet had been created in 1823 by the English physicist William Sturgeon (1753-1850), and Henry improved the technique greatly, observing that the polarity could be reversed by a reversal of the direction of the - current. This led Faraday to his famous experiment of 1831 in which he demonstrated electromagnetic induction. He wound one side of an iron ring with insulated wire, and arranged a secondary winding, connected to a galvanometer, around the other side. When an electric current began to flow through the primary coil, the galvanometer revealed a transient flow in the secondary circuit. A continuous current in the primary circuit had no effect; it was only when the current started or stopped that there was an effect on the galvanometer. Faraday's 1821 discovery of electromagnetic rotation had shown that electrical force could be converted into motion. In 1831 he succeeded in converting mechanical motion into electricity - in other words, in constructing the first dynamo. He rotated a copper disk between the poles of a magnet, and found a steady current flowed from the centre of the disk to its edge. This achievement encouraged Faraday to carry out the further researches which were to lead to his general theory of electricity in 1838. In 1832 Faraday turned his researches in a somewhat different direction by investigating the electrolysis of aqueous solutions. In 1833 he showed that electrolysis can be brought about by electricities produced in a variety of ways, such as from electrostatic generators, voltaic cells, and electric fish. In particular, he showed that electrolysis can occur if an electric discharge is passed through a solution, without any wired being introduced into it. Experiments reported in 1834 convinced him that electrolysis was another electrical phenomenon that cannot be explained in terms of central forces and action at a distance. He performed one experiment in which two solutions were separated from one another by a seventy-foot string soaked in brine. Gases were evolved at the two wires, and Faraday thought it impossible that the effect would extend over such a length if the inverse square law applied. He carried out another experiment in which a solution was placed near a source of static electricity which produced an intense electric field. No electrolysis occurred, and Faraday concluded that it is necessary for a discharge to take place or for a current to flow. He also demonstrated that the effects of electrolysis do not follow straight lines, which they would do if there were action at a distance. Also, Faraday argued, if a substance were attracted to a wire by the inverse square law, would it not remain bound to the wire rather than being released from it? The theory of electricity and magnetism accepted by Faraday from 1838 onwards are neatly summed up in Maxwell's Treatise on Electricity and Magnetism (1873): "...Faraday, in his mind's eye, saw lines of force traversing all space where the mathematicians saw centres of force acting at a distance: Faraday saw a medium where they saw nothing but distance: Faraday sought the seat of the phenomena in real actions going on in the medium, they were satisfied that they had found it in a power of action at a distance impressed on the electric fluids." At first Faraday thought that his lines of force were carried by molecules under strain but later, realizing that they are set up in vacuum, thought in terms of strains in the ether, which was supposed to pervade all space. in the last paper he submitted for publication, in 1860, Faraday included gravity as involving a field of force - an idea that was somewhat ridiculed at the time, but later realized to be correct. For many years Faraday attempted to find support for his ideas by observing some physical effect in matter through which his lines of force were passing. His first discovery of such an effect was in 1845, when he found that plane-polarized light was rotated when it was passed through a piece of glass in a strong magnetic field. This was the first observation of the effect of magnetism on light. The result suggested to Faraday that substances like glass, hitherto regarded as non-magnetic, were not entirely indifferent to a magnetic field. He carried out many experiments in which substances, including gases, were placed between the poles of an electromagnet. He found that some substances, such as iron, tended to align themselves along the lines of force, and were attracted into the more intense parts of the electromagnetic field; he called such substances paramagnetic. Other substances like bismuth, which he called diamagnetic, aligned themselves across the magnetic field, and tended to move into regions of less intense field. He explained the difference between paramagnetics and diamagnetics in terms of the way they distorted a magnetic field. 

Maxwell: Approach to an Electromagnetic Theory (1856-1862) 

Much of Faraday's great work had been completed by the time Maxwell became a student at Cambridge in 1850. Maxwell, who was one of the few to realize its importance, always insisted that he did nothing more than express Faraday's ideas in mathematical form, but here he was being unduly modest. Producing the mathematical equations was far from a routine task that any highly skilled mathematician could have carried out; it also involved clarifying and modifying the basic concepts. Maxwell's first paper, "On Faraday's lines of force", which appeared in 1856 when he was 25, was significant for showing mathematically that Faraday's ideas gave a valid quantitative alternative to Amp�re's treatment based on central forces. The paper is also important for its treatment of electrical action as analogous to the motion of an incomprehensible fluid. Maxwell's final electromagnetic theory in fact differs from all preceding physical theories in being based on an analogy rather than a physical model capable of being visualized. Maxwell's second paper on the subject, "On physical lines of force", appeared in four parts in I ~6 I -62, and was mainly concerned with devising a model for the ether which would account for the stresses associated with Faraday's lines of force. This ether had a rather complicated structure, consisting of spinning vortices, some of them electrical and some magnetic. The model was such that a changing magnetic field gave rise to an electric field, and that a changing electric field produced a magnetic field. This model is today only of historical interest, in showing how Maxwell's ideas developed, since he discarded the model in his final version of his electromagnetic theory, basing it entirely on the mathematical analogy. 

The Speed of an Electromagnetic Wave 

In 1861 the British Association for the Advancement of Science set up a committee under William Thomson's chairmanship to establish a set of electrical and magnetic standards. During the course of their work it became clear to Maxwell and others that important insight can be obtained by comparing results expressed in the two sets of units, electrostatic and electromagnetic, that were being used at the time. The electrostatic units were particularly appropriate to static electricity, and related the force of attraction and repulsion between two charged bodies to the quantities of electricity that they held. The electromagnetic system of units, on the other hand, related force to electric currents. The quantity of electricity residing on a wire at a given time depends on the speed with which the current travels along the wire. It can be shown that the ratio of an electromagnetic unit of charge to an electrostatic unit of charge is the speed with which the current passes along a wire. During the 1860s Maxwell and various colleagues carried out careful experiments in which they compared the two units. Maxwell's own experiments were carried out using equipment made available to him by John Peter Gassiot (1797-1877), a wealthy wine merchant and amateur scientist who had already done some remarkable experiments using vast numbers of electric cells. The conclusion from the experiments comparing the two sets of units was that the speed of an electric current was close to 3 x 10 m/s, which is the speed of light. An alternative approach, used by Maxwell and others, was to compare the electrical quantity now called the permittivity of a vacuum, o, with the magnetic quantity now called the permeability, �o. Maxwell's mathematical treatment of Faraday's lines of force led to the conclusion that the speed v of an advancing electromagnetic field was given by v =1/(o �o) Measurements made by various physicists of �o and o also led to the result that v obtained in this way was the speed of light. These results convinced Maxwell and others that light is an electromagnetic wave; in his own words, emphasized in italics in his 1861-62 papers: "Light consists in the transverse undulations of the same medium which is the cause of electric and magnetic oscillations."  In other words, a single electromagnetic theory is needed for light, an electric field and a magnetic field. The field produced by an electric current has also a magnetic component, and the field produced by a magnet has also an electric component; light also has electric and magnetic components. A significant aspect of this work was that it led to a decision between two alternative theories of electricity that were held at the time. One theory was that there were two electrical fluids, positive and negative, which moved in opposite directions when a current flowed. Use of the method of comparison of units led to the conclusion that if there were two fluids they would each flow with half the speed of light. The evidence thus supports the theory (which Benjamin Franklin among others advocated) that only one type of electricity flows along a wire when a current passes. Today, of course, we know that a flow of electrons is involved. 

Maxwell: Electromagnetic Theory (1864-1873) 

In Maxwell's third and final major paper on the subject, "A dynamical theory of the electromagnetic field" (1864), he ignored his rather elaborate and artificial model he had proposed for the ether, and concentrated on the propagation of electromagnetic waves through space. The position he took, and this is accepted today, is that the mathematical treatment remains valid without any assumptions about the nature of the medium through which the waves travel. In other words, he threw out the bathwater but carefully preserved the baby! In doing so Maxwell made an important break with scientific tradition. Previously it had been felt necessary to base a scientific theory on a model that could be clearly visualized. Maxwell's theory, on the other hand, represented the situation not in terms of a model, but as a mathematical analogue. Maxwell's fiend and colleague William Thomson (Kelvin) always insisted on a mechanical model; in his own words "I never satisfy myself unless I can make a mechanical model of a thing. If I can make a mechanical model I can understand it." As a result, Kelvin never really understood Maxwell's theory, even though he had himself made important contributions to interpreting Faraday's lines of force mathematically. Similarly, he never understood Clausius's concept of entropy - another concept that cannot be understood in terms of a model - even though he had been one of the first to appreciate the second law of thermodynamics. Maxwell's theory can be expressed in terms of a few equations which have been referred to as "simple". They are indeed simple in form, but understanding them involves a considerable background knowledge of electrical and magnetic theory, and vectors. Maxwell himself invented the names "curl", "grad" and "div" for operators that appear in his equations. Maxwell's famous book Treatise on Electricity and Magnetism, which was published by the Clarendon Press, Oxford, in 1873, is in many ways something of a surprise. It is certainly not to be recommended to a student wanting to learn about the theory; the 1864 paper is much easier to follow. The book raises a number of aspects which Maxwell himself had not been able to clarify. The book consists of four parts: Electrostatics, Electrokinetics, Magnetism, and Electromagnetism. The author makes the recommendation that these four parts should be read concurrently, but does not explain how this remarkable feat should be performed; presumably he meant that one should read a little of the first part, then a litlle of the second, and so on. However, in spite of its obscurities, the book was a great inspiration to many physicists, including Einstein. A significant feature of the book is that the word ether is mentioned only once, and that the model for the ether elaborated in his 1861-62 paper is referred to only incidentally. This does not mean that Maxwell had abandoned his belief in the existence of an ether; in his article on "Ether" in the famous 9th edition of the Encyclopedia Brittanica (1875) he expressed very clearly his belief in the existence of an ether. He considered, however, that his theory of electromagnetic radiation was valid whether or not the ether exists, or what its nature is. 

Maxwell's Scientific Legacy 

Maxwell's electromagnetic theory had an enormous impact on later scientific work, and on the development of technology. The theory soon led to the discovery of radiation having wavelengths different from those of near ultraviolet, visible and near infrared radiation, which were the only regions of the spectrum known in Maxwell's time. The discovery in 1888 by Heinrich Hertz (1857 - 1894) of radio transmission was much inspired by Maxwell's theory, and it led to television, radar and microwave techniques. These in turn made possible the exploration of distant space. X-rays were discovered in 1895,and gamma rays in 1900. Einstein recognized that his theory of relativity depended greatly on Maxwell's theory, and it had many other consequences, including the understanding of the structure on atomic nuclei. 

Suggested Reading 

The biographies of Maxwell mentioned in Part 1, by Everitt, Tolstoy and Goldman, give good non-mathematical accounts of electromagnetic theory. Those wishing a mathematical treatment should consult modern textbooks of physics and not Maxwell's Treatise, which is difficult reading. Some of Maxwell's original papers, on the other hand, are very lucid; The Scientific Papers of James Clerk Maxwell (Ed. W.D. Niven, 1890) were reprinted by Dover Publications in 1965. See, for example, Paper XXXVI for a comparison of electrostatic and electromagnetic units. A very clear account, with full mathematical details, of Amp�re's theory of electromagnetism is to be found in R.A.R. Tricker, Early Electromagnetism, Pergamon Press, Oxford, 1965. The Publisher, Editor and Editorial Board of Phys 13 News would like to thank Prof. Keith J. Laidler for this excellent series of three articles on the life and work of James Clerk Maxwell that have appeared in the past three issues of Phys l3 News. It is a series that should be read by every student of physics.