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James Clerk Maxwell
The Creator of the Unified Theory of Electromagnetism
Dr Subodh Mahanti



“The greatest change in the axiomatic basis of physics—in other words, of our conception of the structure of reality—since Newton laid the foundation of theoretical physics was brought about by Faraday’s and Maxwell’s work on electromagnetic phenomena…before Maxwell people conceived of physical reality—in so far as it is supposed to represent events in nature—as material points, whose changes consist exclusively of motions, which are subject to total differential equations. After Maxwell they conceived reality as represented by continuous fields, not mechanically explicable, which are subject to partial differential equations. This change in conception of reality is the most profound and fruitful one that has come to physics since Newton…”

Albert Einstein


“The unification of electricity, magnetism and light represented the crowning achievement of classical physics in the nineteenth century. Maxwell’s equations give us the mathematical basis necessary for understanding electromagnetism in just the same way as Newton’s laws of motion and of universal gravitation enable us to comprehend mechanics. The areas of applications covered by Maxwell’s theory are remarkable. They include all electromagnetic and optical devices such as electric motors, electric generators, radio, television, radar, computers, microscopes, telescopes and telecommunication systems.”

Mauro Dardo in Nobel Laureates and Twentieth Century Physics, Cambridge University Press, 2004

“Like Einstein, and in contrast to Newton or Faraday, Maxwell made his enormous advances in physics without excessive mental strain. He excelled in his sure intuition in physics, in applying visual models or mathematical methods without being tied to them, and above all in freeing himself from preconception and in exercising his creative imaginations.

The Cambridge Dictionary of Scientists (2nd Edition, 2002)

Maxwell was the most able theoretical physicist of the nineteenth century. In fact he is even acclaimed as the father of modern physics. He was a perfect complementary to Michael Faraday, the greatest experimentalist of the nineteenth century. Maxwell developed a revolutionary set of four equations called general equations of the electromagnetic field that verified the existence of electromagnetic fields proposed by Michael Faraday and showed that magnetism and electricity are not two different fields but parts of the same unified field, the electromagnetic field. These equations are now called Maxwell equations. “The whole system of wireless telegraphy is a development of the original and surprising theory of Clerk Maxwell, embodying in mathematical form the experimental researches of Faraday.” Maxwell postulated that light is a form of electromagnetic radiation exerting pressure and carrying momentum. Maxwell expounded his theory in his Treatise on Electricity and Magnetism published in 1873. The special theory of relativity, as Einstein himself stated, owes its origins to Maxwell’s equations of the electromagnetic field. Maxwell is regarded as one of the founders of kinetic theory of gases.

Maxwell was the first Cavendish Professor of Experimental Physics in the Cambridge University. In 1874 Maxwell established the Cavendish Laboratory, a unique institution in physics, which was subsequently to be headed by a succession of men of genius. The Laboratory produced graduates who dominated physics for generations. Maxwell was a shy and somewhat eccentric person.

Maxwell was a deeply religious man. He was a simple man with a strong sense of humour. He was known for his devoutness and modesty. Maxwell did not live long enough to see his theories validated experimentally. He died at an early age of 48. Widespread public recognition of his contribution to science and technology came only in the last years of the nineteenth century. As days passed, the relevance of Maxwell’s contribution became more and more evident. Today, the design of tools and devices for a large number of electrical technologies like radio, microwave, radar, optical communications, lasers, power generation and transmission, electronic components and so on are based on the correct understanding and application of Maxwell’s equations. Even the most exiting new promising technologies like lasers, fiber-optics, induction motors and so on are heavily dependent on the application of Maxwell’s theory.

Maxwell was born on June 13, 1831 in Edinburgh, Scotland. It may be noted that it was in 1831 that Michael Faraday made his most influential discovery, electromagnetic induction. Maxwell’s father John Clerk had taken the name of Maxwell as heir to the estate of Glenlair in the Galloway region of Scotland. The Maxwells were comfortably well-off land owners. Maxwell’s mother died when he was just eight years old. Maxwell’s father, an educated man, well-versed in the law and interested in science and invention had great influence on his son’s education. Shortly after Maxwell’s birth, the family moved to their estate at Glenlair, where he enjoyed a country upbringing. It is said that his natural curiosity displayed at an early age. When Maxwell was just three years old, he was described as follows: “He is a very happy man, and has improved much since the weather got moderate; he has great work with doors, locks, keys etc., and ‘Show me how it doos’ is never out of his mouth. He also investigates the hidden course of streams and bell-wires, the way the water gets from the pond through the wall and a pend or small bridge and down a drain…” His parents had planned that he would be educated at home till the age of 13 and then he would join the Edinburgh University. But the plan could not be carried out as his mother died. He was sent to the Edinburgh Academy, Edinburgh in 1841. His friend P. G. Tait described Maxwell’s school days in the following way “At school he (Maxwell) was at first regarded as shy and rather dull. He made no friendships and spent his occasional holidays in reading old ballads, drawing curious diagrams and making rude mechanical models. This absorption in such pursuits, totally unintelligible to his schoolfellows, who were then totally ignorant of mathematics, procured him a not very complimentary nickname. About the middle of his school career however he surprised his companions by suddenly becoming one of the most brilliant among them, gaining prizes and sometimes the highest prizes for scholarship, mathematics, and English verse.” His mathematical abilities were exceptional. At 15, he submitted to the Royal Society of Edinburgh a paper on the drawing of oval curves. His paper was so impressive that many members of the society felt that it could not have written by someone so young. The paper titled “On the description of oval curves, and those having a plurality of foci”, was read to the Royal Society of Edinburgh on April 06, 1846.

He joined the Edinburgh University at the age of 16. At Edinburgh he first began to direct his attention to physics. In 1850, Maxwell joined the Trinity College of the Cambridge University. At Cambridge he came in contact with some of the finest mathematical and scientific minds in Britain. His tutor at Cambridge was William Hopkins. In 1855, he was elected a Fellow of the Trinity College. P. G. Tait in an article in the Proceedings of the Royal Society of Edinburgh wrote“…he brought to Cambridge in the autumn of 1850, a mass of knowledge which was really immense for so young a man, but in a state of disorder appalling to his methodical private tutor. Though the tutor was William Hopkins, the pupil to a great extent took his own way, and it may safely be said that no high wrangler of recent years ever entered the Senate-house more imperfectly trained to produce ‘paying’ work than did Clerk Maxwell. But by sheer strength of intellect, though with the very minimum knowledge how to use it to advantage under the conditions of the Examination, he obtained the position of Second Wrangler, and was bracketed equal with the Senior Wrangler, in the higher ordeal of the Smith’s Prize.” In 1854 he graduated with a degree in mathematics from Trinity College. He obtained the position of the Second Wrangler. The First Wrangler in that year was Edward John Routh (1831-1907), the British mathematical physicist who made contribution to classical mechanics, including procedure for eliminating cyclic co-ordinates from equations of motion.

Maxwell was short of stature and hesitant to speech but nonetheless he made a deep impression on those around him. Describing Maxwell’s undergraduate days, William Thomson (Lord Kelvin) wrote: “…Scholars dined together at one table. This brought Maxwell into daily contact with the most intellectual set in the College, among whom were many who attained distinction in later life. These in spite of his shyness and some eccentricities recognized his exceptional powers….The impression of power which Maxwell produced on all he met was remarkable; it was often much more due to his personality than to what he said, for many found it difficult to follow him in his quick changes from one subject to another, his lively imagination started so many hares that before he had run one down he was off on another.”

In 1856 Maxwell was appointed a Professor of Natural Philosophy at Marischal College, Aberdeen, Scotland. In 1860 Maxwell moved to London as professor of natural philosophy and astronomy at King’s College, London, where he spent five years and then moved back to Scotland to take care of his family estate where he spent his time by researching and writing. He made periodic trips to Cambridge. In 1871, Maxwell accepted an offer from Cambridge to be the first Cavendish Professor of Experimental Physics at Cambridge. This was the most substantial recognition Maxwell received in his lifetime. He accepted the post rather reluctantly. However, he devoted his time to establish the new Cavendish Laboratory. He designed the laboratory and helped set it up. The Laboratory was formally opened on June 16, 1874. Maxwell was the first Director of the Cavendish Laboratory, which was to become one of the most famous physics laboratories in the world.

Maxwell’s General Equations of the Electromagnetic Field were first presented in his famous memoir entitled “A Dynamical Theory of the Electromagnetic Field” published in 1865. This was one of the greatest papers in theoretical physics of the nineteenth century. Maxwell after reading the works of William Thomson and Michael Faraday, believed that the lines of force conceived by Faraday to visualize the magnetic and electric phenomena represented something real. Beginning in 1856, with his paper “Faraday’s lines of Force”, Maxwell produced a long series of articles which revolutionized ideas about electricity, magnetism and light. Maxwell wrote: “As I proceeded with the study of Faraday, I perceived that his method of conceiving the phenomena was also a mathematical one, though not exhibited in the conventional form of mathematical symbols. I also found that these methods were capable of being expressed in the ordinary mathematical form, and thus compared with those of the professed mathematicians.” After carefully exploring the implications of Faraday’s ideas, Maxwell developed analogies and models to show how these ideas can be related to familiar concept and finally he formulated the mathematical expressions making up famous equations of the electromagnetic field. Before Maxwell came into the picture, it was widely believed that there was a fundamental difference in the descriptions of nature used by mathematicians and those by physicists, with a more purely physical outlook. This was a reason why Faraday’s theoretical ideas were not closely examined by mathematicians. However, Maxwell’s work changed all of this. Maxwell was much influenced by William Thomson. Maxwell wrote: “I was aware that there was supposed to be a difference between Faraday’s way of conceiving phenomena and that of the mathematicians, so that neither he nor they were satisfied with each other’s language. I had also the conviction that this discrepancy did not arise from either party being wrong. I was first convinced of this by Sir William Thomson, to whose advice and assistance, as well as to his published papers, I owe most of what I have learned on the subject.”

While presenting his theory Maxwell wrote: “The theory I propose may…be called a theory of Electromagnetic Field, because it has to do with the space in the neighbourhood of the electric or magnetic bodies…The electromagnetic field is that part of space which contains and surrounds bodies in electric or magnetic conditions…in order to bring these results within the power of symbolical calculation, I then express them in the form of the General Equations of the Electromagnetic Field.”

Maxwell’s equations of electromagnetic field described the evolution in space and time of electric and magnetic fields generated by charges, magnets and currents. These equations also demonstrated that the two cannot be separated. An electric field changing with time would invariably generate a magnetic field, which would induce an electric field in adjacent regions of space and which in turn would generate a magnetic field. And this process goes on. Maxwell demonstrated that electric and magnetic fields are not two different fields but part of a single unified field—the electromagnetic field.

Maxwell’s equations of electromagnetic field predicted the existence of electromagnetic waves—changing electric and magnetic fields propagating outward in all directions result in a wave disturbance traveling in empty space. Maxwell calculated the speed at which the electromagnetic waves propagate. By taking into consideration of the values of purely electric and magnetic measured quantities Maxwell calculated that electromagnetic waves traveled approximately at the speed that of light. From this observation Maxwell came to the conclusion that light itself must be an oscillating electric charge. He concluded that light itself was electromagnetic radiation. Maxwell did not stop there. He proposed that light (and infrared and ultraviolet radiation) was probably just one of a large family of radiations caused by charges oscillating at different velocities. Maxwell wrote: “The velocity is so nearly that of light, that it seems we have strong reasons to conclude that light itself (including radiant heat and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws.” Maxwell predicted the existence of other forms of electromagnetic radiations with frequencies and wavelength outside the infrared and ultraviolet regions. The German physicist Heinrich Rudolf Hertz (1857-1894) detected radio waves in 1887 and this led to the general acceptance of Maxwell’s theory. Maxwell’s theory was developed further by the Dutch physicist Hendrik Antoon Lorenz (1853-1928).

Maxwell proposed that light travelled through an invisible medium, which he named ether. This medium filled all space “unbroken from star to star.” In 1873, Maxwell wrote: “There can be no doubt that the interplanetary and interstellar spaces are not empty but occupied by a material substance or body, which is certainly the largest, and probably the most uniform, body of which we have any knowledge.” Maxwell was not the first to propose that some invisible medium fill the vastness of the space. The genesis of the idea can be traced back to the ancient Greeks. For Maxwell there was an obvious need for proposing the idea of the ether. If light was a wave then it seemed obvious that it had to be wave traveling in some medium. Later it was proved that Maxwell’s idea of the ether was erroneous. Albert Abraham Michelson (1852-1931), an American physicist, while working with Hermann Ludwig Ferdinand von Helmholtz (1821-1894) in Germany, tried to verify the existence of ether experimentally. Michelson set out to measure the speed with which the earth moved through the ether. Michelson thought that in a universe filled with stationary ether, the planet Earth would meet resistance as it moved through the ether. And in the process the moving Earth would create a current, a sort of “wind” in the ether. In such a situation a light beam moving with the current would be carried along it but the light beam moving against the current would be slowed down. To measure such differences Michelson built an instrument called interferometer. This device could split a beam of light into two halves running perpendicular to each other and then it could rejoin the split beam. In this way it was possible for the device to measure the difference in the speeds of the two beams of light with great accuracy. Michelson based on his own experiments concluded that “The result of the hypothesis of a stationary ether is…shown to be incorrect, and the necessary conclusion follows that the hypothesis is incorrect.” Michelson carried out his experiments again and again to rule out any experimental errors. He was joined by Edward Williams Morley (1838-1923). Together they carried out a very precise experiment but failed to detect the existence of ether. Some other experiments designed to demonstrate the existence of ether also failed.

Maxwell made significant contributions to the development of thermodynamics. He was one of the founders of the kinetic theory of gases. His theory brought a new subject, the statistical physics, into being. This linked thermodynamics and mechanics. Maxwell’s theory is still widely used as a model for rarefied gases and plasmas.

Maxwell had written a paper, “On the Stability of the Motion of Saturn’s Rings” for entering the competition for the Adams Prize of 1857 of the St John’s College, Cambridge. In this paper, Maxwell argued that the only structure of Saturn’s rings that was consistent with the accepted laws of mechanics was “one composed of an indefinite number of unconnected particles.” He illustrated his argument, built on a skillful mathematical analysis, with a model. The model constructed by Maxwell still can be seen in the Cavendish Laboratory at Cambridge. The then Astronomer Royal of England, Sir George Biddell Airy (1801-92), described the Maxwell’s paper as “one of the most remarkable applications of Mathematics to Physics that I have ever seen.” In 1610, when Galileo first viewed the planet Saturn with a telescope, he saw what appeared to him to be little stars attached to the planet. In 1655, that is after 45 years of Galileo’s observation, the Dutch physicist and astronomer Christiaan Huygens (1629-1695) discovered that these were in fact rings circling Saturn. In the 1980s, the Voyager space probes showed us that Saturn’s rings are made of millions of particles, ranging in size from dust to many meters in diameter and thus proved the prediction made by Maxwell based on his mathematical skill.

In 1860, Maxwell was awarded the Rumford Medal of the Royal Society for his work on colour perception. By using devices called “colour wheel” and “colour box” constructed by him, Maxwell demonstrated how mixtures of different colours were perceived by different people. In this work he was helped by his wife, Katharine Mary Dewar. Maxwell’s work on colour perception is viewed as the beginning of the science of quantitative colorimetry. Maxwell by using red, green and blue filters produced the first true trichromatic colour photograph, of a Scottish tartan ribbon. He displayed this photograph to Faraday and others at the Royal Institution in 1861. Maxwell’s process of colour photography was the forerunner of today’s modern colour photography. He also invented the “fish-eye” lens.

Maxwell edited Henry Cavendish’s papers. And this work occupied much of his time between 1874 and 1879. Cavendish only published two papers and left twenty packages of manuscript on mathematical experimental electricity. Commenting upon Maxwell’s work in this period, R. L. Smith-Rose in his biography of Maxwell titled James Clerk Maxwell: A physicist of the nineteenth century (1948) wrote: “…Maxwell entered upon this work with the utmost enthusiasm: he saturated his mind with the scientific literature of Cavendish’s period; he repeated many of his experiments, and copied out the manuscript with his own hand…The volume entitled ‘The Electrical Researches of the Honourable Henry Cavendish’ was published in 1879, and is unequalled as a chapter in the history of electricity.”

James Clerk Maxwell died on November 05, 1879 in Cambridge. The year Maxwell died, Albert Einstein was born. “Like Maxwell’s work in the 19th century, Einstein’s would dominate much of the century to come.”

We conclude by quoting Max Plank on Maxwell: “His name stands magnificently over the portal of classical physics, and we can say this of him; by his birth James Clerk Maxwell belongs to Edinburgh, by his personality he belongs to Cambridge, by his work he belongs to the whole world.”


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