The Contributions of James Clerk Maxwell to Science
Whether you are talking on your cell phone, watching your favorite television program, surfing the web, or using your GPS to guide you on a trip, these are all modern conveniences made possible by the foundational work of the 19th century Scottish physicist James Clerk Maxwell. Though Maxwell didn’t discover electricity and magnetism, he did put in place a mathematical formulation of electricity and magnetism that built upon the earlier work of Benjamin Franklin, André-Marie Ampère, and Michael Faraday. This Hub gives a brief biography of the man and explains, in non-mathematical terms, the contribution to science and the world of James Clerk Maxwell.
The Life of James Clerk Maxwell
James Clerk Maxwell was born on June 13, 1831, at Edinburgh, Scotland. Maxwell’s prominent parents were well into their thirties before they married and had one daughter who died in infancy before James was born. James’s mother was nearly forty by the time he was born, which was quite old for a mother in that period.
Maxwell’s genius started to appear at an early age; he wrote his first scientific paper at age 14. In his paper, he described a mechanical means of drawing mathematical curves with a piece of string, and the properties of ellipses, Cartesian ovals, and related curves with more than two foci. Since Maxwell was deemed too young to present his paper to the Royal Society of Edinburgh, rather it was present by James Forbes, a professor of natural philosophy at Edinburgh University. Maxwell’s work was a continuation and simplification of the seventh century mathematician René Descartes.
Maxwell was educated first at the University of Edinburgh and later at Cambridge University, and he became a fellow of Trinity College in 1855. He was professor of natural philosophy at Aberdeen University from 1856 to 1860 and occupied the chair of natural philosophy and astronomy at King’s College, University of London, from 1860 to 1865.
While at Aberdeen, he met the daughter of the principal of Marischal College, Katherine Mary Dewar. The couple were engaged in February 1858 and married in June 1858. They would remain married until James’ untimely death, and the couple did not have any children.
After temporary retirement due to a severe illness, Maxwell was elected the first professor of experimental physics at the University of Cambridge in March 1871. Three years later he designed and equipped the now world-famous Cavendish Laboratory. The laboratory was named after Henry Cavendish, great uncle to the chancellor of the university. Much of Maxwell’s work from 1874 to 1879 was the editing of a large quantity of Cavendish’s manuscript papers on mathematical and experimental electricity.
Although he was busy with academic duties throughout his career, Clerk Maxwell managed to combine these with the pleasures of a Scottish country gentleman in the management of his family’s 1500-acre estate at Glenlair, near Edinburgh. Maxwell’s contributions to science were achieved in his short life of forty-eight years, for he died at Cambridge of stomach cancer on November 5, 1879. After a memorial service in the chapel of Trinity College, his body was interred in the family burying place in Scotland.
Since Maxwell's time, physical reality has been thought of as represented by continuous fields, and not capable of any mechanical interpretation. This change in the conception of reality is the most profound and the most fruitful that physics has experienced since the time of Newton.— Albert Einstein
The Rings of Saturn
Among Maxwell’s earliest scientific work was his investigation of the motions of Saturn’s rings; his essay on this investigation won the Adams Prize at Cambridge in 1857. Scientists had long speculated as to whether the three flat rings which surround the planet Saturn were solid, fluid, or gaseous bodies. The rings, first noticed by Galileo, are concentric with one another and with the planet itself, and lie in Saturn’s equatorial plane. After a long period of theoretical investigation, Maxwell concluded that they are composed of loose particles not mutually coherent and that the conditions of stability were satisfied by the mutual attractions and motions of the planet and the rings. It would take over one hundred years before images from the Voyager Spacecraft verified that Maxwell had indeed been correct in showing that the rings were made of a collection of particles. His success in this work immediately placed Maxwell in the forefront of those working in mathematical physics in the second half of the nineteenth century.
In the 19th century, people did not understand how humans perceived colors. The anatomy of the eye and the ways colors could be mixed to produce other colors was not understood. Maxwell was not the first to investigate color and light, as Isaac Newton, Thomas Young, and Herman Helmholtz had previously worked on the problem. Maxwell’s investigations in color perception and synthesis were begun at an early stage in his career. His first experiments were carried out with a color top on which could be fitted a number of colored discs, each divided along a radius, so that an adjustable amount of each color could be exposed; the amount was measured on a circular scale around the edge of the top. When the top was spun, the component colors—red, green, yellow, and blue, as well as black and white—blended together so that any color could be matched.
Such experiments were not entirely successful because the discs were not pure spectrum colors and also because the effects perceived by the eye depended upon the incident light. Maxwell overcame this limitation by inventing a color box, which was a simple arrangement for selecting a variable amount of light from each of three slits placed in the red, green, and violet parts of a pure spectrum of white light. By a suitable prismatic refracting device, the light from these three slits could be superimposed to form a compound color. By varying the width of the slits it was shown that any color could be matched; this formed a quantitative verification of Isaac Newton’s theory that all colors in nature can be derived from combinations of the three primary colors—red, green, and blue.
Maxwell thus established the subject of the composition of colors as a branch of mathematical physics. While much investigation and development have since been carried out in this field, it is a tribute to the thoroughness of Maxwell’s original research to state that the same basic principles of mixing three primary colors are used today in color photography, movies, and television.
The strategy for producing full-color projected images was outlined by Maxwell in a paper to the Royal Society of Edinburgh in 1855, published in detail in the Society’s Transactions in 1857. In 1861 the photographer Thomas Sutton, working with Maxwell, made three images of a tartan ribbon using red, green, and blue filters in front of the camera lens; this became the world’s first color photograph.
Kinetic Theory of Gases
While Maxwell is best known for his discoveries in electromagnetism, his genius was also exhibited by his contribution to the kinetic theory of gases, which can be regarded as the basis of modern plasma physics. In the earliest days of the atomic theory of matter, gases were visualized as collections of flying particles or molecules with velocities depending upon temperature; the pressure of a gas was believed to result from the impact of these particles on the walls of the vessel or any other surface exposed to the gas.
Various investigators had deduced that the mean velocity of a molecule of a gas such as hydrogen at atmospheric pressure and at the temperature of the freezing point of water was a few thousand meters per second, whereas experimental evidence had shown that molecules of gases are not capable of traveling continuously at such speeds. The German physicist Rudolf Claudius had already realized that the motions of molecules must be greatly influenced by collisions, and he had already devised the conception of “mean free path,” which is the average distance traversed by a molecule of a gas before impact with another. It remained for Maxwell, following an independent train of thought, to demonstrate that the velocities of the molecules varied over a wide range and followed what has since become known to scientists as the “Maxwellian law of distribution.”
This principle was derived by assuming the motions of a collection of perfectly elastic spheres moving at random in a closed space and acting on each other only when they impacted each other. Maxwell showed that the spheres may be divided into groups according to their velocities, and that when the steady state is reached, the number in each group remains the same although the individual molecules in each group are continually changing. By analyzing molecular velocities, Maxwell had devised the science of statistical mechanics.
From these considerations and from the fact that when gases are mixed together their temperatures become equal, Maxwell deduced that the condition which determines that the temperatures of two gases will be the same is that the average kinetic energy of the individual molecules of the two gases is equal. He also explained why the viscosity of a gas should be independent of its density. While a reduction in density of a gas produces an increase in the mean free path, it also decreases the number of molecules available. In this case, Maxwell demonstrated his experimental ability to verify his theoretical conclusions. With the help of his wife, he carried out experiments on the viscosity of gases.
Maxwell’s investigation into the molecular structure of gases was noticed by other scientists, particularly Ludwig Boltzmann, an Austrian physicist who quickly appreciated the fundamental importance of Maxwell’s laws. By this point his work was sufficient to have secured for Maxwell a distinguished place among those who have advanced our scientific knowledge, but his further great achievement—the fundamental theory of electricity and magnetism—was still to come.
Laws of Electricity and Magnetism
Preceding Maxwell was another British scientist, Michael Faraday, who conducted experiments where he discovered the phenomena of electromagnetic induction, which would lead to the generation of electrical power. Some twenty years later, Clerk Maxwell began the study of electricity at a time when there were two distinct schools of thought as to the way electric and magnetic effects were produced. On the one hand were the mathematicians who viewed the subject entirely from the point of view of action at a distance, like the gravitational attraction where two objects, for example the Earth and Sun, are attracted to each other without touching. On the other hand, according to Faraday’s conception, an electric charge or a magnetic pole was the origin of lines of force spreading out in every direction; these lines of force filled the surrounding space and were the agents whereby electric and magnetic effects were produced. The lines of force were not merely geometrical lines, rather they had physical properties; for example, the lines of force between positive and negative electric charges or between north and south magnetic poles were in a state of tension representing the force of attraction between opposite charges or poles. In addition, the density of the lines in the intervening space represented the magnitude of the force.
Maxwell first studied all of Faraday’s work and became familiar with his concepts and line of reasoning. Next, he applied his mathematical knowledge to describe, in the precise language of mathematical equations, a theory of electromagnetism which explained the known facts, but also predicted other phenomena which would not be demonstrated experimentally for many years. At the time little was known about the nature of electricity other than what was associated with Faraday’s conception of lines of force, and its relationship to magnetism was poorly understood. Maxwell showed, however, that if the density of the electric lines of force is changed, a magnetic force is created, the strength of which is proportional to the speed at which the electric lines move. Out of this work came two laws expressing the phenomena associated with electricity and magnetism:
1) Faraday’s law of electromagnetic induction states that the rate of change in the number of lines of magnetic force passing through a circuit is equal to the work done in taking a unit of electric charge around the circuit.
2) Maxwell’s law states that the rate of change in the number of lines of electric force passing through a circuit is equal to the work done in taking a unit of magnetic pole around the circuit.
The expression of these two laws in a mathematical form gives the system of formulas known as Maxwell’s equations, which forms the foundation of all electrical and radio science and engineering. The precise symmetry of the laws is profound, for if we interchange the words electric and magnetic in Faraday’s law, we get Maxwell’s law. In this way, Maxwell clarified and extended Faraday’s experimental discoveries and rendered them in precise mathematical form.
Electromagnetic Theory of Light
Continuing his research, Maxwell began to quantify that any changes in the electric and magnetic fields surrounding an electric circuit would cause changes along the lines of force which permeated the surrounding space. In this space or medium the electric field induced depends on the dielectric constant; in the same way, the flux surrounding a magnetic pole depends on the permeability of the medium.
Maxwell then showed that the velocity with which an electromagnetic disturbance is transmitted throughout a particular medium depends on the dielectric constant and permeability of the medium. When these properties are given numerical values, care must be taken to express them in the correct units; it was by such reasoning that Maxwell was able to show that the velocity of propagation of his electromagnetic waves is equal to the ratio of the electromagnetic to the electrostatic units of electricity. Both he and other workers made measurements of this ratio and obtained a value of 186,300 mile/hour (or 3 X 1010 cm/sec), nearly the same as the results seven years earlier in the first direct terrestrial measurement of the velocity of light by the French physicist Armand Fizeau.
In October 1861, Maxwell wrote to Faraday of his discovery that light is a form of wave motion by which electromagnetic waves travel through a medium at a speed which is determined by the electric and magnetic properties of the medium. This discovery put an end to speculations as to the nature of light and has provided a mathematical basis for explanations of the phenomena of light and accompanying optical properties.
Maxwell followed his line of thought and envisaged the possibility that there would be other forms of electromagnetic wave radiation not sensed by human eyes or bodies, but nevertheless traveling through all space from whatever source of disturbance at which they originated. Maxwell was unable to test his theory, and it remained for others to produce and apply the vast range of waves in the electromagnetic spectrum, of which the portion occupied by visible light is very small compared with the large bands of electromagnetic waves. It would take the work of the German physicist, Rudolf Hertz, two decades later to discover what we now call radio waves. Radio waves have a wavelength that is a million times that of visible light, yet both are explained by Maxwell’s equations.
Maxwell’s work helped us understand phenomena from the small wavelength X-rays that are widely used in medicine to the much longer wavelength waves that allow the propagation of radio and television signals. The follow-up developments of Maxwell’s theory have given the world all forms of radio communication including broadcasting and television, radar and navigational aids, and more recently the smart phone, which allows communication in ways not dreamt of a generation ago. When Albert Einstein’s theories of space and time, a generation after Maxwell’s death, upset almost all of “classical physics,” Maxwell’s equation remained untouched—as valid as ever.
From a long view of the history of mankind—seen from, say, ten thousand years from now—there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics.— Richard P Feynman (physicist)
Have you ever heard of James Clerk Maxwell? (Be honest)
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