Maxwell, James Clerk





Maxwell, James Clerk (1831-1879), British physicist, best known for his work on the connection between light and electromagnetic waves (traveling waves of energy). Maxwell discovered that light consists of electromagnetic waves (see Electromagnetic Radiation) and established the kinetic theory of gases. The kinetic theory of gases explains the relationship between the movement of molecules in a gas and the gas’s temperature and other properties. He also showed that the rings of the planet Saturn are made up of many small particles and demonstrated the principles governing color vision.


Maxwell was born in Edinburgh, Scotland. He was educated at Edinburgh Academy from 1841 to 1847, when he entered the University of Edinburgh. He then went on to study at the University of Cambridge in 1850, graduating with a bachelor’s degree in mathematics in 1854. He became a professor of natural philosophy at Marischal College in Aberdeen in 1856. Then in 1860 he moved to London to become a professor of natural philosophy and astronomy at King's College. On the death of his father in 1865, Maxwell returned to his family home in Scotland and devoted himself to research. In 1871 he moved to Cambridge, where he became the first professor of experimental physics and set up the Cavendish Laboratory, which opened in 1874. Maxwell continued in this position until 1879, when illness forced him to resign.





Maxwell’s first important contribution to science began in 1849, when he applied himself to examining how human eyes detect color. He built on the ideas of British physicist Thomas Young and German scientist Hermann Helmholtz on color vision. Maxwell spun disks painted with sectors of red, green, and blue to mix those primary colors into other colors. He confirmed Young's theory that the eye has three kinds of receptors sensitive to the primary colors and showed that color blindness is due to defects in the receptors. He also fully explained how the addition and subtraction of primary colors produces all other colors. He crowned this achievement in 1861 by producing the first color photograph. Maxwell took this picture, the ancestor of all color photography, printing, and television, of a tartan-patterned ribbon. He used red, green, and blue filters to expose three frames of film. He then projected the images through the appropriate filters to project a colored image. See also Color.


Maxwell worked on several areas of inquiry at the same time, and from 1855 to 1859 he took up the problem of Saturn's rings (see Saturn (planet)). No one had developed a satisfactory explanation that would result in the rings having a stable structure. Maxwell proved that a solid ring would collapse and a fluid ring would break up. However, he found that a ring composed of concentric circles of small satellites could achieve stability. Images from the Pioneer and Voyager spacecraft in the 1970s and 1980s proved beyond a doubt that Saturn’s rings are indeed composed of many small bodies orbiting the planet together.





Maxwell's development of the electromagnetic theory of light took many years. It began with the paper “On Faraday's Lines of Force” (1855–1856), in which Maxwell built on the ideas of British physicist Michael Faraday. Faraday explained that electric and magnetic effects result from lines of force that surround conductors and magnets. Maxwell drew an analogy between the behavior of the lines of force and the flow of a liquid, deriving equations that represented electric and magnetic effects. The next step toward Maxwell’s electromagnetic theory was the publication of the paper “On Physical Lines of Force” (1861–1862). Here Maxwell developed a model for the medium that could carry electric and magnetic effects. He devised a hypothetical medium that consisted of a fluid in which magnetic effects created whirlpool-like structures. These whirlpools were separated by cells created by electric effects, so the combination of magnetic and electric effects formed a honeycomb pattern.


Maxwell could explain all known effects of electromagnetism by considering how the motion of the whirlpools, or vortices, and cells could produce magnetic and electric effects. He showed that the lines of force behave like the structures in the hypothetical fluid. Maxwell went further, considering what would happen if the fluid could change density, or be elastic. The movement of a charge would set up a disturbance in an elastic medium, forming waves that would move through the medium. The speed of these waves would be equal to the ratio of the value for an electric current measured in electrostatic units to the value of the same current measured in electromagnetic units (see Electrical Units). German physicists Friedrich Kohlrausch and Wilhelm Weber had calculated this ratio and found it the same as the speed of light. Maxwell inferred that light consists of waves in the same medium that causes electric and magnetic phenomena.


Maxwell found supporting evidence for this inference in work he did on defining basic electrical and magnetic quantities in terms of mass, length, and time. In the paper “On the Elementary Regulations of Electric Quantities” (1863), he wrote that the ratio of the two definitions of any quantity based on electric and magnetic forces is always equal to the velocity of light. He considered that light must consist of electromagnetic waves but first needed to prove this by abandoning the vortex analogy and developing a mathematical system. He achieved this in “A Dynamical Theory of the Electromagnetic Field” (1864), in which he developed the fundamental equations that describe the electromagnetic field. These equations showed that light is propagated in two waves, one magnetic and the other electric, which vibrate perpendicular to each other and perpendicular to the direction in which they are moving (like a wave traveling along a string). Maxwell first published this solution in “Note on the Electromagnetic Theory of Light” (1868) and summed up all of his work on electricity and magnetism in Treatise on Electricity and Magnetism in 1873.


The treatise also suggested that a whole family of electromagnetic radiation must exist, of which visible light was only one part. In 1888 German physicist Heinrich Hertz made the sensational discovery of radio waves, a form of electromagnetic radiation with wavelengths too long for our eyes to see, confirming Maxwell’s ideas. Unfortunately, Maxwell did not live long enough to see this vindication of his work. He also did not live to see the ether (the medium in which light waves were said to be propagated) disproved with the classic experiments of German-born American physicist Albert Michelson and American chemist Edward Morley in 1881 and 1887. Maxwell had suggested an experiment much like the Michelson-Morley experiment in the last year of his life. Although Maxwell believed the ether existed, his equations were not dependent on its existence, and so remained valid.





Maxwell's other major contribution to physics was to provide a mathematical basis for the kinetic theory of gases, which explains that gases behave as they do because they are composed of particles in constant motion. Maxwell built on the achievements of German physicist Rudolf Clausius, who in 1857 and 1858 had shown that a gas must consist of molecules in constant motion colliding with each other and with the walls of their container. Clausius developed the idea of the mean free path, which is the average distance that a molecule travels between collisions.


Maxwell's development of the kinetic theory of gases was stimulated by his success in the similar problem of Saturn's rings. It dates from 1860, when he used a statistical treatment to express the wide range of velocities (speeds and the directions of the speeds) that the molecules in a quantity of gas must inevitably possess. He arrived at a formula to express the distribution of velocity in gas molecules, relating it to temperature. He showed that gases store heat in the motion of their molecules, so the molecules in a gas will speed up as the gas’s temperature increases. Maxwell then applied his theory with some success to viscosity (how much a gas resists movement), diffusion (how gas molecules move from an area of higher concentration to an area of lower concentration), and other properties of gases that depend on the nature of the molecules’ motion.


Maxwell's kinetic theory did not fully explain heat conduction (how heat travels through a gas). Austrian physicist Ludwig Boltzmann modified Maxwell’s theory in 1868, resulting in the Maxwell-Boltzmann distribution law. Both men contributed to successive refinements of the kinetic theory, and it proved fully applicable to all properties of gases. It also led Maxwell to an accurate estimate of the size of molecules and to a method of separating gases in a centrifuge. The kinetic theory was derived using statistics, so it also revised opinions on the validity of the second law of thermodynamics, which states that heat cannot flow from a colder to a hotter body of its own accord. In the case of two connected containers of gases at the same temperature, it is statistically possible for the molecules to diffuse so that the faster-moving molecules all concentrate in one container while the slower molecules gather in the other, making the first container hotter and the second colder. Maxwell conceived this hypothesis, which is known as Maxwell's demon. Although this event is very unlikely, it is not impossible, and the second law is therefore not absolute, but highly probable.


Maxwell is generally considered the greatest theoretical physicist of the 1800s. He combined a rigorous mathematical ability with great insight, which enabled him to make brilliant advances in the two most important areas of physics at that time. In building on Faraday's work to discover the electromagnetic nature of light, Maxwell not only explained electromagnetism but also paved the way for the discovery and application of the whole spectrum of electromagnetic radiation that has characterized modern physics. Physicists now know that this spectrum also includes radio, infrared, ultraviolet, and X-ray waves, to name a few. In developing the kinetic theory of gases, Maxwell gave the final proof that the nature of heat resides in the motion of molecules.






Maxwell, James Clerk



b. June 13 , 1831, Edinburgh, Scot.

d. Nov. 5, 1879, Cambridge, Cambridgeshire, Eng.



Scottish physicist best known for his formulation of electromagnetic theory. He is regarded by most modern physicists as the scientist of the 19th century who had the greatest influence on 20th-century physics, and he is ranked with Sir Isaac Newton and Albert Einstein for the fundamental nature of his contributions. In 1931, on the 100th anniversary of Maxwell's birth, Einstein described the change in the conception of reality in physics that resulted from Maxwell's work as "the most profound and the most fruitful that physics has experienced since the time of Newton."



The concept of electromagnetic radiation originated with Maxwell, and his field equations, based on Michael Faraday's observations of the electric and magnetic lines of force, paved the way for Einstein's special theory of relativity, which established the equivalence of mass and energy. Maxwell's ideas also ushered in the other major innovation of 20th-century physics, the quantum theory. His description of electromagnetic radiation led to the development (according to classical theory) of the ultimately unsatisfactory law of heat radiation, which prompted Max Planck's formulation of the quantum hypothesis--i.e., the theory that radiant-heat energy is emitted only in finite amounts, or quanta. The interaction between electromagnetic radiation and matter, integral to Planck's hypothesis, in turn has played a central role in the development of the theory of the structure of atoms and molecules.



Early life


Maxwell came from a comfortable middle-class background. The original family name was Clerk, the additional surname being added by his father, who was a lawyer, after he had inherited the Middlebie estate from Maxwell ancestors. James was an only child. His parents had married late in life, and his mother was 40 years old at his birth. Shortly afterward the family moved from Edinburgh to Glenlair, the country house on the Middlebie estate.


His mother died in 1839 from abdominal cancer, the very disease to which Maxwell was to succumb at exactly the same age. A dull and uninspired tutor was engaged who claimed that James was slow at learning, though in fact he displayed a lively curiosity at an early age and had a phenomenal memory. Fortunately he was rescued by his aunt Jane Cay and from 1841 was sent to school at the Edinburgh Academy. Among the other pupils were his biographer Lewis Campbell and his friend Peter Guthrie Tait.


Maxwell's interests ranged far beyond the school syllabus, and he did not pay particular attention to examination performance. His first scientific paper, published when he was only 14 years old, described a generalized series of oval curves that could be traced with pins and thread by analogy with an ellipse. This fascination with geometry and with mechanical models continued throughout his career and was of great help in his subsequent research.


At the age of 16 he entered the University of Edinburgh, where he read voraciously on all subjects and published two more scientific papers. In 1850 he went to the University of Cambridge, where his exceptional powers began to be recognized. His mathematics teacher, William Hopkins, was a well-known "wrangler maker" (a wrangler is one who takes first class honours in the mathematics examinations at Cambridge) whose students included Tait, George Gabriel (later Sir George) Stokes, William Thomson (later Lord Kelvin), Arthur Cayley, and Edward John Routh. Of Maxwell, Hopkins is reported to have said that he was the most extraordinary man he had met with in the whole course of his experience, that it seemed impossible for him to think wrongly on any physical subject, but that in analysis he was far more deficient. (Other contemporaries also testified to Maxwell's preference for geometrical over analytical methods.) This shrewd assessment was later borne out by several important formulas advanced by Maxwell that obtained correct results from faulty mathematical arguments.


In 1854 Maxwell was second wrangler and first Smith's prizeman (the Smith's prize is a prestigious competitive award for an essay that incorporates original research). He was elected to a fellowship at Trinity, but, because his father's health was deteriorating, he wished to return to Scotland. In 1856 he was appointed to the professorship of natural philosophy at Marischal College, Aberdeen, but before the appointment was announced his father died. This was a great personal loss, for Maxwell had had a close relationship with his father. In June 1858 Maxwell married Katherine Mary Dewar, daughter of the principal of Marischal College. The union was childless and was described by his biographer as a "married life . . . of unexampled devotion."


In 1860 the University of Aberdeen was formed by a merger between King's College and Marischal College, and Maxwell was declared redundant. He applied for a vacancy at the University of Edinburgh, but he was turned down in favour of his school friend Tait. He then was appointed to the professorship of natural philosophy at King's College, London.


The next five years were undoubtedly the most fruitful of his career. During this period his two classic papers on the electromagnetic field were published, and his demonstration of colour photography took place. He was elected to the Royal Society in 1861. His theoretical and experimental work on the viscosity of gases also was undertaken during these years and culminated in a lecture to the Royal Society in 1866. He supervised the experimental determination of electrical units for the British Association for the Advancement of Science, and this work in measurement and standardization led to the establishment of the National Physical Laboratory. He also measured the ratio of electromagnetic and electrostatic units of electricity and confirmed that it was in satisfactory agreement with the velocity of light as predicted by his theory.



Later life


In 1865 he resigned his professorship at King's College and retired to the family estate in Glenlair. He continued to visit London every spring and served as external examiner for the Mathematical Tripos (exams) at Cambridge. In the spring and early summer of 1867 he toured Italy. But most of his energy during this period was devoted to writing his famous treatise on electricity and magnetism.


It was Maxwell's research on electromagnetism that established him among the great scientists of history. In the preface to his Treatise on Electricity and Magnetism (1873), the best exposition of his theory, Maxwell stated that his major task was to convert Faraday's physical ideas into mathematical form. In attempting to illustrate Faraday's law of induction (that a changing magnetic field gives rise to an induced electromagnetic field), Maxwell constructed a mechanical model. He found that the model gave rise to a corresponding "displacement current" in the dielectric medium, which could then be the seat of transverse waves. On calculating the velocity of these waves, he found that they were very close to the velocity of light. Maxwell concluded that he could "scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena."


Maxwell's theory suggested that electromagnetic waves could be generated in a laboratory, a possibility first demonstrated by Heinrich Hertz in 1887, eight years after Maxwell's death. The resulting radio industry with its many applications thus has its origin in Maxwell's publications.


In addition to his electromagnetic theory, Maxwell made major contributions to other areas of physics. While still in his 20s, Maxwell demonstrated his mastery of classical physics by writing a prizewinning essay on Saturn's rings, in which he concluded that the rings must consist of masses of matter not mutually coherent--a conclusion that was corroborated more than 100 years later by the first Voyager space probe to reach Saturn.


The Maxwell relations of equality between different partial derivatives of thermodynamic functions are included in every standard textbook on thermodynamics (see thermodynamics). Though Maxwell did not originate the modern kinetic theory of gases, he was the first to apply the methods of probability and statistics in describing the properties of an assembly of molecules. Thus he was able to demonstrate that the velocities of molecules in a gas, previously assumed to be equal, must follow a statistical distribution (known subsequently as the Maxwell-Boltzmann distribution law). In later papers Maxwell investigated the transport properties of gases--i.e., the effect of changes in temperature and pressure on viscosity, thermal conductivity, and diffusion.


Maxwell was far from being an abstruse theoretician. He was skillful in the design of experimental apparatus, as was shown early in his career during his investigations of colour vision. He devised a colour top with adjustable sectors of tinted paper to test the three-colour hypothesis of Thomas Young and later invented a colour box that made it possible to conduct experiments with spectral colours rather than pigments. His investigations of the colour theory led him to conclude that a colour photography could be produced by photographing through filters of the three primary colours and then recombining the images. He demonstrated his supposition in a lecture to the Royal Institution of Great Britain in 1861 by projecting through filters a colour photograph of a tartan ribbon that had been taken by this method.


In addition to these well-known contributions, a number of ideas that Maxwell put forward quite casually have since led to developments of great significance. The hypothetical intelligent being known as Maxwell's demon was a factor in the development of information theory. Maxwell's analytic treatment of speed governors is generally regarded as the founding paper on cybernetics, and his "equal areas" construction provided an essential constituent of the theory of fluids developed by Johannes Diederik van der Waals. His work in geometrical optics led to the discovery of the fish-eye lens. From the start of his career to its finish his papers are filled with novelty and interest. He also was a contributor to the ninth edition of Encyclopædia Britannica.


In 1871 Maxwell was elected to the new Cavendish professorship at Cambridge. He set about designing the Cavendish Laboratory and supervised its construction. Maxwell had few students, but they were of the highest calibre and included William D. Niven, Ambrose (later Sir Ambrose) Fleming, Richard Tetley Glazebrook, John Henry Poynting, and Arthur Schuster.


During the Easter term of 1879 Maxwell took ill on several occasions; he returned to Glenlair in June but his condition did not improve. He died on November 5, after a short illness. Maxwell received no public honours and was buried quietly in a small churchyard in the village of Parton, in Scotland.





Maxwell's demon



hypothetical intelligent being (or a functionally equivalent device) capable of detecting and reacting to the motions of individual molecules. It was imagined by James Clerk Maxwell in 1871, to illustrate the possibility of violating the second law of thermodynamics. Essentially, this law states that heat does not naturally flow from a cool body to a warmer; work must be expended to make it do so. Maxwell envisioned two vessels containing gas at equal temperatures and joined by a small hole. The hole could be opened or closed at will by "a being" to allow individual molecules of gas to pass through. By passing only fast-moving molecules from vessel A to vessel B and only slow-moving ones from B to A, the demon would bring about an effective flow from A to B of molecular kinetic energy. This excess energy in B would be usable to perform work (e.g., by generating steam), and the system could be a working perpetual motion machine. By allowing all molecules to pass only from A to B, an even more readily useful difference in pressure would be created between the two vessels. About 1950 the French physicist Léon Brillouin exorcised the demon by demonstrating that the decrease in entropy resulting from the demon's actions would be exceeded by the increase in entropy in choosing between the fast and slow molecules.





Ampère's law


one of the basic relations between electricity and magnetism, stating quantitatively the relation of a magnetic field to the electric current or changing electric field that produces it. The law is named in honour of André-Marie Ampère, who by 1825 had laid the foundation of electromagnetic theory. An alternative expression of the Biot-Savart law, which also relates the magnetic field and the current that produces it, Ampère's law is generally stated formally in the language of calculus: the line integral of the magnetic field around an arbitrarily chosen path is proportional to the net electric current enclosed by the path. James Clerk Maxwell is responsible for this mathematical formulation and for the extension of the law to include magnetic fields that arise without electric current, as between the plates of a capacitor, or condenser, in which the electric field changes with the periodic charging and discharging of the plates but in which no passage of electric charge occurs. Maxwell also showed that even in empty space a varying electric field is accompanied by a changing magnetic field. The complete Ampère's law describes all these effects.




Historical survey

Development of the classical radiation theory


The classical electromagnetic radiation theory "remains for all time one of the greatest triumphs of human intellectual endeavor." So said Max Planck in 1931, commemorating the 100th anniversary of the birth of the Scottish physicist James Clerk Maxwell, the prime originator of this theory. The theory was indeed of great significance, for it not only united the phenomena of electricity, magnetism, and light in a unified framework but also was a fundamental revision of the then-accepted Newtonian way of thinking about the forces in the physical universe. The development of the classical radiation theory constituted a conceptual revolution that lasted for nearly half a century. It began with the seminal work of the British physicist and chemist Michael Faraday, who published his article "Thoughts on Ray Vibrations" in Philosophical Magazine in May 1846, and came to fruition in 1888 when Hertz succeeded in generating electromagnetic waves at radio and microwave frequencies and measuring their properties.



Maxwell's equations


four equations that, together, form a complete description of the production and interrelation of electric and magnetic fields. The physicist James Clerk Maxwell in the 19th century based his description of electromagnetic fields on these four equations, which express experimental laws.


The statements of these four equations are, respectively: (1) electric field diverges from electric charge, an expression of the Coulomb force, (2) there are no isolated magnetic poles, but the Coulomb force acts between the poles of a magnet, (3) electric fields are produced by changing magnetic fields, an expression of Faraday's law of induction, and (4) circulating magnetic fields are produced by changing electric fields and by electric currents, Maxwell's extension of Ampère's law to include the interaction of changing fields. The most compact way of writing these equations in the metre-kilogram-second (mks) system is in terms of the vector operators div (divergence) and curl. In these expressions the Greek letter rho, , is charge density, J is current density, E is the electric field, and B is the magnetic field; here, D and H are field quantities that are proportional to E and B, respectively. The four Maxwell equations, corresponding to the four statements above, are: (1) div D = , (2) div B = 0, (3) curl E = -dB/dt, and (4) curl H = dD/dt + J.

Copyright © 1994-2000 Encyclopædia Britannica, Inc.








Maxwell-Boltzmann distribution law



a description of the statistical distribution of the energies of the molecules of a classical gas. This distribution was first set forth by the Scottish physicist James Clerk Maxwell in 1859, on the basis of probabilistic arguments, and gave the distribution of velocities among the molecules of a gas. Maxwell's finding was generalized (1871) by a German physicist, Ludwig Boltzmann, to express the distribution of energies among the molecules.


The distribution function for a gas obeying Maxwell-Boltzmann statistics ( fM-B) can be written in terms of the total energy (E) of the system of particles described by the distribution, the absolute temperature (T) of the gas, the Boltzmann constant (k = 1.38 10-16 erg per kelvin), and a normalizing constant (C) chosen so that the sum, or integral, of all probabilities is unity--i.e., fM-B = Ce-E/kT, in which e is the base of the natural logarithms. The distribution function implies that the probability dP that any individual molecule has an energy between E and E + dE is given by dP = fM-BdE. The total energy (E) usually is composed of several individual parts, each corresponding to a different degree of freedom of the system. In fact, the total energy is divided equally between these modes. See energy, equipartition of.


The law can be derived in several ways, none of which is absolutely rigorous. All systems observed to date appear to obey Maxwell-Boltzmann statistics provided that quantum-mechanical effects are not important.


Copyright © 1994-2000 Encyclopædia Britannica, Inc.