Maxwell,
James Clerk
I INTRODUCTION
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.
II COLOR VISION
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.
III ELECTROMAGNETIC
THEORY OF LIGHT
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.
IV KINETIC THEORY OF
GASES
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.
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.
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.