JAMES CLERK MAXWELL

Maxwell's equations, 1873.

James Clerk Maxwell was truly a genius. Although his greatest
contribution to science was his theory of electromagnetic radiation, and
his second greatest contribution was his theory of the distribution of
the speeds of molecules in gases, he made significant and important advances
in a number of other areas as well. Altogether he wrote about 100 scientific
papers and 4 books. He was also the joint scientific editor of the 9th
edition of the *Encyclopaedia Britannica* and wrote many of the articles
therein. During the last few years of his life he devoted a great deal of
time to editing the un-published researches of Henry Cavendish, which is
now recognized as a classic in the history of science. He tended to work on
several topics simultaneously with the result that there was often an interval
of several years between papers on the same subject! Indeed, twelve years
elapsed between his two most important papers on the kinetic theory (1867
and 1879) and six years between his two papers on his electromagnetic theory
(1855 and 1861).

Of the major achievements in science since the birth of 'modern science'
in the 16th
century, arguably there are two that stand out because of their
significance and
influence and the way they unified 'ideas'. The first was due to Newton;
as we have
already seen, his *Principia* unified, in terms of a few simple
laws, pretty much everything that was known
about motion. Apart from some 'corrections' required to make his ideas
consistent
with relativity (i.e., for objects traveling at speeds approaching that
of light),
which we rarely encounter except in the study of atomic and subatomic
particles, his laws
remain the corner-stone for the science of mechanics. Nearly two
centuries later
another 'unification' occurred when James Clerk Maxwell united what was
known about
electricity, magnetism and light. At the time of Newton, little was
known about electricity
and magnetism and light. Electrostatic and magnetostatic phenomena had
been studied
by Franklin, Gilbert and others but no one suspected any connection
between them although in the decade or so beginning in 1820 some
interesting phenomena were observed. For instance, in 1820 Hans Oersted
(1777-1851) discovered that an electrical current would deflect a nearby
magnet; Andre-Marie Ampere (1775-1836) discovered that two parallel wires
carrying an electrical current would attract (or repel) each other (depending
on the relative directions of the current) and in 1832 Michael Faraday
(1791-1867) discovered that a changing (or moving) nagnetic field gave rise
to an electrical current. Clearly, then, electrical and magnetic effects
were very much related to each other. It was Maxwell who showed how the
two phenomena could be unified; he provided a very neat mathematical
description, now known
as *Maxwell's equations,* appearing fully developed in 1873, that
form the basis of our understanding of his
*electromagnetic theory.* He predicted that electrical charges that
were accelerating - for example, oscillating or moving in a circle - would
produce
*electromagnetic waves* that propagate through space at the speed of
light. Indeed, he proposed that visible light itself is therefore an
electromagnetic wave:

The first such wave was discovered by Heinrich Hertz (1857-1894). Maxwell did not restrict himself to electromagnetic phenomena; he made very important contributions to our understanding of the kinetic theory of gases. By treating gases statistically in 1866 he formulated, independently of Ludwig Boltzmann, the Maxwell-Boltzmann theory that showed that temperatures and heat involved only molecular motion.

Maxwell was born into a well-off family in Edinburgh, Scotland, on June 13, 1831. He grew up in a period noted chiefly, in physics, for progress in electricity, thermodynamics (i.e., the study of heat), the kinetic theory of gases, and for the first clear formulation by Herman von Helmholtz (1821-1894) of a general principle of energy conservation. He was an insatiably inquisitive child; just before he was three years old his mother wrote that he was forever demanding

It is reported that he scurried around the house tracing the wiring that
connected
the room bells to the servant's quarters and would excitedly drag his
parents around
showing them his discoveries. He was privately tutored until he entered
Edinburgh
Academy at the age of ten. His curiosity remained unscathed although his
schoolmates
considered him odd and often taunted him with the nickname "Dafty". At
the Academy,
after a slow start, he began to display extraordinary talents, in both
mathematics
and the writing of English verse. He maintained an interest in building
models of polyhedra and devising new ways to draw curves, and when he was
15 he won the Academy's mathematics medal for a paper he published on
drawing generalized ovals with pins and thread. When he was 16 he
visited William Nicol, the inventor of the polarizing prism, and on
returning home he built a device to study the patterns for colored
polarized
light. He made careful colored drawings of his observations and sent
them to Nicol.
He was rewarded with a set of polarizing prisms that he treasured for
the rest of his
life. A few years later he presented two papers to the Royal Society;
one *"On the
Theory of Rolling Curves"* and another *"On the Equilibrium of
Elastic Solids".* Both papers were read before the Society by
somebody else because "it was not thought proper
for a boy in a round jacket to mount the rostrum there." After six years
at the
Academy and three years at the University of Edinburgh, he entered
Peterhouse College,
Cambridge in 1850, where most Scottish students went. He transferred to
Trinity College
shortly afterwards where it was easier to obtain a fellowship. He became
a favorite
with his professors ... it was said that it is

He was second on the Mathematical Tripos examination and won a Trinity fellowship. He graduated with a degree in mathematics with high honors in 1854.

Maxwell remained at Trinity for another two years, studying Michael Faraday's works on electricity and following his own researches on mathematics, geometrical optics and the theory of color. In 1856 he was elected to the Professorship in Natural Philosophy at Marischal College, Aberdeen, where he completed the first of his many remarkable contributions in mathematical physics. An essay he wrote on the rings of Saturn won the Adams Prize for 1857 [1]; he showed that their stability could be achieved only if they comprised numerous small solid particles (an explanation now confirmed by the Voyager spacecraft). Two years later he married Katherine Dewar, the daughter of the Principal, and in a note to his aunt he said

It was also at Aberdeen that he became interested in the kinetic theory
of gases and
solved the problem of the distribution of velocities among the molecules
of a gas,
the *Maxwellian* distribution. While the formal proof was
challenged there is no doubt of the correctness of the final result. The
theory was statistical, meaning a change from the concept
of certainty - heat viewed as flowing from hot to cold - to one of
probability -
molecules at high temperature (high velocity) have a high probability of
moving towards
those at low temperature (low velocity). The earlier ideas of
thermodynamics were
not rejected; they were simply recast in a better theory that explained
observations
and experiments. In 1860 a reorganization at Aberdeen left him without a
position. After failing to get the vacant Chair at Edinburgh he was
appointed Professor of
Natural Philosophy at King's College, London in 1860, where he remained
for five
extremely creative years. He made the acquaintance of Faraday, who was
Director of the Royal Institution until 1861. He completed his work on
the theory of color, developed
his theory of electricity and magnetism, refined further his kinetic
theory of gases
and investigated experimentally the viscosity of air at different
temperatures and pressures;
the latter formed the subject of a Bakerian Lecture to the Royal Society,
which he
presented in 1866. Also in 1866 he published a paper on the *Dynamical
Theory of Gases* in which some errors in his earlier publication on
the kinetic theory - pointed out
by Rudolph Clausius (1822-1888) - were corrected. He worked also with
Stewart and
Jenkin in experiments to determine the absolute value of the unit of
resistance,
the *ohm.*

At the end of the 1865 academic session, shortly after finishing his
paper on the
*Dynamical Theory of Gases,* he resigned his professorship and moved
to his estate, Glenair, near Edinburgh. There, he could devote more time
to his scientific studies and to the study of English literature. During
the next few years he completed the major part of his treatise on
electromagnetic theory, although it was not published until 1873 [2]. Meanwhile at Cambridge, it was felt that students
were not receiving an adequate background in the growing field of
experimental physics. Maxwell partly inspired and lent active support to
the movement to establish a new school of physics, with a Chair in
experimental physics, and a fine physical laboratory. In 1871 the
University approved the Chair and Maxwell was appointed professor of
experimental physics and director of the newly established Cavendish
Laboratory, named after Henry Cavendish.

Maxwell devoted a good deal of time and effort to the building and furnishing of the new Cavendish Laboratory. It was officially opened in 1874 and rose rapidly to prominence to become one of the premier laboratories in the world. His personal interests during this period were given chiefly to lecturing and to editing the unpublished papers of Henry Cavendish [3] whose work on electricity greatly impressed Maxwell not only because of its originality - outlined in the brief biography of Cavendish - but because it anticipated several discoveries made later by others. Sadly, he did not live to see his crowning achievement - the theory of the electromagnetic field - verified by experiment, for he died at the age of 48 years in November 1879, some eight years before Hertz demonstrated the existence of electric waves. It was after Hertz verification that Maxwell's genius was fully recognized.

As a lecturer, Maxwell was often too far above the heads of his audience, but as a teacher his curiosity and enthusiasm excited his students. As Director of the Cavendish Laboratory he brought his dog, Toby, to his office. He remained just outside the social mainstream, in a world of his own; he hated starched clothes, he recycled everything he could, he traveled 3rd class preferring the hard seats, he never drank wine, and would be distracted by such simple things by the refraction of light by water glasses. He adored poetry and wrote a good deal himself, both serious and humorous.

Maxwell gave mathematical form to Faraday's ideas of electrical phenomena. He derived a set of equations that relate all known electric and magnetic phenomena; the equations give quantitative relations between electric and magnetic fields, and the charges, currents and time-varying currents producing these fields. They contain Coulomb's law of the force between electrical charges as well as the corresponding law for magnetic poles; Oersted's discovery, in 1820, that moving charges, i.e., an electrical current, could produce a magnetic field, an effect that Ampere studied in detail over the next seven years; Faraday's discovery that a changing magnetic field would induce an electrical current in a circuit and Lenz's law on the direction of the induced current. The equations contain all of this information plus a lot more for they include Maxwell's hypothesis that electric waves should proceed from oscillating electrical currents and travel through space at the velocity of light. Given the electric and magnetic forces at some initial time, Maxwell's equations allow one to determine them for all future time. It was Richard Feynman who said

Maxwell's work is not that well known by non-scientists because it is entirely theoretical but he showed that four relatively simple mathematical equations could express the behavior of electric and magnetic fields and their interrelation. These four equations, now known as Maxwell's equations, first appeared in 1873.

For years there appeared to be no way to test Maxwell's theory. However, Heinrich Hertz (1857-1894) succeeded in producing and detecting electromagnetic waves. Although his life was relatively short, Hertz was very much a "hands-on" scientist. By generating sparks between two metal spheres, which he was able to detect at some distance from the source, he proved the presence of electromagnetic waves. By moving the detector around he found that the signal increased and decreased in intensity, just like a standing wave. He measured the wavelength and frequency of these waves and deduced that they traveled with the speed of light, as Maxwell had predicted. Hertz also went on to show that these waves could be reflected, refracted, polarized and made to interfere. He showed that in every way his waves behaved exactly like light waves. Hertz' studies led to the development of radio communications, which, today, represent one of the major branches of our civilization.

**
FOOTNOTES
**

[1] The Prize, established in 1848 and awarded at intervals for the best solution to some problem of great scientific importance proposed by the examiners, put Maxwell among the highest ranks of his contemporaries in science.

[2] J.C. Maxwell, *A Treatise on Electricity and
Magnetism*
(1st ed., 1873; 2nd ed. 1881, 3rd ed. 1891).

[3] J.C. Maxwell, *The Electrical Researches of the
Hon. Henry Cavendish*
(Cambridge University; Cambridge, England, 1879).

**
REFERENCES
**

__Books__

M. Shamos *Great Experiments in Physics*
(Dover Publications Inc., New York, 1987).

__Web-sites__