Maxwell + faraday
Part 3. The Electromagnetic Field
by Keith J. Laidler,
Department of Chemistry,
University of Ottawa,
Maxwell's theory of electromagnetic radiation alone places
him among the great scientists of all time. It is contained in
three substantial papers, and his Treatise on Electricity and
Magnetism. The first of the papers appeared in 1856 when he was
aged 25 and had the previous year been elected a Fellow of Trinity
College, Cambridge. In this paper he gave a mathematical treatment
of Faraday's unconventional ideas about electricity and magnetism.
The second paper appeared in 1861-62, and suggested a rather
complex and artificial model for the ether. In the third paper,
published in 1864, Maxwell dispensed with the model and relied
entirely on mathematical equations for the electromagnetic field.
His book, published in 1873, was to some extent a survey of the
whole field, but it raised a number of questions for further
treatment. Perhaps if he had lived longer he would have answered
many of them. In all his publications Maxwell emphasized his
great debt to Michael Faraday. In the preface to his book he
said that his main task had been to convert Faraday's physical
and qualitative ideas into mathematical form. To understand Maxwell's
theory of electromagnetic radiation it is therefore important
to have a clear idea of Faraday's experimental results and of
his conclusions. It is useful to start with Oersted's discovery
of electromagnetism, and its interpretation by Ampère,
as it was this interpretation that led Faraday to think along
different lines.
Oersted: Electromagnetism (1820)
In l820 Hans Christian Oersted (1777- l851), professor of
physics at the University of Copenhagen, brought a compass needle
near to a wire through which an electric current was passing.
He found that the needle tended to turn towards a direction at
right angles to the wire. When the direction of the current was
reversed, the needle turned in the opposite direction. A remarkable
feature of this famous discovery is that it was made in front
of a class of students. Oersted and his assistant had set up
the experiment but had not had time to try it out before the
students arrived. Oersted first decided to defer the experiment
until later, but during the lecture began to feel confident that
it would work, and performed it successfully. Another remarkable
feature is that, since the deflection of the needle had been
small, Oersted was so little impressed by the result that he
performed no further experiments on the subject for three months.
Then having confirmed the effect, he sent a four-page announcement
of it, in Latin, to many leading scientific journals, and to
a number of scientists. The announcement appeared, in various
languages, in a considerable number of journals, such as the
Annals of Philosophy, Gilbert's Annalen der Physik und physikalische
Chemie, and the Annales de chimie et de physique. Further publicity
was given to the discovery by the fact that the distinguished
scientific statesman François Arago (1786-1853) called
attention to the discovery at a meeting of the Académie
des Sciences in Paris in September, 1820. Oersted's experiment
was the first to show a connection between electricity and magnetism,
and can be called the birth of electromagnetism. At the time,
in the scientific tradition established in particular by Newton,
theories were formulated in terms of forces acting in straight
lines between points; these were known as central forces. In
1767 the English chemist Joseph Priestly (1733-1804) showed that
the forces followed the inverse square law. Later the French
military engineer Charles Augustin de Coulomb (1736-1806) carried
out careful experiments on bodies charged with static electricity,
and on magnets, and in 1794 confirmed that the attractions and
repulsions followed the inverse square law. The fact that the
magnetized needle moved towards a position at right angles to
the wire, rather than parallel to it, was therefore particularly
surprising. It suggested a force not acting in a straight line
but circularly, which most scientists thought to be unreasonable.
However, within a short time many scientific investigators had
confirmed the result. During the next six years much progress,
along both experimental and theoretical lines, was made by the
French physicist André Marie Ampère (1775-1836),
who had been in the audience when Arago announced Oersted's discovery
in Paris. Besides confirming Oersted's results, Ampère
made careful studies of the effects of electric currents on one
another. He found that if currents travelled in the same direction
along two parallel wires, there was attraction between them;
if the currents travelled in the opposite directions there was
repulsion. He also worked out a detailed mathematical treatment
of the interactions, on the basis of the assumption that current-carrying
elements of the wire interacted with one another according to
the inverse square law. By integrating the effects of all the
elements he arrived at expressions that were consistent with
the experimental results. This was a very impressive treatment,
and because of it Maxwell in his Treatise (1873) referred to
Ampère as the "Newton of electricity". To explain
the effect on an electric current on a magnet, Ampère
supposed that magnetism arises from electricity moving in circular
orbits around the axis of the magnet. He carried out experiments
with wires wound around glass tubes, and confirmed that when
a current passed, a magnetic effect was obtained. He then developed
an elegant mathematical treatment of the interactions between
electric currents and the circular currents around the magnets,
and was able to explain Oersted's results in terms of central
forces. Ampère's work was at once recognized by most investigators
as an achievement of great significance, but some objections
were raised. It was pointed out that there was no experimental
evidence for a flow of electricity around magnets, and no suggestion
as to how it might arise. Volta had found that a current results
when two dissimilar metals are present, but not if only one metal
is present. Ampère's later modified his theory to relate
to the molecules in the magnets, suggesting that perpetual electric
currents moved in orbits around them. It must be remembered that
at the time there was no understanding of the nature of electricity;
the electron was not to be discovered until over half a century
later. Michael Faraday (1791-1867) was particularly unhappy with
Ampère's treatment. Since he knew little mathematics,
and was ill-versed in physical theories, he simply could not
understand it. He was quite content to think of a circular force
arising from a current flowing in a wire. Hardly anyone brought
up on the physics of the time could accept such an idea, and
yet it was the origin of the important concept of the electromagnetic
field, which was to be the core of the later ideas of Faraday
and Maxwell.
Faraday: Fields of Force (1821-1860)
Michael Faraday's background was very different from Maxwell's,
but they grew up to be very alike in many ways; both were men
of the utmost kindness and simplicity of character. Faraday was
the son of a blacksmith who could do little more than provide
the bare necessities of life to his wife aid many children. At
the age of 14 Michael left school and was apprenticed to a good
natured bookbinder who encouraged him to read the books he was
binding. One particular book, Jane Marcet's Conversations on
Chemistry, made a particular impression on Faraday, and perhaps
did more than anything else to arouse his interest in science.
He attended some of Sir Humphry Davy's lectures at the Royal
Institution, and by a fortunate chance managed in 1813 to obtain
a position as Davy's assistant. He was so successful in the research
that he did there that only twelve years later he succeeded Davy
as Director of the Royal Institution laboratories. In 1821, soon
after Ampère had presented his interpretation of Oersted's
result, Faraday's friend Richard Phillips, an editor of the Philosophical
Magazine, persuaded Faraday to look into the subject of electromagnetism.
Like other editors of scientific journals, Phillips had been
inundated with papers on the subject The situation is a little
like that in 1989, when the submission of the original paper
on "cold fusion" (Chem 13 News, October 1984, pp 6-7)
produced an avalanche of submitted papers, in some of which the
authors made claims that they hoped would bring them fame and
fortune. Happily, Oersted's announcement was more fruitful. Faraday
accepted Phillips's suggestion rather reluctantly, as previously
his work had been on chemistry and rather far from electromagnetism.
Posterity must be grateful to Phillips for his gentle prodding.
Faraday at once repeated Oersted's experiments, and he noted
that when a small magnetic needle was moved around a wire carrying
a current, one of the poles turned in a circle. He then speculated
that a single magnetic pole, if it could exist, would move continuously
around a wire as long as the current flowed. This led him to
perform an experiment of great simplicity and also of great importance.
In 1821 he attached a magnet upright to the bottom of a deep
basin, and then filled the basin with mercury so that only the
pole of the magnet was above the surface. A wire free to move
was attached above the bowl and dipped into the mercury. When
Faraday passed a current through the wire and the magnet, the
wire continuously rotated around the magnet. In an adaptation
of the experiment, he made the magnet rotate around the wire.
The great significance of these simple demonstrations is that
electrical energy was being converted into mechanical energy
for the first time. To Faraday the results implied that there
were circular "lines of force" around the current-carrying
wire, and he accepted this as a simple experimental fact. Almost
everyone else concluded that the force could not be simple, but
must be explained in some way in terms of central forces. For
the next ten years Faraday worked only sporadically on electricity.
In 1831 he learned of the experiments of Joseph Henry (1797-1878)
in Albany, New York. The first electromagnet had been created
in 1823 by the English physicist William Sturgeon (1753-1850),
and Henry improved the technique greatly, observing that the
polarity could be reversed by a reversal of the direction of
the - current. This led Faraday to his famous experiment of 1831
in which he demonstrated electromagnetic induction. He wound
one side of an iron ring with insulated wire, and arranged a
secondary winding, connected to a galvanometer, around the other
side. When an electric current began to flow through the primary
coil, the galvanometer revealed a transient flow in the secondary
circuit. A continuous current in the primary circuit had no effect;
it was only when the current started or stopped that there was
an effect on the galvanometer. Faraday's 1821 discovery of electromagnetic
rotation had shown that electrical force could be converted into
motion. In 1831 he succeeded in converting mechanical motion
into electricity - in other words, in constructing the first
dynamo. He rotated a copper disk between the poles of a magnet,
and found a steady current flowed from the centre of the disk
to its edge. This achievement encouraged Faraday to carry out
the further researches which were to lead to his general theory
of electricity in 1838. In 1832 Faraday turned his researches
in a somewhat different direction by investigating the electrolysis
of aqueous solutions. In 1833 he showed that electrolysis can
be brought about by electricities produced in a variety of ways,
such as from electrostatic generators, voltaic cells, and electric
fish. In particular, he showed that electrolysis can occur if
an electric discharge is passed through a solution, without any
wired being introduced into it. Experiments reported in 1834
convinced him that electrolysis was another electrical phenomenon
that cannot be explained in terms of central forces and action
at a distance. He performed one experiment in which two solutions
were separated from one another by a seventy-foot string soaked
in brine. Gases were evolved at the two wires, and Faraday thought
it impossible that the effect would extend over such a length
if the inverse square law applied. He carried out another experiment
in which a solution was placed near a source of static electricity
which produced an intense electric field. No electrolysis occurred,
and Faraday concluded that it is necessary for a discharge to
take place or for a current to flow. He also demonstrated that
the effects of electrolysis do not follow straight lines, which
they would do if there were action at a distance. Also, Faraday
argued, if a substance were attracted to a wire by the inverse
square law, would it not remain bound to the wire rather than
being released from it? The theory of electricity and magnetism
accepted by Faraday from 1838 onwards are neatly summed up in
Maxwell's Treatise on Electricity and Magnetism (1873): "...Faraday,
in his mind's eye, saw lines of force traversing all space where
the mathematicians saw centres of force acting at a distance:
Faraday saw a medium where they saw nothing but distance: Faraday
sought the seat of the phenomena in real actions going on in
the medium, they were satisfied that they had found it in a power
of action at a distance impressed on the electric fluids."
At first Faraday thought that his lines of force were carried
by molecules under strain but later, realizing that they are
set up in vacuum, thought in terms of strains in the ether, which
was supposed to pervade all space. in the last paper he submitted
for publication, in 1860, Faraday included gravity as involving
a field of force - an idea that was somewhat ridiculed at the
time, but later realized to be correct. For many years Faraday
attempted to find support for his ideas by observing some physical
effect in matter through which his lines of force were passing.
His first discovery of such an effect was in 1845, when he found
that plane-polarized light was rotated when it was passed through
a piece of glass in a strong magnetic field. This was the first
observation of the effect of magnetism on light. The result suggested
to Faraday that substances like glass, hitherto regarded as non-magnetic,
were not entirely indifferent to a magnetic field. He carried
out many experiments in which substances, including gases, were
placed between the poles of an electromagnet. He found that some
substances, such as iron, tended to align themselves along the
lines of force, and were attracted into the more intense parts
of the electromagnetic field; he called such substances paramagnetic.
Other substances like bismuth, which he called diamagnetic, aligned
themselves across the magnetic field, and tended to move into
regions of less intense field. He explained the difference between
paramagnetics and diamagnetics in terms of the way they distorted
a magnetic field.
Maxwell: Approach to an Electromagnetic Theory (1856-1862)
Much of Faraday's great work had been completed by the time
Maxwell became a student at Cambridge in 1850. Maxwell, who was
one of the few to realize its importance, always insisted that
he did nothing more than express Faraday's ideas in mathematical
form, but here he was being unduly modest. Producing the mathematical
equations was far from a routine task that any highly skilled
mathematician could have carried out; it also involved clarifying
and modifying the basic concepts. Maxwell's first paper, "On
Faraday's lines of force", which appeared in 1856 when he
was 25, was significant for showing mathematically that Faraday's
ideas gave a valid quantitative alternative to Ampère's
treatment based on central forces. The paper is also important
for its treatment of electrical action as analogous to the motion
of an incomprehensible fluid. Maxwell's final electromagnetic
theory in fact differs from all preceding physical theories in
being based on an analogy rather than a physical model capable
of being visualized. Maxwell's second paper on the subject, "On
physical lines of force", appeared in four parts in I ~6
I -62, and was mainly concerned with devising a model for the
ether which would account for the stresses associated with Faraday's
lines of force. This ether had a rather complicated structure,
consisting of spinning vortices, some of them electrical and
some magnetic. The model was such that a changing magnetic field
gave rise to an electric field, and that a changing electric
field produced a magnetic field. This model is today only of
historical interest, in showing how Maxwell's ideas developed,
since he discarded the model in his final version of his electromagnetic
theory, basing it entirely on the mathematical analogy.
The Speed of an Electromagnetic Wave
In 1861 the British Association for the Advancement of Science
set up a committee under William Thomson's chairmanship to establish
a set of electrical and magnetic standards. During the course
of their work it became clear to Maxwell and others that important
insight can be obtained by comparing results expressed in the
two sets of units, electrostatic and electromagnetic, that were
being used at the time. The electrostatic units were particularly
appropriate to static electricity, and related the force of attraction
and repulsion between two charged bodies to the quantities of
electricity that they held. The electromagnetic system of units,
on the other hand, related force to electric currents. The quantity
of electricity residing on a wire at a given time depends on
the speed with which the current travels along the wire. It can
be shown that the ratio of an electromagnetic unit of charge
to an electrostatic unit of charge is the speed with which the
current passes along a wire. During the 1860s Maxwell and various
colleagues carried out careful experiments in which they compared
the two units. Maxwell's own experiments were carried out using
equipment made available to him by John Peter Gassiot (1797-1877),
a wealthy wine merchant and amateur scientist who had already
done some remarkable experiments using vast numbers of electric
cells. The conclusion from the experiments comparing the two
sets of units was that the speed of an electric current was close
to 3 x 10 m/s, which is the speed of light. An alternative approach,
used by Maxwell and others, was to compare the electrical quantity
now called the permittivity of a vacuum, o, with the magnetic
quantity now called the permeability, µo. Maxwell's mathematical
treatment of Faraday's lines of force led to the conclusion that
the speed v of an advancing electromagnetic field was given by
v =1/(o µo) Measurements made by various physicists of
µo and o also led to the result that v obtained in this
way was the speed of light. These results convinced Maxwell and
others that light is an electromagnetic wave; in his own words,
emphasized in italics in his 1861-62 papers: "Light consists
in the transverse undulations of the same medium which is the
cause of electric and magnetic oscillations." In other words,
a single electromagnetic theory is needed for light, an electric
field and a magnetic field. The field produced by an electric
current has also a magnetic component, and the field produced
by a magnet has also an electric component; light also has electric
and magnetic components. A significant aspect of this work was
that it led to a decision between two alternative theories of
electricity that were held at the time. One theory was that there
were two electrical fluids, positive and negative, which moved
in opposite directions when a current flowed. Use of the method
of comparison of units led to the conclusion that if there were
two fluids they would each flow with half the speed of light.
The evidence thus supports the theory (which Benjamin Franklin
among others advocated) that only one type of electricity flows
along a wire when a current passes. Today, of course, we know
that a flow of electrons is involved.
Maxwell: Electromagnetic Theory (1864-1873)
In Maxwell's third and final major paper on the subject, "A
dynamical theory of the electromagnetic field" (1864), he
ignored his rather elaborate and artificial model he had proposed
for the ether, and concentrated on the propagation of electromagnetic
waves through space. The position he took, and this is accepted
today, is that the mathematical treatment remains valid without
any assumptions about the nature of the medium through which
the waves travel. In other words, he threw out the bathwater
but carefully preserved the baby! In doing so Maxwell made an
important break with scientific tradition. Previously it had
been felt necessary to base a scientific theory on a model that
could be clearly visualized. Maxwell's theory, on the other hand,
represented the situation not in terms of a model, but as a mathematical
analogue. Maxwell's fiend and colleague William Thomson (Kelvin)
always insisted on a mechanical model; in his own words "I
never satisfy myself unless I can make a mechanical model of
a thing. If I can make a mechanical model I can understand it."
As a result, Kelvin never really understood Maxwell's theory,
even though he had himself made important contributions to interpreting
Faraday's lines of force mathematically. Similarly, he never
understood Clausius's concept of entropy - another concept that
cannot be understood in terms of a model - even though he had
been one of the first to appreciate the second law of thermodynamics.
Maxwell's theory can be expressed in terms of a few equations
which have been referred to as "simple". They are indeed
simple in form, but understanding them involves a considerable
background knowledge of electrical and magnetic theory, and vectors.
Maxwell himself invented the names "curl", "grad"
and "div" for operators that appear in his equations.
Maxwell's famous book Treatise on Electricity and Magnetism,
which was published by the Clarendon Press, Oxford, in 1873,
is in many ways something of a surprise. It is certainly not
to be recommended to a student wanting to learn about the theory;
the 1864 paper is much easier to follow. The book raises a number
of aspects which Maxwell himself had not been able to clarify.
The book consists of four parts: Electrostatics, Electrokinetics,
Magnetism, and Electromagnetism. The author makes the recommendation
that these four parts should be read concurrently, but does not
explain how this remarkable feat should be performed; presumably
he meant that one should read a little of the first part, then
a litlle of the second, and so on. However, in spite of its obscurities,
the book was a great inspiration to many physicists, including
Einstein. A significant feature of the book is that the word
ether is mentioned only once, and that the model for the ether
elaborated in his 1861-62 paper is referred to only incidentally.
This does not mean that Maxwell had abandoned his belief in the
existence of an ether; in his article on "Ether" in
the famous 9th edition of the Encyclopedia Brittanica (1875)
he expressed very clearly his belief in the existence of an ether.
He considered, however, that his theory of electromagnetic radiation
was valid whether or not the ether exists, or what its nature
is.
Maxwell's Scientific Legacy
Maxwell's electromagnetic theory had an enormous impact on
later scientific work, and on the development of technology.
The theory soon led to the discovery of radiation having wavelengths
different from those of near ultraviolet, visible and near infrared
radiation, which were the only regions of the spectrum known
in Maxwell's time. The discovery in 1888 by Heinrich Hertz (1857
- 1894) of radio transmission was much inspired by Maxwell's
theory, and it led to television, radar and microwave techniques.
These in turn made possible the exploration of distant space.
X-rays were discovered in 1895,and gamma rays in 1900. Einstein
recognized that his theory of relativity depended greatly on
Maxwell's theory, and it had many other consequences, including
the understanding of the structure on atomic nuclei.
Suggested Reading
The biographies of Maxwell mentioned in Part 1, by Everitt,
Tolstoy and Goldman, give good non-mathematical accounts of electromagnetic
theory. Those wishing a mathematical treatment should consult
modern textbooks of physics and not Maxwell's Treatise, which
is difficult reading. Some of Maxwell's original papers, on the
other hand, are very lucid; The Scientific Papers of James Clerk
Maxwell (Ed. W.D. Niven, 1890) were reprinted by Dover Publications
in 1965. See, for example, Paper XXXVI for a comparison of electrostatic
and electromagnetic units. A very clear account, with full mathematical
details, of Ampère's theory of electromagnetism is to
be found in R.A.R. Tricker, Early Electromagnetism, Pergamon
Press, Oxford, 1965. The Publisher, Editor and Editorial Board
of Phys 13 News would like to thank Prof. Keith J. Laidler for
this excellent series of three articles on the life and work
of James Clerk Maxwell that have appeared in the past three issues
of Phys l3 News. It is a series that should be read by every
student of physics.
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