The Science Book

184 JAMES CLERK MAXWELL

Maxwell’s models
Maxwell began to develop his
theory of electromagnetism in a
pair of papers published in 1855
and 1856. These were an attempt
to model Faraday’s lines of force
geometrically in terms of the flow
in a (hypothetical) incompressible
fluid. He had limited success and
in subsequent papers tried an
alternative approach, modeling the
field as a series of particles and
rotating vortices. By analogy,
Maxwell was able to demonstrate
Ampère’s circuital law, which relates
the electric current passing through
a conducting loop to the magnetic
field around it. Maxwell also
showed that in this model, changes
in the electromagnetic field would
propagate at a finite (if high) speed.
Maxwell derived an approximate
value for the speed of propagation,
at about 193,060 miles/s
(310,700 km/s). This value was
so suspiciously close to the speed
of light as measured in numerous
experiments that he immediately
realized that Faraday’s intuition
about the nature of light must be
correct. In the final paper of the
series, Maxwell described how

magnetism could affect the

orientation of an electromagnetic

wave as seen in the Faraday effect.

Developing the equations

Satisfied that the essentials of

his theory were correct, Maxwell

set out in 1864 to put it on a

sound mathematical footing.

In A Dynamical Theory of the

Electromagnetic Field, he described

light as a pair of electrical and

magnetic transverse waves,

oriented perpendicular to each

other and locked in phase in such

a way that changes to the electric

field reinforce the magnetic field,

and vice versa (the orientation of

the electrical wave is the one that

normally determines the wave’s

overall polarization). In the last

part of his paper, he laid out a

series of 20 equations that offered a

complete mathematical description

of electromagnetic phenomena in

terms of electrical and magnetic

potentials—in other words, the

From a long view of the history
of mankind...there can be
little doubt that the most
significant event of the
19th century will be judged
as Maxwell’s discovery of the
laws of electrodynamics.
Richard Feynman

amount of electrical or magnetic

potential energy a point charge

would experience at a specific

point in the electromagnetic field.

Maxwell went on to show

how electromagnetic waves

moving at the speed of light

arose naturally from the

equations, apparently settling

the debate about the nature of

electromagnetism once and for all.

He summed up his work on the

subject in the 1873 Treatise on

Electricity and Magnetism, but,

convincing as the theory was, it

remained unproven at the time of

Maxwell’s death, since the short

wavelength and high frequency of

light waves made their properties

impossible to measure. However,

eight years later, in 1887, German

physicist Heinrich Hertz provided

the final piece of the puzzle (and

made an enormous technological

breakthrough) when he succeeded

in producing a very different form

of electromagnetic wave with low

The electrical and magnetic

components of an electromagnetic

wave move through space while

oscillating at right angles to each other

and in phase, so that both elements

reach their maximum amplitudes at

the same time, and constantly

reinforce each other by induction.

Wavelength

Magnetic field

Propagation

direction

Electric field