1864: Maxwell’s equations - The book of science

Maxwell’s equations
Fields
James Clerk Maxwell
Commentary

Maxwell’s equations

Like little rafts, an electric current
runs along a river of force vectors
oriented perpendicular to a surface.
Bundles of magnetic lines of force
are like small tubes that carry a magnetic flux
in arcs above and below a charged surface.
The work needed to circulate a charge
around a closed curve in an electric field is related to
the work needed to circulate a magnetic monopole,
if one were to exist, in a magnetic field.
The imputed magnetic monopole
is a magnet with only one end,
like an electron, a point in time
whose negative charge is in our world
and whose positive charge is in a deformation
of the field in a minuscule invisible dimension.
Modern physics can explain everything
using the properties of fields. Fields, rafts, tubes,
magnetic monopoles, and numerous invisible dimensions
are, to those who understand them, like poetry.

Fields

The properties of a field can be described
by a set of numbers associated
with each point of the field.
First, mathematicians say a point is a location
with no extent.
Second, any extent, however small,
contains an infinite number of points.
Third, a field is an extent.
The relation between reality and a mathematical system
cannot be determined mathematically.
The relation rests on the faith
that each step from the known to the unknown
might help us recognize something new or useful.
In particular, it would be useful to explain
things that our senses
cannot determine—how gravity
acts at a distance, why light
travels at a certain speed, and whether the universe
will end in fire or in ice.

James Clerk Maxwell

James Clerk, named Maxwell after his mother died,
studied at Edinburgh, Cambridge, and Trinity,
earned honors, prizes, and a mathematics degree at 23;
taught at Marischal College and married the daughter of the principal,
planned the famous Cavendish laboratory
and became the first Cavendish professor at Cambridge,
was the first to use probability and statistics
to explain the behavior of gases,
studied color blindness and color vision,
resulting in the first color photograph,
extended Michael Faraday’s theories of electromagnetism
suggesting that “light consists in the transverse undulations
of the same medium which is the cause
of electric and magnetic phenomenon.”
Nine years after he died in 1879 at 48,
according to his theory, Heinrich Hertz
demonstrated that an electric disturbance
is transmitted through space in waves,
and, nearly one-hundred years after he died,
NASA’s Voyager space probe
confirmed Maxwell’s theory that the rings of Saturn
are composed of many small particles.

James Clerk Maxwell was the first to realize how electricity, magnetism, and light are manifestations of the same physical forces—electromagnetic radiation—described as photons or waves with different energies, wavelength, and frequencies. As Einstein wrote, Maxwell realized “that electromagnetic fields spread in the form of polarised waves, and at the speed of light!” Maxwell wrote that “light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.”

Electric charges and currents create electric and magnetic fields (physical lines of force) that can be described mathematically. Maxwell’s equations describe and improve work by Carl Friedrich Gauss, Micael Faraday, and André-Marie Ampère, that is, Gauss’s law, Gauss’s law for magnetism, Faraday’s law of induction, and Ampère’s circuital law.