Maxwell’s equations Fields James Clerk Maxwell Commentary

James Clerk Maxwell electromagnetism

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.