The Lines of Force
Michael Faraday and the Visual Geometry of Electromagnetic Fields
On August 29, 1831, in the stone basement laboratory of the Royal Institution on Albemarle Street in London, Michael Faraday sat before a welded ring of soft wrought iron six inches in diameter and seven-eighths of an inch thick. Around one half of the iron torus—which he labeled Side A—Faraday had wound three coils of copper wire totaling seventy-two feet, insulating every turn by hand with cotton twine and calico cloth. Around the opposite half of the ring—Side B—he wound sixty feet of copper wire separated from Side A by bare iron, extending its two leads three feet away to pass above a delicately balanced magnetic compass needle.
Eleven years earlier, in 1820, Hans Christian Ørsted in Copenhagen had shown that a steady electric current flowing from a voltaic battery deflects a nearby magnetic compass needle. Since electric current produces magnetism, every physicist in Europe had tried and failed for a decade to produce the reverse effect: using a stationary magnet to generate a steady electric current. Armed with differential calculus and Isaac Newton's law of universal gravitation, French mathematical physicists led by André-Marie Ampère and Siméon Denis Poisson assumed that electricity and magnetism were weightless fluids exerting instantaneous forces at a distance across empty space along straight lines joining two charges. They therefore placed strong permanent bar magnets next to copper wires and waited in vain for a steady current to flow.
Faraday possessed no calculus at all. The son of a Yorkshire blacksmith who had migrated to Southwark in London, Faraday had left school at age thirteen knowing little more than basic arithmetic, working for seven years as a bookbinder's apprentice in Blandford Street. Reading the science books he stitched together at night—especially Jane Marcet's Conversations on Chemistry and the electricity article in the Encyclopædia Britannica—he had secured a post as laboratory assistant to Humphry Davy in 1813 after sending Davy a bound three-hundred-page notebook of his lecture transcripts.
Because Faraday could not write algebraic force equations, he was forced to think entirely in physical geometry. When he connected Side A of his iron ring to a ten-plate copper-zinc battery trough filled with dilute acid on August 29, 1831, the compass needle three feet away on Side B twitched violently, oscillated, and then settled back to dead north even while the battery remained fully connected. When Faraday broke the battery contact on Side A, the compass needle jerked again in the exact opposite direction and went still. Current was induced not by the static presence of magnetism, but only while the magnetic state in the surrounding space was actively rising or collapsing.
To understand why changing magnetism drove current across an air gap where no wires touched, Faraday sprinkled fine iron filings onto sheets of stiff white paper coated with melted wax, held the sheets over bar magnets and current-carrying coils, tapped the paper lightly, and warmed the wax to fix the curving chains of iron particles permanently in place. Where Continental mathematicians saw empty space across which distant bodies pulled each other instantaneously, Faraday saw space packed with continuous, elastic curves of physical tension that he named lines of force:
- - Action-at-a-Distance Orthodoxy (Ampère and Weber): Electric charges and magnetic poles interact instantaneously across an empty vacuum along the straight geometric line connecting them, with space itself serving as an inert, featureless container.
- - Continuous Elastic Lines of Force: Every magnet and electric charge fills the surrounding space with continuous closed loops of tension that pull longitudinally like stretched rubber bands while repelling adjacent lines laterally.
- - Electromagnetic Induction by Cutting Lines: An electric current flows in a conducting wire if and only if the wire physically cuts across moving magnetic lines of force, with the induced electromotive force proportional to the exact number of lines intersected per second.
- - The Electro-Tonic State and Dielectric Medium: Insulators and empty space are not passive barriers to electricity, but the active physical seat where electrostatic and magnetic strain energy is stored before discharging.
- - Magneto-Optical Rotation (September 1845): Passing polarized light through a two-inch block of heavy lead-borate glass placed between the poles of a powerful electromagnet rotated the plane of optical polarization, proving that light itself is a vibration propagating along electromagnetic lines of force.
For twenty-four years, mathematical physicists dismissed Faraday's curved lines as the crude visual crutch of an unlettered experimenter. In 1855, James Clerk Maxwell read Faraday's three-volume Experimental Researches in Electricity and declared that Faraday's visual lines of force were in fact a rigorous geometric calculus waiting to be transcribed into the twenty partial differential equations of the electromagnetic field.