Ampère & the Founding of Electrodynamics

An “Incident” in Ampère's Life?

It is through his work on electromagnetism that the name Ampère has endured in history. His Essai sur la philosophie des sciences was read by Einstein, yet it never shaped the history of philosophy as Ampère had hoped. In contrast, his Théorie [mathématique] des phénomènes électrodynamiques, uniquement déduite de l'expérience (1826) was studied and debated by physicists from Weber to Maxwell and well beyond.

Yet his research on electrodynamics occupied only six years of his life (1820–1826) — what his biographer De Launay called “a considerable incident, a six-year incident, but an incident nonetheless, in a life occupied before and after by entirely different work.”

In truth, electrodynamics fully occupied Ampère's mind for only a few months — from September 1820 to January 1821. A pulmonary illness first prevented him from continuing, then family, health, and professional problems conspired to make his research far more discontinuous.

The Young André-Marie (1775–1820)

Born in Lyon in 1775, André-Marie Ampère received an essentially home-based education, supplemented by a few private mathematics lessons. His interests were remarkably diverse: ancient literature, poetry, the search for a universal language, botany, astronomy, mathematics, physical sciences, and the construction of instruments and technical objects. It was in mathematics that he first showed the strongest aptitude, mastering the essential mathematics of his era by adolescence.

His father, Jean-Jacques Ampère — a prosperous merchant and admirer of Rousseau — was guillotined on 24 November 1793 during the Jacobin Terror. This devastating event profoundly shaped the young man. In 1797, leaving his village of Poleymieux to earn a living in Lyon, he set up a small laboratory and gave private lessons in mathematics, physics, and chemistry.

In 1801, stimulated by Napoleon's grand prize for galvanism following Volta's invention of the pile, Ampère began work on electricity, even starting to draft a book on the subject. But he quickly abandoned physics for mathematics. In 1804, he was appointed répétiteur d'analyse at the École Polytechnique, and in 1814 he entered the Académie des Sciences thanks to his mathematical research on the theory of games.

Though he had become a mathematician, his interest in chemistry was at least equally strong, and he was also passionate about philosophy, metaphysics, and religion. The only research that occupied his mind virtually without interruption from 1802 to his death in 1836 was the quest for a classification of all the sciences — seeking to grasp the unity and foundation of all human knowledge.

Ampère's Key Dates

1820: A Strange Experiment from the Northern Mists

In August 1820, Hans Christian Ørsted's memoir on the “electric conflict” reached Geneva. The physicist Gaspard de la Rive hastened to reproduce the Dane's experiments using his particularly powerful pile: a metallic wire placed above a compass needle deflected the needle from its North-South orientation when connected to a battery.

There was now a direct link between electricity and magnetism. This connection had been sought by Ørsted, who — sensitive to the “Romantic” vision of nature then dominant in Germanic countries — had long affirmed the unity of physical phenomena. But in Paris, mathematicians and physicists like Laplace, Poisson, and Biot were convinced of the complete independence between electricity and magnetism.

Moreover, the observed effect was astonishing in its revolutionary character. Newtonian forces between masses, electric charges, or magnetic poles are always directed along the line joining the interacting elements. Ørsted's experiment did not fit this scheme. The needle oriented itself perpendicular to the wire, as if carried by a vortex swirling around the wire — evoking the Cartesian vortices that physics had long abandoned.

“An Important Circumstance of My Life”

François Arago, visiting Geneva in August 1820, witnessed de la Rive's experiments. Enthusiastic, he reported them upon his return to Paris at the session of the Académie des Sciences on 4 September 1820. But the members remained incredulous. As Ampère wrote to a friend:

“[Coulomb's theory] absolutely excluded any idea of action [of electricity on magnetism]. The prejudice was such that when M. Arago spoke of these new phenomena at the Institut, they rejected it just as they had rejected stones fallen from the sky [...]. They all declared it was impossible.”— Ampère to Jacques Roux-Bordier, 21 February 1821

It took Arago himself reproducing the experiment the following week for eyes to open. Ampère was present. It was the starting point of a few extraordinary weeks of creation and invention, during which he would lay the foundations of electrodynamics:

“All my moments have been consumed by an important circumstance of my life. Since I first heard of M. Ørsted's beautiful discovery [...] on the action of galvanic currents on the magnetic needle, I have thought of it continuously, I have done nothing but write a grand theory on these phenomena and all those already known about the magnet, and attempt experiments suggested by this theory, which have all succeeded and revealed to me as many new facts. [...] And here is a new theory of the magnet [...]. It resembles nothing that was said about it before.”— Ampère to his son Jean-Jacques, 19–25 September 1820

Divergent Research Paths

What was this “grand theory”? For Ampère, the goal was to unify two domains of physics by reducing all magnetic phenomena to purely electrical phenomena. The interactions between currents that Ampère discovered were radically new. Magnetic fluids became for him a “gratuitous supposition” that could be eliminated from science.

The dominant view among most French scientists was that with Newton's and Coulomb's theories, physics was “a finished science, stable and impossible to overturn” (Biot, 1824). For them, the natural approach was to reduce the unknown — Ørsted's experiment — to the known: the properties of magnetic fluids. Biot proposed reducing the wire-compass interaction to purely magnetic interactions.

By opening an entirely personal path with his interactions between electric currents, Ampère founded a new branch of electricity: electrodynamics. As early as 18 September he stated his fundamental hypothesis on the existence of electric currents within magnets, and imagined that the compass's usual orientation could be explained by electric currents inside the Earth.

One Week for the Fundamental Hypotheses

Just one week after witnessing the reproduction of Ørsted's experiment, Ampère summarized his first results at the Académie:

“I showed that the current in the pile acts on the magnetic needle just as that of the connecting wire. [...] I described the instruments I proposed to have built, and among them galvanic spirals and helices. I announced that these helices would in all cases produce the same effects as magnets. I then entered into some details on the manner in which I conceive magnets, as owing their properties solely to electric currents in planes perpendicular to their axis, and on the similar currents I suppose to exist within the terrestrial globe; so that I reduced all magnetic phenomena to purely electrical effects.”— Journal de physique, de chimie, vol. 91, 1820, pp. 76–78

An Instrument and a Figure Destined for a Great Future

By showing that the magnetic needle deflected uniformly along the entire conducting wire — even very far from the pile — Ampère revealed a new property characteristic of the circuit as a whole. He introduced the concept of current intensity: “the electric current exists everywhere [in a circuit] with the same intensity.”

He also proposed calling this detecting instrument a galvanometer, and formulated the famous “right-hand rule” as the bonhomme d'Ampère(Ampère's little man):

“If one places oneself mentally in the direction of the current, so that it flows from the feet to the head of the observer, and the observer faces the needle, it is constantly to his left that the action of the current will deflect the north pole of the needle from its ordinary position.”

The bonhomme d'Ampère inspired generations of French lycée students to all manner of mental contortions — and occasionally excited their humorous wit.

“Tension Electricity” vs. “Current Electricity”

Ampère classified electrical phenomena into two apparently disjoint categories:

For Ampère, tension and current were incompatible — an error that persisted until Ohm's work established \(U = RI\), showing that tension and current coexist in a circuit. Ampère's error rested on the observation that when a pile is short-circuited, an electrometer connected to a pole shows no deflection, while intense current effects are observed in the wire.

“Spirals and Galvanic Helices Produce the Same Effects as Magnets”

Announced on 18 September and presented at the historic session of 25 September 1820, the “decisive experiment” showed that two conducting wires wound in spirals attract or repel each other when carrying current, depending on the direction of the current — exactly as two magnetic poles would.

To succeed in this experiment, initially attempted with batteries too weak, Ampère had to purchase the large pile intended for the physics course at the Faculté des Sciences. He showed that one could substitute a magnet pole for one of the spirals — in all cases, the attractions and repulsions demonstrated that one face of the spiral behaved as a south pole, the other as a north pole.

The analogy between circular currents and magnets became even more striking when Ampère replaced the spiral with a solenoid — a term he invented to designate a helical winding.

“The Manner in Which I Conceive Magnets”

Ampère proposed that on the surface and in the interior of a magnet there exist “as many electric currents, in planes perpendicular to the axis of the magnet, as one can conceive of lines forming, without crossing each other, closed curves.”

Initially this seemed to imply macroscopic currents. But by 15 January 1821, following a suggestion from Fresnel, Ampère presented a different hypothesis: molecular currents. Each particle of the magnet would be surrounded by a circular current with its axis parallel to that of the magnet. Though both hypotheses were equivalent, Ampère came to prefer the microscopic currents, which also aligned with his atomist convictions in chemistry.

The Interaction Between Two Parallel Currents

On 9 October 1820, Ampère performed before the Académie the fundamental experiment demonstrating his law: two parallel currents of the same direction attract, while two currents of opposite direction repel.

Ampère had to emphasize an essential difference from ordinary electrostatics: while similarly charged bodies repel, similar currents (same direction) attract. Moreover, the conductor connected to the battery carries no detectable electric charge.

A “Primitive Fact”?

To defend the fundamental character of the interaction between electric currents, Ampère made a profound argument about the historical and contingent nature of scientific knowledge:

“The order in which facts were discovered has nothing to do with their reality in nature. Thus chance could have led to the discovery of the action that voltaic conductors exert on each other before their action on magnets, and then one would naturally have considered the former as the principle of the latter.”— Ampère to Simon Speyert van der Eyk, 1821

“All explanation in the sciences consists in discovering a primitive fact expressed by a general law which, once established, serves to deduce all the others. [...] This manner of reducing a multitude of facts to a single fact verified by experiment, and whose mathematical law is confirmed by its agreement with all phenomena, is what I call explaining, even when the cause of the primitive fact from which one starts is absolutely unknown.”— Ampère, 1821

The Search for the Mathematical Law

For a professor of analysis like Ampère, the natural approach to computing the fundamental interaction between two electric currents was to mentally decompose each conductor into an infinity of small rectilinear elements. If one knew the force between two infinitesimal current elements, the interactions between circuits of any shape could then be deduced by integration.

He gave a first sketch as early as October 1820. The elementary force must satisfy Newton's principle of action and reaction, and be directed along the line joining the two current elements. Like gravitational force, he supposed it proportional to the inverse square of the distance. But unlike gravity, the force between two arbitrary current elements depends on their relative orientation, defined by three angles.

The difficulty was extreme. Infinitesimal current elements are a mathematical idealization — experiments always involve macroscopic circuits. While it is always possible (at least theoretically) to deduce from an infinitesimal force the force between macroscopic circuits by integration, going in reverse is far more complex. This would be the work of several years, culminating in the great synthesis of 1826: the Mémoire sur la théorie [mathématique] des phénomènes électrodynamiques, uniquement déduite de l'expérience.

Ampère's Legacy

“The experimental investigation by which Ampère established the laws of the mechanical action between electric currents is one of the most brilliant achievements in science. The whole, theory and experiment, seems as if it had leaped, full grown and full armed, from the brain of the ‘Newton of Electricity’.”— James Clerk Maxwell, A Treatise on Electricity and Magnetism, 1873

Sources & Further Reading

• Blondel, C. & Wolff, B. — Ampère jette les bases de l'électrodynamique, CNRS/CRHST, ampere.cnrs.fr
• Ampère, A.-M. — Mémoire [...] sur les effets des courants électriques, Annales de chimie et de physique, 1820, vol. 15
• Ampère, A.-M. — Théorie des phénomènes électrodynamiques, Paris, 1826
• Hofmann, J.R. — André-Marie Ampère, Cambridge University Press, 1996
• Blondel, C. — Ampère et la création de l'électrodynamique, Bibliothèque nationale, 1982
• Locqueneux, R. — Ampère, encyclopédiste et métaphysicien, EDP sciences, 2008