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Faraday, Ampere, and the mystery of continuous rotations

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By Christine Blondel and Bertrand Wolff
Translated by Andrew Butrica

Ampère's astonishment in front of a Faraday discovery

In September 1821, Faraday announced in the Journal of the Royal Institution that he had obtained the continuous rotation of a magnet under the action of a conductor and vice versa: the rotation of a conductor through the influence of a magnet.

The apparatus with which Faraday performed his demonstration of the movement of continuous rotation.
The two vessels (seen in cross-section) are filled with mercury. At left, a cylindrical magnet is fixed to the bottom of the container by a wire attached to one of the poles. Because the iron is less dense than the mercury, the other pole of the magnet rises above the surface. A copper conductor connected to a battery enters the mercury through the bottom of the vessel. A second conductor, fixed and vertical, enters the mercury in the center of the vessel.

"When the poles of a voltaic apparatus are connected with [these two conductors]", wrote Faraday, "the upper pole of the magnet immediately rotates round the wire which dips into the mercury; and in one direction or the other, according as the connexions are made."

On the right, the vertical magnet is fixed vertically at the center of the vessel. A moveable conducting wire whose lower end is immersed in the mercury is suspended from the arms and can move freely about the point of suspension while maintaining electrical contact.

"When the connections are so made [...] that the current of electricity shall pass through this moveable wire, it immediately revolves round the pole of the magnet, in a direction dependent on the pole [north or south] used and the manner in which the connexions are made."

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Faraday, Experimental Researches in Electricity, Vol. II, pl. IV

On returning from his inspection tour during the summer of 1821, Ampere had somewhat forgotten electromagnetism. Faraday's memoir relaunched his researches. "This memoir contains very singular electromagnetic facts that confirm perfectly my theory, although the author tries to contest it by substituting one of his own invention." Additionally, Ampere thought that these continuous rotations produced, to his great astonishment, the permanent production of a vis viva [in modern terms, kinetic energy] capable of overcoming friction without any expenditure of work.

How can one explain such an apparently "free" production of motion? And what was the nature of the theoretical opposition between the two physicists?

Ampere provisionally put aside the first question, but straight away returned to Faraday's experiments and sought to integrate them into his theory.

The continuous rotations of Ampere and the debate with Faraday

Ampere made numerous modifications to Faraday's experiments. He replaced Faraday's vertical wire with a horseshoe-shaped circuit and substituted acidulated water for the mercury in order to reduce friction.

He succeeded in rotating the conductor with a magnet under solely the action of terrestrial magnetism, as he wrote to Faraday on 23 January 1822 [See the letter]

A friendly dialog, and very rewarding for designing experiments, was established between the two scientists through letters and exchanged memoirs. However, their interpretations differed radically. The fundamental difference was the nature of the "primary fact" involved in the interactions between a magnet and a current. For Faraday, the "primary fact" was the rotation of the magnet's pole around the current and vice versa. Accordingly, he explained Oersted's experiment: the north pole of the compass rotates around the wire. For Ampere, the "primary fact" had to be sought "in the action of two things of the same nature as the two conductors and not in that of the two heterogeneous things such as a conductor and a magnet". His ultimate goal in effect was to reduce electromagnetic phenomena to the forces of attraction or repulsion between current elements [See the page Ampère lays the foundations of electrodynamics].

One apparatus among many others devised by Ampere.
Rotation of moveable horseshoe-shaped circuit OLM under the action of a magnet.
AB, AB' and AB" represent different positions of the magnet.

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Of all the complex arrangements that Ampere successively built, the one he imagined in December 1821 addressed this debate in particular. If the fundamental fact was the mutual action between two currents, one should be able to obtain a continuous rotation without a magnet by the action of one circuit on another circuit. In Faraday's second experiment, Ampere replaced the vertical fixed magnet with a circular circuit placed around the reservoir. When this circuit carried a sufficiently intense current, the horseshoe circuit began to rotate, just like under the action of the magnet.


Continuous rotation of a current under the action of a current.
In this experiment, there is no longer any magnet. The moveable circuit, in equilibrium on the small cup S, consists of the conductor AEFG soldered to a circular copper strip placed horizontally. The circular strip enters a vessel of acidulated water. When a circular circuit is placed around the vessel and carries a sufficiently intense current, the mobile mechanism turns as long as the current circulates.

Faraday: "I wait for further proofs"

To explain the continuous rotations involving magnets, Ampere called on his hypothesis of the existence of electric currents inside magnets. From his formula that gives the force acting between two current elements, it is indeed possible, at least theoretically, to "submit the phenomena to calculations" [See the page In Search of a Newtonian Law of Electrodynamics]. The rotation of a conductor around the pole of a magnet, or vice versa, thus appears for Ampere as a composite result arising from a multitude of elementary actions. For Faraday, in contrast, it was the rotation itself that constituted the "primary fact", while the hypothesis of currents in magnets seemed to him to be superfluous and risky.

"I am naturally skeptical in the matter of theories and therefore you must not be angry with me for not admitting the one you have advanced immediately. The ingenuity and applications are astonishing and exact, but I cannot comprehend how the currents are produced and particularly if they be supposed to exist round each atom or particle and I wait for further proofs of their existence before I finally admit them." (2 February 1822) See the letter]

The rotation of a current under the action of a current obtained by Ampere was not enough to change Faraday's opinion. For the latter, it was the attraction and repulsion between currents that must be considered as composite facts resulting from a combination of rotational actions. However, he did not pursue the debate, attenuating his disagreement with the mention of his "deficiency in mathematical knowledge" and his weakness in the domain of theory.

"On reading your papers and letters, I have no difficulty on following the reasoning, but still at last I seem to want something more on which to steady the conclusions. I fancy the habit I got into of attending too closely to experiment has somewhat fettered my power of reasoning and chains me down [...]. With regard to electromagnetism also feeling my insufficiency to reason as you do, I am afraid to receive at once the conclusions you come to (though I am strongly tempted by their simplicity and beauty to adopt them) [...] It delays not because I think them hasty or erroneous, but because I want some facts to help me on." (3 September 1822) See the letter]

Perpetual motion from electricity?

The candidate experiments for the title of ancestor of the electric motor are not lacking. [See the page Did Ampere invent the galvanometer . . . the electric motor?]. Don't Faraday's continuous rotation experiments show the possibility of using electromagnetic force to product a continuous rotational motion? Nonetheless, it was the theoretical implications, not an eventual motor application, that aroused the interest of Ampere and his contemporaries.

First of all, the continuous rotations furnished Ampere with an argument that to him seemed decisive against the electromagnetic theories resting, like that of Biot, on the magnetization of the conductors. Indeed, it is impossible to obtain these continuous rotations only with magnets.

In addition, one aspect of Ampere's and Faraday's experiments aroused great astonishment among theorists. As we have seen, Ampere believed that he saw in them a free production of vis viva [kinetic energy]. This is what he expressed in his Exposé sommaire that he read at the public meeting of the Academy of Sciences on 8 April 1822:

"A movement that continues always in the same direction, despite friction, despite resistance from the environment, and [...] produced by the mutual action of two bodies that remain constantly in the same state, is a fact without precedent in all that we know of the properties that inorganic matter can exhibit."

A movement produced by the mutual action of two bodies remaining in the same state: is that not the definition of perpetual motion, even if one dares not utter the term? Such motion obtained without the expenditure of work is certainly a "fact without precedent" that the Academy of Sciences refused to take into consideration since 1775!

The phenomenon no longer astonishes us as it amazed Ampere and his contemporaries, because we take into account the principle of the conservation of energy formulated in the middle of the nineteenth century. Chemical transformations occur within the battery, and these convert chemical energy into electrical energy. With the rotation of the moveable circuit, this electrical energy is converted into mechanical energy. For his part, taking into account the fact that electricity at rest had never caused this type of phenomenon, Ampere advanced the hypothesis according to which "one cannot attribute this action [responsible for continuous rotation] but to fluids in motion."

Further information: Was Ampere the author of "Ampere's theorem"?

During the continuous rotation of a magnet's pole around a wire, the speed of the pole increases to a value limited by friction. It is Maxwell who in 1856 gave the expression for the work of the electromagnetic force acting on the rotating pole: for a magnetic unit, this work is equal, to a numerical coefficient close, to the intensity of the current in the wire. Maxwell added, "one can then make [with this work] a measure of the magnitude of the current." He next gave an abstract and more general form for this theorem, the form that one finds under the label of "Ampere's theorem" in modern treatises on electricity (the circulation of the magnetic field along a closed curve is equal to the current that passes through a surface bounded by the curve).

In his lectures at the College de France in 1826, as recorded in the notes of the young mathematician Liouville, Ampere developed calculations in which we recognize the work of the force (given by the law of Biot and Savart) undergone by the rotating magnetic pole. Unlike Newtonian forces for which the work is zero along a closed curve, he obtained an expression that grew in arithmetic progression at every turn, but he did not bother to specify the value corresponding to a single turn and did not exploit this result. One must however emphasize that the notion of mechanical work was not explained until 1829 by Coriolis. On the other hand, Ampere saw in his calculations only "pure curiosity ... because we cannot isolate the poles of a magnet".

Ampere thus did not mathematically formulate the theorem that bears his name, but he did provide the essential physical elements.

 

Further readings

Faraday, Michael. Faraday's Experimental Researches in Electricity: Guide to a First Reading, ed. by Howard J. Fisher. Santa Fe, New Mexico: Green Lion Press, 2001.

Locqueneux, Robert. Ampère, encyclopédiste et métaphysicien. Paris, Lille: USTL, 2008.
Hofmann, James R. André-Marie Ampère. Cambridge: Cambridge University Press, 1996.
Blondel, Christine. André-Marie Ampère et la création de l'électrodynamique, 1820-1827. Paris: Bibliothèque nationale, 1982.

A bibliography of "secondary sources" on the history of electricity.



French version: June 2009 (English translation: March 2014)