Arago's Rotations: The Spinning Copper Disc That Puzzled Physics

Hang a compass needle on a thread a little above a copper disc. Copper is not magnetic: a magnet will not pick up a penny-sized piece of it, and a compass held next to a copper pot points north as usual. Now spin the disc. The needle, which has nothing touching it, starts to turn in the same direction as the disc. Spin faster and it turns further. Spin fast enough and it whirls around continuously, chasing the copper beneath it.

This is Arago's rotation, named after the French scientist François Arago, who announced the effect in 1824. For seven years it was one of the great puzzles of physics. It was clearly magnetic, yet it involved a metal that showed no ordinary magnetism. It appeared only when something was moving, and vanished when everything was at rest. Some of the best scientists in Europe, including Charles Babbage, John Herschel, Siméon Denis Poisson and André-Marie Ampère, studied it without reaching a satisfying explanation. The answer finally came from Michael Faraday's discovery of electromagnetic induction in 1831. The spinning copper carries electric currents, induced by its motion relative to the magnet, and those currents push back on the magnet.

Today the same physics drives the eddy-current brakes on trains and roller coasters, the induction motor in your washing machine and the spinning disc of the old-fashioned electricity meter. This article tells the story of the discovery, explains the physics in plain language, works through some numbers, and clears up a few common misunderstandings.

What the effect looks like

The basic arrangement

The classic demonstration has two parts that can each turn freely:

A disc of copper (or another good conductor, such as aluminium or silver) mounted on a vertical axle so it can be spun.
A magnet, often a compass needle or a small bar magnet, suspended or pivoted just above the disc, with something non-conducting such as a sheet of glass or paper between them so that moving air cannot carry the needle along.

With both at rest, the needle points north (or wherever the local magnetic field and any nearby magnets direct it). Nothing about the copper affects its resting direction.

When the disc spins, the needle is dragged around in the same direction. At low speeds it is merely deflected from north by an angle that increases with the speed of the disc. At higher speeds the drag exceeds the restoring pull of the Earth's magnetic field, and the needle rotates continuously, but always more slowly than the disc. The effect weakens rapidly as the needle is raised further from the disc.

Reversing the roles

The effect is mutual, as any pair of forces must be. If the copper disc is free to turn and you rotate the magnet beneath or above it instead, the disc begins to turn in the same direction as the magnet. If the disc is spinning and the magnet is held fixed, the disc slows down faster than it would on its own: the magnet acts as a brake.

The common thread is relative motion. Whenever the magnet and the conductor move relative to each other, a force appears that tends to reduce that relative motion. When they move together, or both sit still, there is no force at all.

Which materials work

Arago and his successors tested many substances. Good electrical conductors, especially silver and copper, produced strong effects. Poorer metallic conductors, such as lead and bismuth, produced weak ones. Non-conductors such as wood and glass produced none that could be reliably detected. At the time, nobody had the concept needed to see why electrical conductivity should matter for a magnetic effect. That connection is the heart of the explanation.

The scientific setting in 1824

Electricity meets magnetism

Until 1820, electricity and magnetism were thought to be separate phenomena. In that year the Danish physicist Hans Christian Ørsted showed that an electric current in a wire deflects a nearby compass needle. The discovery spread across Europe within weeks and set off a burst of research.

Ampère in Paris quickly showed that two current-carrying wires attract or repel each other and developed a mathematical theory of the forces between currents. Arago himself showed in 1820 that a current-carrying wire could magnetise iron filings and needles. Faraday, in London, built the first device to produce continuous rotation from electromagnetism in 1821: a wire carrying current that circled around a magnet in a cup of mercury.

So by 1824 it was known that currents produce magnetic effects. What was not known, and what many people were looking for, was the reverse: whether magnetism could produce electricity. Several experimenters had tried to induce currents with stationary magnets and failed, because induction requires change, a point no one yet understood.

Who Arago was

Dominique François Jean Arago (1786–1853) was one of the leading figures of French science. He had entered the École Polytechnique in 1803, worked at the Paris Observatory, and in 1806 went with Jean-Baptiste Biot to Spain to extend the measurement of the meridian arc used to define the metre. War between France and Spain left him stranded and in danger for years; he returned to France in 1809 and was elected to the Académie des Sciences at the age of 23. He worked in astronomy, optics and magnetism, supported Augustin-Jean Fresnel's wave theory of light, and later became Permanent Secretary of the Académie and a prominent politician.

The discovery

Damping in a copper box

The trail began with an observation about compass needles coming to rest. A magnetic needle that is disturbed swings back and forth around north several times before settling. Arago, working with Alexander von Humboldt on measurements of magnetic intensity in 1822, noticed that a needle settled much sooner when it was in its box than when it was suspended well away from other objects. According to Arago's later accounts, the Paris instrument maker Henri-Prudence Gambey had also noticed that needles in copper-bottomed compass boxes settled faster than those in wooden ones. Peter Barlow and a colleague at the Royal Military Academy in Woolwich had independently reported an effect of rotating iron on a needle, which is more expected, since iron is magnetic.

What was surprising was that copper, which does not attract a needle at all, could calm its swings. Arago investigated by counting how many swings a disturbed needle made before its amplitude decayed by a set amount, with rings of different materials placed around it. Nineteenth-century accounts of his experiments report that, for the swing to fall from 45° to 10°, the needle made about 145 oscillations inside a wooden ring, 66 inside a thin copper ring and only 33 inside a stout one.

Material around the needle	Swings for amplitude to decay from 45° to 10°
Wooden ring	about 145
Thin copper ring	about 66
Thick copper ring	about 33

More copper meant faster damping. Yet with the needle at rest, the copper had no influence on where it pointed. Whatever force the copper exerted, it acted only on a moving needle.

The announcement and the rotating disc

Arago presented his results to the Académie des Sciences in Paris on 22 November 1824. He reasoned that if a stationary copper ring can slow a moving needle, then a moving copper disc should drag a stationary needle. On 7 March 1825 he reported to the Académie the complementary experiment: a copper disc spun beneath a suspended needle pulls the needle round after it. This is the experiment now usually called Arago's rotation, or Arago's disc.

Arago called the phenomenon "magnetism of rotation". He also found that the force on the needle was not only a sideways drag in the direction of rotation. There were components directed along the radius of the disc and perpendicular to it, including a repulsion pushing the needle away from the disc. These extra components would later become an important clue.

Recognition

The Royal Society in London awarded Arago its Copley Medal for 1825, citing his discoveries of the magnetic properties shown by substances that do not contain iron. The same year's medal also went to Peter Barlow for his communications on magnetism. That the Royal Society honoured the work so quickly shows how surprising it seemed: here was a magnetic effect in copper, a material regarded as non-magnetic.

A race to explain it

Babbage and Herschel

In England, Charles Babbage, now remembered for his calculating engines, and John Herschel, the astronomer and son of William Herschel, repeated and extended Arago's experiments. Their paper, "Account of the repetition of M. Arago's experiments on the magnetism manifested by various substances during the act of rotation", was read to the Royal Society on 16 June 1825 and published in the Philosophical Transactions for that year.

They made two contributions of lasting importance.

First, they reversed the experiment. Instead of spinning the disc under a needle, they spun a magnet beneath a copper disc that was free to turn, and the disc followed the magnet. This is the form of the experiment that most closely anticipates the induction motor.

Second, they measured how the strength of the effect depended on the material and the shape of the disc. Silver and copper gave the strongest effects, followed by gold and zinc, while lead, mercury and bismuth gave much weaker ones. Most strikingly, they cut radial slits into the copper disc, running from the edge toward the centre, and found that each additional slit reduced the drag. Taking an uncut disc as 100, their reported values were:

Radial slits in the disc	Relative drag
0	100
1	88
2	77
4	48
8	24

This was a remarkable clue. Cutting a disc does not change how much copper there is or how close it is to the magnet. It only interrupts paths around the disc. Something was travelling around inside the copper, and the slits were blocking it. In hindsight, that something was electric current. At the time, Babbage and Herschel interpreted their results in terms of magnetism induced in the copper. Babbage later suggested in an 1826 paper that metals take time to acquire and lose this induced magnetism, so that a moving disc's induced magnetism lags behind the magnet, producing a drag.

Barlow, Christie and the question of priority

Other British researchers were also active. Peter Barlow had begun related experiments in December 1824, and his paper was received by the Royal Society in April 1825 and read in May. Samuel Hunter Christie, a mathematician at Woolwich, also read a paper on the subject in May 1825.

An unsigned 1826 article in the Edinburgh Journal of Science, which Arago believed to be by its editor David Brewster, suggested that the British should share much of the credit for discovering rotational magnetism. Arago answered firmly that priority belongs to whoever first publishes or presents a result, pointed to his announcement of 22 November 1824, and noted that the Babbage–Herschel work was itself framed as a repetition of his own. The discovery is generally credited to Arago today.

Poisson's theory

In France, Siméon Denis Poisson, one of the great mathematical physicists of the era, attempted a mathematical theory. Working in the tradition of Charles-Augustin de Coulomb, who described magnetism as forces acting at a distance between magnetic "fluids", Poisson supposed that the metal of the disc acquires a temporary magnetism under the influence of the needle, and that in copper this magnetism decays slowly rather than instantly. A spinning disc would then carry its induced magnetism a little way along before it faded, so the induced poles would lag behind the needle and pull it forward.

The idea is clever, and it gives a drag in the right direction. But Arago argued that it did not fit the facts, and the slit-disc results are hard to reconcile with it: cutting the disc should not much affect magnetism induced at each point in the metal.

Ampère, Sturgeon and others

Ampère showed in 1826 that a rotating copper disc also exerts a turning force on a nearby wire carrying a current, which strengthened the case that the phenomenon belonged to electromagnetism rather than ordinary magnetism. In Germany Thomas Johann Seebeck, in Switzerland Prévost and Colladon, and in Italy Leopoldo Nobili and Bacelli published further observations, some confirming the English results and some disputing Arago's. Arago replied to Nobili and Bacelli that they had not reported the distance between needle and plate or their oscillation counts, so their contradictory results could not be judged.

The English experimenter William Sturgeon, inventor of the electromagnet, found that placing a second magnet pole of opposite polarity beside the first reduced the damping effect. He later concluded that the effect must be an electrical disturbance in the metal, but Faraday's publication on induction came out before he had completed his explanation.

Faraday's explanation

The discovery of induction

On 29 August 1831, Michael Faraday at the Royal Institution in London wound two separate coils of insulated wire on an iron ring. When he connected one coil to a battery, a galvanometer connected to the other coil gave a brief kick, and when he disconnected the battery, it kicked the other way. There was no steady current in the second coil, only a pulse when the current in the first was switched on or off. A changing magnetic effect produced a current.

Over the following weeks he showed that moving a magnet into or out of a coil also produced a current, and that the current flowed only while the motion lasted. Magnetism could produce electricity after all, but only through change or motion. That was the missing piece that had defeated everyone who had tried with stationary magnets.

The copper disc between magnet poles

Faraday saw at once that his discovery might explain Arago's rotations. On 28 October 1831, using the large horseshoe magnet belonging to the Royal Society, which was then kept at the house of Samuel Hunter Christie, he mounted a copper disc about 12 inches across so that its edge passed between the magnet's poles. He connected one wire to the axle of the disc and another to a sliding contact pressing on its rim, and joined both to a galvanometer. When he turned the disc, the galvanometer needle moved, and it stayed deflected as long as the disc kept turning. Reversing the direction of rotation reversed the current.

This was the first demonstration of a continuous electric current produced by ordinary permanent magnets. It is the ancestor of every electrical generator, and the arrangement is known today as the Faraday disc or homopolar generator.

"A full explanation of Arago's magnetic phenomena"

Faraday presented his results to the Royal Society on 24 November 1831, as the First Series of his Experimental Researches in Electricity, published in the Philosophical Transactions in 1832. The paper's fourth section, "Explication of Arago's Magnetic Phenomena", set out the solution. In a letter to his friend Richard Phillips a few days later, on 29 November 1831, Faraday wrote that his new results enabled him to explain all of Arago's phenomena of the rotating magnet or copper plate, while expecting that his account would disagree with those of Arago, Babbage and Herschel.

The explanation is this. As any part of the copper moves through the magnet's field, an electric current is induced in it, running across the metal at right angles to the direction of motion. These currents are not led away through wires, as in Faraday's generator; instead they circulate within the disc, flowing out through the part of the disc nearest the magnet and returning through the surrounding copper. Electric currents feel forces in a magnetic field, and they also produce magnetic fields of their own. The forces between these induced currents and the magnet act to reduce the relative motion: they drag the magnet along with the disc, or brake the disc if the magnet is held still.

Faraday also showed that there was no need to suppose any induced magnetic polarity in the copper. The effect depends on currents, and the currents exist only during relative motion, so the effect disappears when motion stops. That is exactly the property that had made the phenomenon so puzzling. He confirmed that cuts in a plate reduced the effect, because they interrupt the paths of the circulating currents, which explains Babbage and Herschel's slit-disc results. He also suggested that because the currents take a little time to build up and decay, their effect would include a component perpendicular to the plane of rotation, which could account for the repulsion Arago had observed.

The Royal Society awarded Faraday the Copley Medal for 1832 for his discovery of magneto-electricity. Eight years after Arago, and seven after Babbage and Herschel had cut slits into a disc without quite seeing what the slits were blocking, the puzzle was solved.

A note on non-conductors

Some early experimenters, including William Snow Harris, had reported effects with wood, marble and glass. Faraday found those reports difficult to reconcile with his explanation, which predicts no drag from good insulators, since they cannot carry the induced currents. On the eddy-current account, any effect from a true insulator must be negligible, and modern demonstrations with wood, glass or plastic discs show none. (Some materials do respond weakly to magnetic fields in other ways, through paramagnetism or diamagnetism, but those effects do not depend on motion and are not Arago's rotation.)

The physics in plain language

Moving conductors and magnetic fields

Electrons in a metal are free to move. When a piece of metal moves through a magnetic field, the electrons move with it, and a magnetic field exerts a sideways force on any moving charge. This force, called the Lorentz force, pushes the electrons at right angles both to their velocity and to the magnetic field.

In a spinning disc beneath a magnet pole, the part of the disc under the pole is moving sideways through a field that points up or down. The electrons in that part are pushed along the radius of the disc, either inward or outward depending on the direction of the field and the rotation. That push is an electromotive force (EMF), the same thing a battery provides. Since the disc is a continuous sheet of metal, the electrons can flow: current runs along the radius in the region under the magnet and returns through the parts of the disc that are not under the magnet, forming two whirlpool-like loops on either side.

These loops of current are called eddy currents, from the swirling eddies in a stream. They are also known, especially in French and some other languages, as Foucault currents, after Léon Foucault, who studied their heating effect in 1855. Some historians have pointed out that the name is odd, since Arago observed their effects and Faraday explained them long before Foucault.

Why the force opposes the motion

The induced currents are in a magnetic field, and a magnetic field exerts a force on a current. The direction of that force is fixed by a general rule formulated by the Russian-German physicist Heinrich Lenz in 1834: an induced current always flows in the direction that opposes the change producing it. In Arago's disc, the "change" is the relative motion between disc and magnet, so the force on the disc opposes that motion, and the equal and opposite force on the magnet drags it in the disc's direction.

Lenz's law is not an extra assumption. It is a consequence of energy conservation. If the induced currents helped the motion instead of opposing it, a disc given a small push would speed itself up indefinitely, creating energy from nothing. Because they oppose it, someone has to keep doing work to keep the disc spinning against the drag, and that work ends up as heat in the copper. Foucault demonstrated exactly this in 1855 by turning a copper disc between the poles of an electromagnet by hand: with the magnet on, the disc became hard to turn and grew noticeably warm.

Why the needle always lags

The force exists only while there is relative motion. If the needle ever caught up with the disc and turned at exactly the same speed, the copper beneath the needle would be stationary relative to it, no currents would be induced, and the drag would vanish. Any friction or restoring force would then slow the needle, and as soon as it fell behind, the drag would return. So the needle always turns more slowly than the disc. The difference in speeds is called the slip, and the same word is used for exactly the same reason in induction motors today.

Why conductivity matters

For a given EMF, the current is larger in a better conductor, because there is less resistance. More current means more force. So the strength of the effect, at least at modest speeds, scales with the electrical conductivity of the metal. Compare the ranking that Babbage and Herschel found with modern measured conductivities at 20 °C:

Metal	Conductivity (million siemens per metre)	Relative to copper
Silver	63.0	106
Copper	59.6	100
Gold	41.1	69
Aluminium	35.5	60
Zinc	16.9	28
Lead	4.55	8
Mercury	1.02	2
Bismuth	0.775	1

Silver and copper at the top, gold and zinc next, lead, mercury and bismuth far below: this is the same order Babbage and Herschel reported in 1825, decades before anyone could explain why. Glass and dry wood have conductivities more than a billion billion times smaller still, which is why they show nothing.

Why slits weaken the effect

The induced EMF pushes current along the radius under the magnet, but the current must find a way back. In an uncut disc, it returns through the copper on either side, in two closed loops. A radial slit cuts some of these return paths, forcing the current to take longer routes or stopping it entirely. The EMF itself is unchanged, but the current, and therefore the force, drops. With many slits, the disc behaves more like a set of separate spokes and the eddies have little room to form.

The same principle explains why the iron cores of transformers and motors are built from thin sheets (laminations) insulated from each other. A solid iron core would carry large eddy currents that waste energy as heat. Laminations, oriented so that they cut across the paths the eddies would take, suppress them. The Italian physicist Carlo Matteucci showed this with a laminated cube: eddy currents were suppressed when the laminations lay in planes that blocked the current loops.

Why the drag does not grow forever

At low speeds, the drag force is roughly proportional to the relative speed, like the drag of a spoon stirring thick syrup. That is why the needle's deflection grows steadily with the disc's speed. At high speeds this stops being true. The eddy currents produce their own magnetic field, which partially cancels the magnet's field inside the metal and pushes it out. This is closely related to the skin effect, which keeps rapidly changing fields from penetrating deep into a conductor. As a result the drag force rises to a maximum and then levels off or even declines at very high relative speeds. At these speeds the eddy currents also produce a noticeable repulsion between magnet and conductor, which is the principle behind some forms of magnetic levitation and is consistent with the repulsive component Arago reported.

Some numbers

The following calculations are simplified models, meant to show orders of magnitude rather than precise engineering values.

The voltage in Faraday's disc

For a conducting disc of radius R spinning at angular speed ω in a uniform magnetic field B perpendicular to the disc, the EMF between the axle and the rim is

EMF = ½ B ω R²

To see where this comes from: a small piece of the disc at distance r from the centre moves at speed v = ωr, and the EMF per unit length along the radius is vB = Bωr. Adding this up from the centre to the rim gives ½BωR².

Take a disc of radius 0.15 m (roughly the 12-inch disc Faraday used, though his magnet's field did not cover the whole disc), spinning at 10 revolutions per second (600 revolutions per minute), so ω = 2π × 10 ≈ 62.8 radians per second, in a field of 0.5 tesla:

EMF = ½ × 0.5 × 62.8 × (0.15)² ≈ 0.35 volts.

That is less than a quarter of the voltage of an ordinary AA battery. Homopolar generators give low voltages, but because the disc has very low resistance, they can deliver very large currents. That is why large homopolar machines have been used for applications needing huge pulsed currents rather than for ordinary power generation.

An estimate of eddy-current drag

A rough estimate of the braking force on a conducting sheet moving through a patch of magnetic field is

F ≈ σ v B² × (volume of metal in the field)

where σ is the conductivity and v the relative speed. The formula assumes the induced currents can return freely through the surrounding metal, so it is an overestimate, typically by a factor of a few, but it shows how the force depends on each quantity.

For a copper disc 2 mm thick, moving at 1 metre per second through a field of 0.1 tesla covering a patch of 1 square centimetre:

Volume in the field: 1 × 10⁻⁴ m² × 2 × 10⁻³ m = 2 × 10⁻⁷ m³
F ≈ (5.96 × 10⁷)(1)(0.1)²(2 × 10⁻⁷) ≈ 0.12 newtons

That is about the weight of a 12-gram mass, a small but easily felt force from a small magnet. The power dissipated as heat is F × v ≈ 0.12 W. Several features are worth noticing:

The force is proportional to v, so doubling the speed doubles the drag (at low speeds). This is why magnetic damping smoothly slows a swinging needle or a sensitive balance without any contact.
The force goes as B², so doubling the strength of the magnet quadruples the drag. Stronger magnets make dramatically better brakes.
An aluminium disc, with 60% of copper's conductivity, would give about 0.07 N in the same arrangement.
For Arago's original needle, the field reaching the disc was far weaker than 0.1 tesla, and the force correspondingly much smaller. But a compass needle is light and delicately suspended, so a tiny force was enough to deflect it.

How deep the currents go

When a magnetic field oscillates at frequency f in a conductor, the induced currents are concentrated within a skin depth

δ = √(2 / (μ₀ σ ω)), with ω = 2πf.

For copper at 50 Hz: δ = √(2 / (4π × 10⁻⁷ × 5.96 × 10⁷ × 314)) ≈ 9.2 mm.

Each part of a rotating disc sees the field of a passing magnet pole as a pulse, so a similar idea applies. For thin discs spinning slowly, the field penetrates the whole thickness and the simple drag formula works reasonably well. For thick discs or high speeds, the currents crowd into a thin layer near the magnet, and the drag stops growing in proportion to speed.

From curiosity to technology

Later experiments

Through the nineteenth century, researchers kept finding new aspects of the effect. Faraday hung a copper cube on a twisted thread between the poles of an electromagnet: set spinning, the cube stopped almost at once when the magnet was switched on and started spinning again when it was switched off. Matteucci studied eddy currents in detail with laminated and divided conductors. The French physicist Le Roux showed that a disc rotating between ring-shaped (annular) poles, arranged so that every part of the disc sees the same field all the time, experiences no drag and is not heated, because no closed current loops can form. Jochmann and later Heinrich Hertz worked out the mathematics of induction in rotating spheres and discs.

In 1879 Frederick Guthrie and Charles Vernon Boys hung a copper disc from a torsion thread above a rotating magnet and found that the twist in the thread was proportional to the magnet's speed, so the device could serve as a speed meter. Because the torque was also proportional to the conductivity of the material, they used the method to measure the conductivity of liquids.

The rotating magnetic field and the induction motor

Arago's rotation shows that a rotating magnet can drag a conductor around without touching it. In 1879 the English engineer Walter Baily presented to the Physical Society of London a way of producing Arago's rotation with no moving magnet at all. He used a set of fixed electromagnets switched on and off in sequence, so that the magnetic field itself rotated, and a copper disc above them turned. In 1880 de Fonvielle and Lontin kept a copper disc spinning using alternating current in a surrounding coil, which they called an "electromagnetic gyroscope".

In the 1880s, the Italian physicist Galileo Ferraris and the Serbian-American inventor Nikola Tesla independently developed motors that used alternating currents to create a smoothly rotating magnetic field. Place a conductor in that rotating field and it is dragged around, always with some slip, exactly as Arago's disc drags a needle. This is the induction motor, and it remains the most widely used electric motor in the world, found in fans, pumps, compressors, washing machines and many electric vehicles. The British physicist Silvanus P. Thompson, in his 1895 book Polyphase Electric Currents and Alternate-Current Motors, explicitly traced the induction motor back to Arago's rotations.

The "squirrel cage" rotor of a typical induction motor, made of conducting bars joined by rings at each end, can be thought of as Arago's disc reshaped. The bars give the induced currents defined paths, and the rotor is laminated iron so that the magnetic field is strong but unwanted eddies in the iron are suppressed.

Eddy-current brakes

The braking side of Arago's effect is used wherever smooth, contact-free, wear-free braking is valuable. Many roller coasters and drop towers use rows of permanent magnets on the track and copper or aluminium fins on the cars: the faster the car moves, the stronger the braking, and the brakes work even if the power fails, because permanent magnets need no electricity. Some high-speed trains, heavy trucks and buses use eddy-current brakes as supplementary retarders. Fitness machines such as exercise bikes often adjust resistance by moving a magnet closer to or farther from a spinning metal flywheel.

Because eddy-current braking force falls toward zero as the speed falls, these brakes are excellent at slowing things down but cannot hold a vehicle stationary. A mechanical brake is still needed for the final stop.

Electricity meters and speedometers

The electromechanical electricity meter, with its slowly turning aluminium disc visible behind a glass window, used Arago's physics twice. Coils carrying the household current and voltage produced a shifting magnetic field that dragged the disc around at a speed proportional to the power being used. A permanent magnet near the disc acted as an eddy-current brake, making the disc's speed proportional to the driving torque rather than allowing it to accelerate freely. Counting the disc's revolutions gave the energy consumed.

Traditional mechanical speedometers in cars used a similar principle. A magnet spun by a cable from the gearbox rotated inside a metal cup attached to the pointer. The eddy-current drag on the cup was proportional to the magnet's speed and was balanced by a hairspring, so the pointer's deflection showed the vehicle's speed. This is essentially the Guthrie–Boys speed meter in a dashboard.

Damping, sensing and heating

Eddy-current damping is used to stop the needles of analogue meters and the pans of precision balances from oscillating, the same effect Arago noticed in a copper compass box. Eddy-current testing sends changing magnetic fields into metal parts, such as aircraft skins and pipes, and detects cracks and corrosion by the way they disturb the induced currents. Metal detectors and coin-sorting machines identify metals by their eddy-current response. Induction cooktops and industrial induction furnaces use high-frequency fields to drive eddy currents in the metal itself, so the pan heats without the cooktop surface getting hot except by contact.

A classroom favourite

A popular demonstration of the same physics is dropping a strong neodymium magnet down a vertical copper or aluminium tube. Instead of falling freely, the magnet drifts down slowly, because as it falls it induces eddy currents in the tube walls that oppose its motion. A non-magnetic object of the same size drops straight through. A slit cut along the length of the tube lets the magnet fall noticeably faster, the same lesson Babbage and Herschel learned from their slit discs in 1825.

Common misconceptions

"Copper becomes magnetic when it spins"

This was roughly the view of Poisson and of Babbage and Herschel, and it is not correct. The copper does not acquire permanent or induced magnetism in the ordinary sense. It carries electric currents, and those currents produce a magnetic field. When the motion stops, the currents die away almost instantly, and so does the field. Copper is very weakly diamagnetic, but that tiny effect is unrelated to Arago's rotation.

"The air drags the needle around"

A spinning disc does stir the air above it, and a careless experiment could confuse air currents with a magnetic effect. Arago and his successors guarded against this with screens of glass or paper between disc and needle. Better still, the effect depends strongly on the material of the disc, and a wooden or glass disc spun at the same speed has no comparable effect. Air drag cannot explain that.

"The needle could catch up with the disc"

It cannot, as long as anything resists its motion. The drag depends on relative motion and vanishes at equal speeds, so the needle must always lag. A motor that runs at exactly the speed of its rotating field is a different kind of machine, a synchronous motor, and it needs magnetised or magnetically shaped rotor parts rather than eddy currents.

"Eddy-current brakes make energy disappear"

Energy is conserved. The kinetic energy removed from a braked train or roller-coaster car becomes heat in the metal of the brake, which is why large eddy-current brakes need cooling. Foucault's hot disc showed this in 1855.

"Arago explained the effect"

Arago discovered it and studied it carefully, but neither he nor his contemporaries had the concept of electromagnetic induction needed to explain it. The explanation came from Faraday in 1831. Arago's careful measurements, and Babbage and Herschel's slit-disc results, were important evidence that the explanation had to account for.

"Faraday discovered induction by studying Arago's disc"

The order is the other way round. Faraday discovered induction with his iron ring in August 1831, and then recognised that it explained Arago's phenomenon, which he had certainly known about for years. His famous disc generator was built in October 1831 partly to test that idea.

Frequently asked questions

Does Arago's rotation work with any magnet?

Yes. A compass needle, a bar magnet, an electromagnet or a rotating magnetic field from alternating currents all work. Stronger magnets give much stronger effects, since the force grows with the square of the field.

Can it work through a non-metal barrier?

Yes. The magnetic field passes through glass, paper, plastic and air essentially unaffected. Arago and others put glass sheets between disc and needle. A metal sheet in between would carry its own eddy currents and change the result.

Does the disc need to be copper?

No. Any good conductor works. Aluminium is common in modern demonstrations and devices because it is light and cheap and conducts well. Iron also works but adds the complication of ordinary magnetic attraction.

Why does the effect weaken so quickly with distance?

The magnet's field falls off rapidly with distance, and the force depends on the square of the field at the conductor. A small increase in the gap therefore produces a large decrease in drag.

Is Arago's rotation the same as the Faraday disc?

They are closely related but not identical. In Faraday's disc generator, the currents induced in a rotating disc are led away through sliding contacts to an external circuit. In Arago's rotation, the currents circulate within the disc as eddies, and their effect is felt as a force on the magnet. The same induction is at work in both.

Who first explained it, Faraday or Lenz?

Faraday explained the effect in 1831 in terms of induced currents. Lenz's 1834 rule about the direction of induced currents gave a simple general statement of why the force always opposes the relative motion. Maxwell later gave the full mathematical theory of electromagnetism in which both are special cases.

Summary

Arago's rotations are the forces that appear between a magnet and a nearby non-magnetic conductor such as copper when one moves relative to the other. A spinning copper disc drags a suspended needle round after it; a spinning magnet drags a pivoted disc; a fixed magnet brakes a spinning disc. François Arago discovered the effect, starting from the observation that copper calms a swinging compass needle, and announced it to the Académie des Sciences on 22 November 1824. He received the Royal Society's Copley Medal for 1825.

For seven years the effect resisted explanation. Babbage and Herschel showed that it was mutual, that its strength followed the ranking of metals by what we now know is electrical conductivity, and that radial slits weakened it. Poisson tried to explain it with temporary magnetism in the metal. The answer came in 1831 from Michael Faraday's discovery of electromagnetic induction. Relative motion induces electric currents in the conductor; those eddy currents, by Lenz's rule, produce forces that oppose the relative motion; and their dependence on closed current paths explains the slit results.

What began as a puzzle about a compass in a copper box became the physics behind the induction motor, eddy-current brakes, electricity meters, speedometers, metal detectors and induction cooktops. It is a fine example of a small, careful observation of something that should not have happened, pursued until it opened up a whole new branch of technology.