One of the challenges of doing physics outreach is that there are so many cool phenomena which simply can’t be demonstrated in an eye-catching way, because they are too small, too subtle, or too complicated.  So whenever I find a demo that really has a “WOW!” factor to it, I treasure it.

A perfect example of this is a demonstration of what are known as eddy currents, which can be done with a simple copper pipe and a neodymium magnet that fits easily inside it. I took the following video a few days back:

Isn’t this the coolest thing? The magnet seems to float down the tube, only occasionally touching the walls of the pipe, seeming to defy gravity.

The phenomenon is cool, and the way it was discovered is also fascinating: it was first observed by the Most Interesting Physicist in the World™, François Arago, using an ordinary compass!  It is one of those remarkable discoveries that is, however, largely unknown to most physicists, much less the general public — I only came across a chance mention of it recently that led me to explore further. In this post I want to look at both the physics and the history — and the arguments that followed.

Let’s start with the explanation of eddy currents first; this will, unsurprisingly, also involve a bit of a discussion of the history of electricity and magnetism.  Before the 19th century, electricity and magnetism were largely considered independent phenomena.  Magnetism was connected with compasses and bar magnets and north and south poles, and electricity was associated with lightning and static shocks and making frog legs jump.  But, in 1820, the Danish physicist Hans Christian Oersted discovered that an electric current could make a compass move, thus demonstrating that electrical currents are a source of magnetism!  The story behind this discovery is a fascinating one that I’ve blogged about at length in the past.

In modern terms, we now say that moving electric charges, such as a current which we label I, produces a magnetic field that circulates around it; we label the magnetic field as B.  The fields around a current in a long straight wire may therefore be visualized as shown below.

It did not take very long for researchers to wonder if the opposite might be true: could magnetism somehow generate electricity, just as electricity generates magnetism?  This question was answered in the affirmative by British chemist and physicist Michael Faraday in 1832, after a thorough and ingenious series of experiments.

What Faraday found is that a changing magnetic field results in a circulating electric field; this is roughly illustrated below.

If we imagine a magnetic field pointing upwards, as shown in the figure, as we increase or decrease the field, a circulating electric field E is produced.  As illustrated in the figure, the field circulates around the magnetic field, with the direction of circulation — clockwise or counterclockwise — depending on whether the field is increasing or decreasing.

But what determines the direction the electric field circulates? Let us imagine that our electric field is actually circulating inside a wire, so that it produces an electrical current, as shown in the first picture below.  These magnetism-induced currents are what are referred to as eddy currents.

But that electric field creates a new magnetic field, shown in blue in the second picture above, that opposes the change in the  magnetic field!  This outcome is built into Faraday’s law: any electric field created by a changing magnetic field rotates in such a way that it would create a magnetic field that resists the change.  This observation was first made by the physicist Heinrich Friedrich Emil Lenz in 1834, and is consequently known as Lenz’s law.  It is used by physicists to this day as an easy way to figure out which way the induced electric field points when doing calculations related to Faraday’s law.

This brings us back to the really cool neodymium magnet/copper tube demonstration!  Because the magnet is falling down the tube, the magnetic field is constantly changing both in the metal of the tube and its interior. and therefore creates an electric field that circulates in the tube.  According to Lenz’s law, the current created by this field is such that it will resist the changing magnetic field.  This means that the magnetic field created in the tube will resist the motion of the magnet down the tube!  The magnet therefore floats slowly down the tube, opposed by the currents induced in it.

This same effect will arise any time a magnet is moving near a conductive material that can support electric currents.  This includes swinging magnetic compass needles sitting above a bowl of water or a metal plate, and this is exactly what François Arago very astutely observed in 1822.

Before we describe his discovery, a little background on François Arago is probably in order.  Born in 1786 in a small town to a well-off family, Arago is one of those scientific geniuses who uncharacteristically did not have initial ambitions to do science.  He was most interested in joining the military and entering the artillery service, and his intense early work in mathematics was done to prepare him for such a career.  He was too smart for his own good, however, and upon entrance to the prestigious Paris École Polytechnique in 1803, he concluded that they had nothing to teach him that he did not already know!  He took a job as a secretary to the Paris Observatory in 1804, and in 1806 he undertook a trip to Spain to complete measurements of the meridian arc with Jean-Baptiste Biot.

It is during that journey that Arago earned the title of Most Interesting Physicist in the World™ from me, as he spent the next few years on the run for his life after war broke out between France and Spain; I have blogged about this amazing adventure in detail.  When he returned home in 1809, after having been presumed dead by his family, he became something of a national hero, even getting to meet Napoleon in person. Honors were bestowed upon him, though he was only 23 years old: he was elected a member of the French Academy of Sciences, he was appointed to the chair of analytical geometry at the École Polytechnique, and the emperor himself named him as an astronomer of the Paris Observatory.

With this success and freedom, Arago embarked upon a variety of scientific studies. In 1810, he made an attempt to measure variations in the speed of light, a failed experiment that could be said to be one of the earliest confirmations of Einstein’s special relativity, though of course only in hindsight.  In 1818, when Arago’s friend Augustin-Jean Fresnel argued that light in fact acts as a wave, Arago performed a crucial experiment to confirm Fresnel’s theory.

For his magnetic experiments, we rely on two sources: his original 1824 French publication on his findings¹, and an 1855 revised essay², including additional commentary and reflections from Arago.

In the later document, Arago describes his initial discovery as follows.

While engaged with my friend Alexander von Humboldt, in 1822, on the slope of Greenwich Hill, in a determination of the intensity of the magnetic force, I had recognized that the horizontal needle, after being put in motion, came to rest much sooner when placed in its box than when suspended at a distance from all foreign bodies. It had appeared to me that this remark ought to conduct to important inferences on the generality of phenomena which had till then remained circumscribed and as it were isolated in the midst of science.

This was a magnificently subtle observation to make — Arago managed to see past the ordinary function of the compass and noticed how quickly it took for the compass to settle to magnetic north.

On the 22nd of November 1824, after doing a series of follow-up experiments, he presented his results to the French Academy of Sciences.  They were reported simply as follows.

M. Arago communicated verbally the results of some experiments which he had made on the influence which metals, and many other substances, exercise on the magnetic needle, the effect of which is to produce a rapid diminution of the arc of vibration of a needle without sensibly affecting its time of vibration.

But what sort of experiments did Arago perform?  Again in his own words,

I suspend a magnetic needle horizontally over water, and I draw the needle 53° out of its natural position; being then left to itself, the needle vibrates to and fro on either side of the magnetic meridian, in arcs of diminishing magnitude. I try to seize the moment when the semi-arc has decreased to 43°, and I count how many vibrations have taken place from the commencement.

When the distance of the under surface of the needle from the surface of the water is .0256 of an English inch, a reduction of 10° of arc takes place in the course of 30 vibrations. When the distance is 2.055 inches, 60 vibrations are required to effect a similar reduction.

I attempt to sketch this below.  A freely-hanging compass needle pulled from its equilibrium position at magnetic North will oscillate back and forth over magnetic North for some time before friction and air resistance causes it to stop moving.  When the compass is placed close over a body of water, eddy currents are excited in the water that reduce the oscillations even faster!

Arago’s discovery was surprising, novel, and, at the time, inexplicable.  It was only natural then, that two things would happen:

1. Some scientists would say that the results were incorrect,
2. Other scientists would claim that they had made the discovery first.

In Arago, who in his youth had struggled for his very life in hostile foreign lands, they found a man who was not afraid to back down or even be particularly polite.  In his 1826 paper, he answered both groups of critics in his own devastating style.

Regarding the claims that Arago was mistaken, he had this to say:

On the 22nd of November, 1824, I had the honor of providing the Academy with some experiments of which I had been engaged almost two years ago, concerning a peculiar and very intense action which all the bodies of nature exercise upon a magnetic needle in motion. Several English, Swiss, and Italian physicists have, since that time, studied the same phenomena and generally confirmed my results: I have just, however, found in the number of the Bibilothèque universelle of January 1826 a Memoir from Mister Leopold Nobili and Mister Bacelli, of Modena, which contains various experiments in direct opposition with some of mine; the recognized merit of these savants imposes upon me the duty of not leaving their assertions unanswered.

“MM. Nobili and Bacelli have oscillated, they say, magnetic needles above non-metallic substances … without finding any appreciable difference between the oscillations made by the needles above the disks and out of their influence…”

If the physicists of Modena had given the distance which separated their needle from the non-metallic plate, and the number of oscillations which they counted, I could perhaps assign the cause of the error in which they fell; all I can do today is to oppose to their negation, exact measures, and to indicate the circumstances in which they have been obtained…

The last paragraph seems to me to be some pretty intense shade to the Italian physicist, as Arago basically flat-out says that the pair had not provided enough information to even assess whether they had done their experiment correctly!

The question of priority was a bit more complicated to unravel, and in fact depends on additional experiments that Arago performed after his initial compass experiments. Noting that a stationary conducting body ( like water or a metal plate) can influence a moving compass, he reasoned that a moving conducting body could influence a stationary compass.  And he was in fact correct: he found that a rotating metal disk under a conductor would deflect a compass needle.  The result may be thought of as a curious precursor to the classic physics demonstration known as a Faraday disk.

Arago presented³ these new results to the Paris Academy on Monday, March 7th, 1825.  He was no doubt irritated, then, to read in an 1826 volume of the Edinburgh Journal of Science⁴,

There are few branches of modern science that are likely to excite a greater interest than that which relates to the influence of rotation on the phenomena of magnetism. We are proud to think that this remarkable discovery was first made in our own country, and that, with the exception of a few important experiments made in France, it has been prosecuted solely by the Fellows of the Royal Society of London.

This statement seems to diminish Arago’s role in the discovery of such “rotatory magnetism,” but an even worse offense would follow.   In discussing the experiments of Peter Barlow on the subject, the article states:

They were begun in December 1824, and completed last January, but the publication of them was delayed till June, in order that Mr. Christie’s paper might appear at the same time, the similarity of the inquiries rendering this measure desirable.  During this interval, M. Arago discovered the magnetic effect of copper and other metals while in rotation…

Emphasis mine.  Basically, the “correspondent” for the Edinburgh Journal — who Arago took to be its editor, David Brewster — says that Barlow and Christie deserve credit for the discovery, because they “completed” the work earlier, even though they did not publish it until later.

There were, in fact, four British researchers working on rotatory magnetism at the same time as Arago: the aforementioned Barlow and Christie, and also Babbage and Herschel working together. This seems in part to be an example of a common phenomenon in physics: as science progresses, there is a tendency for certain subjects to become “ripe” for study at a particular time, and often multiple people will independently begin working on it.  Personally, I think claims of “FIRST” in such cases, when days or months separate the individual’s discoveries, are rather meaningless, and all should be given some credit as co-discoverers.

In Brewster’s case, assuming he wrote the article, his enthusiasm to claim this discovery as a purely British one apparently combined with a bit of pure dickishness to make him practically discount Arago’s work.

But as we have noted, he picked a fight with the wrong fight in the person of the fearless Arago, who in his 1826 paper savagely and roundly mocked Brewster and all claims of priority over his discovery.  His (translated) writings are worth reproducing in their full sarcastic glory, in which he takes the stance that only the publication date or the date at which the results are first presented publicly matter:

On the 22nd of November, 1824, I communicated to the Academy of Sciences the experiments relating to the influence of a metallic body, or of any other nature at rest, on magnetic needles which oscillate at a little distance from its surface. This experiment was recorded on November 23 and 24, in most Gazettes of the capital. Mr. Brewster has himself reported it, according to a letter from Paris, in the number of his Journal which appeared from January 1, 1825.

The following passage is taken from the minutes of the Academy of Monday, March 7, it was published almost verbatim in several newspapers of 9 and 10.

“Mr. Arago puts under the eyes of the Academy an apparatus (it was a pendulum all copper), which shows in a new form the action that the bodies magnetized and those who are not exercised on each other.”

“In his early experiments, Mr. Arago had proved that a plate of copper or other solid or liquid substance, placed beneath a magnetized needle, exerts on this needle an action which has the immediate effect of altering the amplitude of the oscillations. The phenomenon of which he has maintained the Academy today is the opposite of the previous one; since a moving needle is stopped by a plate at rest M. Arago thought that it followed that a needle at rest would be driven by a moving plate: If a plate is rotated, , etc., etc. ”

The experience of rotation is therefore only that of November 22 in a new form; it is deduced from this principle of mechanics, generally admitted, that the reaction is equal to the action. The rotation serves to study the phenomena whenever we need very great velocities; the oscillations are preferably used when it is necessary to operate on liquids or on dusts. The consequences are the same in both cases. Let us now move on to the dates of the English Memoirs.

Arago first argues that the case of rotatory magnetism and the case of his oscillating compass needle are one and the same phenomenon, and that his original announcement of November 24, 1824 should count as the first publication of these results.  With that thesis laid out, Arago looks at the dates of the British publications:

Mr. Barlow has deposited with the Royal Society his Memoir on the modification which the magnetism of a rotating iron sphere causes on April 14, 1825; this memoir was only read on the 5th of May.

The reading of Mr. Christie’s Brief is May 12, 1825.

The Memory of MM. Babbage and Herschel, of which Mr. Brewster probably did not hear in his Note, since the authors had the kindness to call it: Repetition of the Experiments of Mr. Arago, is of June 16, 1825.

The Scots scholar therefore has only one means of establishing the priority which he so voluntarily gratifies his compatriots: it is to prove that November 22, 1824 and the following March 7, are subsequent to May 5 and 12, 1825.

That last sentence made me laugh out loud!  Arago is saying that the only way that Brewster can claim that the British were first is if time itself runs backwards.  Furthermore, he notes that Babbage and Herschel’s results were based directly on Arago’s.

Arago was not done, however, and he went on to point out what he considered to be Brewster’s explicit dishonesty:

Mr. Barlow announces that he has begun his experiments on the effects of the rotation of an iron sphere, in the month of December comes after November, so I have no personal interest in challenging that date; I will only maintain, as a general proposition, that publication by any means whatsoever is the only title to be admitted in the history of science, although I deprive myself of the advantage of proving that The results mentioned in this note had been communicated to a large number of French and English scholars, nearly two years before I spoke of them at the Academy. Moreover, this month of December, indicated by Mr. Barlow himself in all that he has written, as the time when his experiments began, is no longer suitable for Mr. Brewster; here is, indeed, what one reads in the number 8 of his Journal, published in April 1826.

“Towards (about) the month of November, 1824, the experiment of Mr. Barlow in which he produced a certain deviation of the magnetic needle, by the influence of an iron sphere turning on itself, became the object of the conversation at the Royal Society, etc. ”

Mr. Barlow said that he had only begun to deal with the phenomena produced by the rotation of iron in December, and that is really unfortunate, since November is the date of my first publication! How to escape this difficulty? The problem seemed embarrassing; we see, however, that Mr. Brewster has solved it in a very ingenious manner: it was enough for him to forget that the last month of the year had a name; December is definitely a word he will never write again; What good is it? Are the dates relating to this month not more properly defined by this formula: Towards (about) the month of November?

This glorious savaging of Brewster is the sort of thing one rarely gets to see in scientific publications.  Arago ends his publication with some faux conciliatory remarks:

I am very sorry to see a scholar of Mr. Brewster’s merit descend to such miserable expedients. Carried away by a blind passion which he perhaps decorates with the name of national spirit, he did not even notice that, in this circumstance, the voluntary errors to which he subscribes and which he seeks to propagate, would not lead him to his goal. If anything, indeed, can justify the insignificant favor of which my experiments have been the object of the Royal Society of London, it is the proof which furnish of the immense magnification which the magnetic properties of the bodies experience, either when they move under a needle at rest, or when a needle oscillates a little distance from their surface; this consequence in no way arises from the work of Mr. Barlow. In order to live in peace with Mr. Brewster, I therefore willingly consent to see him now print, against the evidence of the facts, that the experiments of the professor at Woolwich were begun in the month of November, and even, as long as he desires it, about the month of October.

Arago’s efforts seem to have been successful in the long run: the discovery of eddy currents and rotatory magnetism is generally credited to Arago’s original work.

It is worth noting that Arago later made amends with David Brewster, and became friends with him.  In his revised 1855 essay, Arago notes key changes to passages in the original paper.

Meanwhile I have to repel certain objections which at the time I believed to proceed from Dr. Brewster. What I then wrote still remains; but I no longer address the language then used to that illustrious physicist, in whom I have since recognised a true love of science, and who has become a foreign associate of the Academy, and my friend.

So we have a bit of a happy ending, at least as far as Brewster and Arago are concerned.

I was tempted to immediately test out Arago’s compass experiments myself, using a store-bought compass, but realized that there is a big difficulty: the needles of most store-bought compasses don’t oscillate!  The endless oscillation which Arago used to discover a new physical phenomenon are an annoyance when trying to use a compass to find one’s way, and commercial compasses usually have a built in damping mechanism.   Some compasses are filled with liquid to reduce the motion of the needle; others, I suspect, actually use eddy currents for the same effect!

One of these days I will build myself a simple hanging compass and try to repeat Arago’s experiments myself, so stay tuned!

 

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¹ F. Arago, “Note concernant les Phénomènes magnétiques auxquels le mouvement donne naissance,” Annal. de Chimie 32 (1826), 213-223.

² F. Arago, Meteorological Essays (Longman, Brown, Green and Longmans, 1855).

³ F. Arago, Annal. de Chimie  28 (1825), 325-326.

⁴ Correspondent, “A popular summary of the experiments of Messrs Barlow, Christie, Babbage, and Herschel, on the magnetism of iron and other metals, as exhibited by rotation,” 4 (1826), 13-18.