by Brian Clegg
Maxwell’s electromagnetic spheres
Maxwell’s first attempt with his mechanical model was to imagine that the magnetic field was made up of a collection of spheres,‡‡ tightly packed to fill space. These spheres or ‘cells’ would be spinning around. Generally speaking, when a physical object spins, the centrifugal forces§§ acting on it make it spread out in the middle and contract at the poles. This happens, for example, to the Earth, which it had been known since Newton’s time has a bulge around the equator and so is an oblate spheroid rather than a perfect sphere.
But, unlike the Earth, Maxwell’s spheres were surrounded by other spheres. So, if the equator of a sphere expanded as it was spinning, it would push on the surrounding spheres. In this model, the axes of the spins were aligned to the lines of force that Faraday had demonstrated in the magnetic field. The result would be very close to what was observed. At right angles to the lines of force – the direction of the equators – the forcing outwards of the spheres would produce a repulsive effect, while along the lines of force – the direction of the poles – the spheres would be pushed closer together and the effect would be an attraction.
Conveniently, the faster the spheres rotated, the bigger this effect would be – so the spin rate in the model corresponded to the strength of the magnetic field. In this kind of mechanical model, it’s perfectly possible for the components to be allowed to be frictionless, but Maxwell thought it better to allow for a degree of interaction between the spheres. If two spheres alongside each other are turning in the same direction, then at the point of contact, the surfaces will be moving in opposite directions.
If you imagine two spheres, moving clockwise, with their axes pointing out of the page, the left sphere’s surface moves down at the point of contact while the right sphere’s surface moves upwards (Figure 3).
To avoid direct interaction between the spheres, Maxwell imagined a large number of much smaller spheres acting like ball bearings between the main spheres. But unlike the ball bearings in a traditional device, which are usually constrained by a bearing, these would be free to flow as they like. And if these little spheres were considered as particles of electricity (what we’d now call electrons), when an electrical circuit was made, the little spheres would flow in the channels between the bigger ones. (Let’s call the bigger spheres cells, as Maxwell did, to avoid getting our assorted spheres confused.)
FIG. 3. Two spheres rotating in contact.
What’s particularly neat about this model is that we now have an interaction between electricity (little spheres) and magnetism (cells). If an electrical current flows, the result is that the cells start to rotate and a magnetic field is produced.
Maxwell was also able to extend the model to allow for different materials – the better the conductor, the more easily the spheres were able to flow. In an insulator, the magnetic cells clung onto the little electrical spheres sufficiently that it was very hard to get any electrical current. So now his model dealt with the difference between insulators and conductors as well as electromagnets. But this was not all there was to electromagnetism. He would also have to cope with induction.
As we have seen, this was something that Faraday had investigated. He had shown that a changing magnetic field would produce a flow of electricity – this was how electrical generators worked. Induction also occurs when a current is started in a wire that is near another wire. When the electricity is switched on it produces a magnetic field. As far as the other wire is concerned, to begin with there is no magnetic field, then one surges into place and becomes steady. As the field is established there is a changing magnetic field, so a blip of current flows briefly in the second wire. The same thing happens if the first wire’s current is switched off.¶¶
Vortices and idle wheels
By now, as Maxwell refined the model, his cells had become hexagons, which made the model clearer visually. His original diagram had rather more hexagons than are necessary to make the point, but we can envisage what he had in mind with just three rows of hexagons. I am indebted to Basil Mahon for the following neat representation of Maxwell’s reasoning. The row of tiny spheres|||| between the top cells and the middle row is connected to a loop of wire – this is where the induction will take place. And the row of spheres between the middle row and the bottom row of cells is connected to a wire with a battery and a switch. We are ready to induce some current.
The experiment starts in the state of diagram I in Figure 4. The switch is yet to be thrown so there is no electrical current flowing.
After the switch is thrown, in diagram II, the spheres start to flow left to right between the middle and bottom sets of cells. The middle cells begin to rotate in the opposite direction to the bottom row. Maxwell had identified the direction of the magnetic field as the direction of rotation in his model, so the magnetic field above and below the electrical current flowing is in opposite directions – it is circling around the wire.
FIG. 4. Maxwell’s mechanical model of electromagnetism.
Meanwhile, the spheres between the top and middle cells are being pushed by the rotating cells in the middle row. These little spheres start to rotate clockwise and to flow right to left, causing a brief current in the upper wire. However, there is no battery in this circuit to keep the current flowing. The resistance in the wire slows the spheres down until they stop moving, but they are still rotating clockwise. This rotation causes the upper row of cells to rotate in the same direction as the middle row, as in diagram III.
When the switch is opened (diagram IV), the bottom flow of spheres rapidly stops, slowing the bottom and middle rows of cells. But the top row is still rotating – the rotating cells act as tiny flywheels, enabling the ether (see below) to briefly store energy which then generates another brief flow of current in the top wire before the whole system settles down to stillness.
By this stage Maxwell’s remarkable and very Victorian feeling model*** had explained three of the main aspects of electromagnetism, though he had not yet managed to incorporate the attraction and repulsion between electrical charges. If you feel that this construction of arbitrary mechanical components seems a little unlikely – too far abstracted from reality to be useful – you are not alone. The French physicist Henri Poincaré remarked that there was a ‘feeling of discomfort and even of mistrust’ among his fellow countrymen when faced with Maxwell’s mechanism. This was taking a model, a mechanical analogy of reality, and stretching it to what seemed to him a ludicrous extreme. And yet it was working.
The power of analogy
For, Maxwell, this novel use of analogy – building models – was the way forward to better understand the physical principles of the natural world. While still a student at Cambridge, he had written:
Whenever [men] see a relation between two things they know well, and think they see there must be a similar relation between things less known, they reason from one to the other. This supposes that, although pairs of things may differ widely from each other, the relation in the one pair may be the same as that in the other. Now, as in a scientific point of view the relation is the most important thing to know, a knowledge of the one thing leads us a long way towards knowledge of the other.
… and this philosophy, initially based on mechanical and later on purely mathematical models, would be the key to his remarkable success.
It was relatively easy to see how Maxwell’s earlier model of fluid flows through a porous medium had come about from the influence of Thomson’s work on heat, but this far more sophisticated model seems to have come out of nowhere. However, Maxwell was very fond of having actual mechanical models built – think, for example, of his colour top, or the mechanical model he had made to illustrate waves in the rings of Saturn.
At the same time, he was now in London, where Charles Babbage had dreamed up his remarkable mechanical computers, the difference engine and the analytical engine. Though neither was built, Babbage had completed a working model of part of the difference eng
ine and had worked, with the help of Ada, Countess of Lovelace, on the principles of the far more sophisticated analytical engine. Babbage was still alive when Maxwell spent his time in London. It is surely likely that it was the experience of the many brass miracles of Victorian engineering that led Maxwell to his remarkable hexagons and ball structure.
What is certainly without doubt is that Maxwell’s electromagnetic model proved surprisingly flexible, given its nature. For example, different materials vary widely in their magnetic properties. Even between metals, the differences are stark, and when you bring in other materials, such as wood, it’s clear that there is a major difference in the way magnetism operates (or doesn’t) between different substances.
What Maxwell had constructed was a mechanical model of the ether, the fluid that was thought to fill all space, allowing light waves to pass through a vacuum and acting as the transmission mechanism for the electrical and magnetic fields. What he suggested was that when that ether was overlaid on different materials the result would be a change in the nature of the hexagonal cells in the model. The better the magnetic properties of the material, the more dense was the cell in the model. With increasing density, the cells would produce a greater centrifugal force, producing more magnetic flux – the measure of the strength of the magnetic field.
In building this model, we need to reiterate, Maxwell did not suggest that space was full of rotating hexagonal cells and tiny ball bearings – not even invisible cells and bearings – but rather he was suggesting that the way the ether behaved produced a result that had the same effect as his imagined mechanical structures. There was, however, a big difference between this new model and his original fluid idea. Although Maxwell did not see the exact detail of the model with its ball bearings and hexagonal cells as what was actually happening in the ether, he did think that he had now come much closer to reality. There seems little doubt that his thoughts on what was really happening were influenced by William Thomson, who had firmly stated that there were actual vortices in the magnetic field, reflected in the way that the magnetic field influenced light.
Maxwell never lost his belief in the existence of the ether,††† a substance that would be thrown into doubt by an experiment carried out by the American scientists Albert Michelson and Edward Morley in 1887 and eventually dismissed altogether by Einstein’s work at the start of the twentieth century. And Maxwell did think that the magnetic field involved actual rotating vortices in that invisible, undetectable medium. The ball bearings part of the model proved more of an embarrassment.
Maxwell commented that ‘The conception of a particle having its motion connected with that of a vortex by perfect rolling contact may appear somewhat awkward. I do not bring it forward as a mode of connexion existing in nature …’ On the other hand, he points out that it works well and as long as it is taken as provisional and temporary, it should help rather than hinder a search for the true interpretation of the phenomena.
So, Maxwell was making it clear that the ether is not a matter of having space full of hexagons and ball bearings, any more than the crystal spheres of the ancient view of the universe. Even so, the ether had to be a remarkable substance indeed. It was invisible, impossible to detect, yet provided the medium for light to wave through, and was elastic, as it would have to be for waves to pass through it, but was somehow also so rigid that light could continue to travel for vast distances, seemingly without losing any energy the way that a conventional mechanical wave would. The ether was such a firmly established part of scientists’ mental model of reality that it was extremely hard to shake off.‡‡‡ For Maxwell, the specific details of his model provided an effective mechanical analogy for a more complex fluid reality.
He therefore tried to measure the effects of the vortices in the ether directly by having a device built that involved a small electromagnet free to rotate in all three dimensions; this, he hoped, would detect the impact of nearby vortices. Nothing was discovered, which merely underlined for him that the vortices appeared to be very small. Similarly, he believed that the electric field was directly linked to elastic deformation of the ether – again, he was not saying that his specific model was an accurate portrayal of reality, but that the key features, such as vortices and the elastic response, were a reflection of reality and so should have the kind of impact we would expect the components of the model to produce.
This belief of Maxwell’s in what we now know not to exist should not be used to belittle his achievements – it was a perfectly reasonable possibility at the time. But it also illustrates that he was only part-way towards the acceptance of a model as something totally isolated from the reality it reflected, which would enable the eventual development of purely mathematical models that have come to dominate physics.
There was no doubt that, at King’s College, Maxwell had begun to really make something of the insights that drove him. He published his findings in a two-part paper. His original work on electromagnetism had been called On Faraday’s Lines of Force – the new paper was On Physical Lines of Force, emphasising that he had moved on to a more practical model. It was published in Philosophical Magazine,§§§ with Part 1 in the March 1861 edition and Part 2 split between the April and May editions.
Notes
1 – The extract from Maxwell’s inaugural lecture is taken from Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 1 (Cambridge: Cambridge University Press, 1990), p. 671.
2 – The description of Maxwell borrowing books from the King’s College library for his students is from Lewis Campbell and William Garnett, The Life of James Clerk Maxwell (London: Macmillan, 1882), p. 177.
3 – The description of the wet collodion photographic process is taken from Brian Clegg, The Man Who Stopped Time (Washington, DC: Joseph Henry Press, 2007), p. 34.
4 – The representation of Maxwell’s reasoning here, using four sequential diagrams, is adapted from Basil Mahon, The Man Who Changed Everything: The Life of James Clerk Maxwell (Chichester: Wiley, 2003) pp. 100–03.
5 – Poincaré’s observation of his contemporaries’ mistrust for Maxwell’s mechanical model is from John Heilbron, ‘Lectures on the history of atomic physics 1900–1922’, in History of twentieth century physics: 57th Varenna International School of Physics, ‘Enrico Fermi’ (New York: Academic Press, 1977), pp. 40–108.
6 – Maxwell’s remarks on the benefit of analogy are taken from James Clerk Maxwell, ‘Analogies in nature’ (1856), in Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 1 (Cambridge: Cambridge University Press, 1990) pp. 376–83.
7 – William Thomson’s assertions that vortices existed in the magnetic field are made in William Thomson, ‘Dynamical Illustrations of the Magnetic and Helicoidal Rotatory Effects of Transparent Bodies on Polarized Light’, Proceedings of the Royal Society (1856), 8: 150–58.
8 – Maxwell’s admission that the ball bearings in his model were ‘awkward’ is from William Davidson Niven (ed.), The Scientific Papers of James Clerk Maxwell, Vol. 1 (Cambridge: Cambridge University Press, 1890), p. 486.
* The concept of a natural law is rather an elusive one. Laws are written down in black and white. A natural law is more an analogy of what nature is like, as we can arguably never directly interact with reality, merely observe phenomena. But that’s all too philosophical for me – there’s a special breed of demons who specialise in philosophy.
† Calculating present value of historical salaries is something of a black art (a speciality of demons). Maxwell’s salary would be the equivalent of around £39,000 in terms of the goods it could buy. However, it would be the equivalent of around £300,000 in proportion to the change in the earnings of an average worker between the two periods.
‡ In practice King’s could not award BA or MA degrees at the time, but on successful completion, a student became an AKC – an Associate of King’s College.
§ Just as dangerous as it sounds. Used at the time as the e
xplosive charge of mines and torpedoes, and for blasting (and later as a rocket propellant), though oddly, given the name, not typically used in guns.
¶ The ribbon is usually described as being tartan, but pedants point out that tartans usually have two colours, where the ribbon had three.
|| Don’t let scientists ever tell you that they don’t sometimes benefit from luck. The photographic plates Maxwell used were not sensitive enough for the relatively low-energy red light to produce a good red image when the red filter was used. But, luckily, the red sections of the tartan were also good emitters of ultraviolet, which passed unhampered through the red filter and made the appropriate impact on the plate.
** In the absence of antigravity, which despite many YouTube videos and conspiracy theories to the contrary, is yet to be demonstrated. It was speculated at one time by serious physicists that the gravitational force between matter and antimatter could be repulsive rather than attractive, but there is as yet no evidence for this.
†† Known as a magnetic monopole.
‡‡ It should be stressed that, as with his fluid model, the spheres were just an analogy. There was no suggestion that space really was filled with spheres, though eventually the picture would resolve as something Maxwell felt was closer to reality.
§§ Ever since Newton, some have liked to mock the idea of centrifugal force flinging things outwards as a body rotates, pointing out that the flung objects are simply following their natural trajectory in a straight line, and the ‘real’ force involved is usually a ‘centripetal’ force, towards the centre, countering the inclination to move outwards. However, this is just a distinction of the frame of reference used to examine the forces – it depends where you look at the effect from – and centrifugal force can still be a useful way to describe an effect.
