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towards James Clerk Maxwell 3 – Benjamin Franklin and Coulomb’s Law

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Coulomb’s law – attraction and repulsion

Canto: So we’ve been looking at electricity and magnetism historically, as researchers, scientists, thinkers, experimenters and so on have managed to piece these processes together and combine them into the one thing, electromagnetism, culminating in J C Maxwell’s equations…

Jacinta: Or going beyond those equations into the implications. But of course we’re novices regarding the science and maths of it all, so we should recommend that real students of this stuff should go to the Khan academy lectures, or Matt Anderson’s lectures for the real expert low-down. As will we. But we need to point out, if only to ourselves, that what we’re trying to get our heads around is really fundamental stuff about existence. Light, which is obviously fundamental to our existence, is an electromagnetic wave. So, think magnetism, think electricity, and think light.

Canto: Right, so we’re going back to the eighteenth century, and whatever happens after Hauksbee and Polinière.

Jacinta: Well, scientists – or shall we say physical scientists, the predecessors of modern physicists – were much influenced throughout the eighteenth century by Newton, in particular his inverse square law of gravity:

F=G{\frac {m_{1}m_{2}}{r^{2}}}\

Newton saw gravity as a force (F), and formulated the theory that this force acted between any two objects (m1 and m2 – indicating their masses) in a direct line between their respective centres of mass (r being the length of that line, or the distance between those centres of mass). This force is directly proportional to the product of the two masses and inversely proportional to the distance. As to G, the gravitational constant, that’s something I don’t get, as yet. Anyway, the success of Newton’s theory, especially the central insight that a force diminishes, in a precise way, with distance, affected the thinking of a number of early physical scientists. Could a similar theory, or law (they didn’t think in terms of theory then) apply to electrical forces? Among those who suspected as much were the mathematician Daniel Bernoulli, who made major contributions to fluid dynamics and probability, and Alessandro Volta, who worked on electrical capacitance and storage, the earliest batteries.

Canto: And Joseph Priestley actually proposed an inverse square law for electricity, but didn’t work out the details. Franz Aepinus and Benjamin Franklin were also important 18th century figures in trying to nut out how this force worked. All of this post-Newtonian activity was putting physical science on a more rigorous and mathematical footing. But before we get to Coulomb and his law, what was a Leyden Jar?

Jacinta: Leyden jars were the first capacitors. They were made of glass. This takes us back to the days of Matthias Bose earlier in the 18th century, and even back to Hauksbee. Bose, a professor of natural philosophy at the University of Wittenberg, worked with and improved Hauksbee’s revolving glass-globe machine to experiment with static electricity. He added a metal ‘prime conductor’ which accumulated a higher level of static charge, and gave spectacular public demonstrations of the sparks he created, using them to set alcohol alight and to create ‘beatification’ effects on a woman wearing a metal helmet. All great japes, but it promoted interest in electricity on the continent. The trick with alcohol inspired another experimenter, Jurgen von Kleist, to invent his Leyden jar, named for Kleist’s university. It was a glass container filled with alcohol (or water) into which was suspended a metal rod or wire, connected to a prime conductor. The fluid collected a great deal of electric charge, which turned out to be very shocking to anyone who touched the metal rod. Later Leyden jars used metal foil instead of liquid. These early capacitors could store many thousands of volts of electricity.

Canto: At this time, in the mid-eighteenth century, nobody was thinking much about a use for electricity, though I suppose the powerful shocks experienced by the tinkerers with Leyden jars might’ve been light-bulb moments, so to speak.

Jacinta: Well, take Ben Franklin. He wasn’t of course the first to notice that electrostatic sparks were like lightning, but he was possibly the first to conduct experiments to prove the connection. And of course he knew the power of lighting, how it could burn down houses. Franklin invented the lightning rod – his proudest invention – to minimise this damage.

Canto: They’re made of metal aren’t they? How do they work? How did Franklin know they would work?

Jacinta: Although the details weren’t well understood, it was known in Franklin’s time that some materials, particularly metals (copper and aluminium are among the best), were conductors of electricity, while others, such as glass, were insulators. He speculated that a pointed metal rod, fixed on top of buildings, would provide a focal point for the electrical charge in the clouds. As he wrote: “The electrical fire would, I think, be drawn out of a cloud silently, before it could come near enough to strike….” He also had at least an inkling of what we now call ‘grounding’, as per this quote about the design, which should use “upright Rods of Iron, made sharp as a Needle and gilt to prevent Rusting, and from the Foot of those Rods a Wire down the outside of the Building into the Ground”. He was also, apparently the inventor of the terms negative and positive for different kinds of charge.

Canto: There are different kinds of charge? I didn’t know that.

Jacinta: Well you know of course that a molecule is positively charged if it has more protons than electrons, and vice versa for negative charge, but this molecular understanding came much later. In the eighteenth century electricity was generally considered in terms of the flow of a fluid. Franklin posited that objects with an excess of fluid (though he called it ‘electrical fire’) were positively charged, and those with a deficit were negatively charged. And those terms have stuck.

Canto: As have other other electrical terms first used by Franklin, such as battery, conductor, charge and discharge.

Jacinta: So let’s move on to Charles-Augustin De Coulomb (1736-1806), who was of course one of many scientists and engineers of the late eighteenth century who were progressing our understanding and application of electricity, but the most important one in leading to the theories of Maxwell. Coulomb was both brilliant and rich, at least initially, so that he was afforded the best education available, particularly in mathematics…

Canto: Let me write down Coulomb’s Law before you go on, because of its interesting similarity to Newton’s inverse-square gravity law. It even has one of those mysterious ‘constants’:

{\displaystyle F=k_{e}{\frac {q_{1}q_{2}}{r^{2}}},}

where F is the electrostatic force, the qs are particular magnitudes of charges, and r is the distance between those charges.

Jacinta: Yes, the Coulomb constant, ke, or k, is a constant of proportionality, as is the gravitational constant. Hopefully we’ll get to that. Coulomb had a varied, peripatetic existence, including a period of wise retirement to his country estate during the French revolution. Much of his work involved applied engineering and mechanics, but in the 1780s he wrote a number of breakthrough papers, including three ‘reports on electricity and magnetism’. He was interested in the effect that distance might have on electrostatic force or charge, but it’s interesting that these papers placed electricity and magnetism together. His experiments led him to conclude that an inverse square law applied to both.

Canto: I imagine that these constants required a lot of experimentation and calculation to work out?

Jacinta: This is where I really get lost, but I don’t think Coulomb worked out the constant of proportionality, he simply found by experimentation that there was a general law, which he more or less stated as follows:

The magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them.
The force is along the straight line joining them. If the two charges have the same sign, the electrostatic force between them is repulsive; if they have different signs, the force between them is attractive.

It seems the constants of proportionality are just about units of measurement, which of course were different in the days of Coulomb and Newton. So it’s just about measuring stuff in modern SI units using these laws. It’s about conventions used in everyday engineering, basically. I think.

Canto: Equations like these have scalar and vector forms. What does that mean?

Jacinta: Basically, vector quantities have both magnitude and direction, while scalar quantities have magnitude only. The usual example is speed v velocity. Velocity has magnitude and direction, speed only has magnitude. Or more generally, a scalar quantity has only one ‘dimension’ or feature to it in an equation – say, mass, or temperature. A vector quantity has more than one.

Canto: So are we ready to tackle Maxwell now?

Jacinta: Hell, no. We have a long way to go, with names like Gauss, Cavendish and Faraday to hopefully help us along the path to semi-enlightenment. And I think we need to pursue a few of these excellent online courses before we go much further.

References

Khan academy physics (160 lectures)

Matt Anderson physics (191 lectures)

https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation

https://www.britannica.com/technology/Leyden-jar

http://www.americaslibrary.gov/aa/franklinb/aa_franklinb_electric_1.html

http://www.revolutionary-war-and-beyond.com/benjamin-franklin-and-electricity-letters.html

https://en.wikipedia.org/wiki/Coulomb_constant

https://www.britannica.com/biography/Charles-Augustin-de-Coulomb

https://www.britannica.com/science/Coulombs-law

https://en.wikipedia.org/wiki/Coulomb%27s_law

Written by stewart henderson

May 18, 2019 at 6:04 pm

Towards James Clerk Maxwell 2 – Francis Hauksbee’s experiments

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an electrostatic generator – one of Hauksbee’s many ingenious experimental devices

Canto: So we’ve witnessed electricity since we’ve had the wit to witness, in lightning. And through our attempts to understand and harness those scary bursts of energy we’ve transformed our world.

Jacinta: We’ve written about lightning before, but the info we presented there was accumulated over centuries. Now we’re going to travel back to the early years of the Royal Society in England, the early 1700s, a mere 300 years ago, to reflect on the first experiments with electricity – remembering that there was no electric power and light in those days, that gods were in the air and much was mysterious.

Canto: Electricity from the start was much sexier, and scarier, than magnetism – lightning very very frightning was the most obvious physical manifestation, and its power was easily recognised. It could kill at a stroke, while magnetism seemed all about metals getting stuck together, and needles pointing north. Interesting, but hardly earth-shattering.

Jacinta: Lightning was all about gigantic sparks shattering the sky, and the ancients, who spent so much of their time in darkness, must have seen other, less impressive and dangerous sparks, the sparks of static electricity, and wondered.

Canto: In the recent BBC documentary The story of electricity, narrator Jim Al-Khalili begins by describing Francis Hauksbee‘s experiments with static electricity and electroluminescence in the early 1700s, which dazzled visitors to the Royal Society. These were the first properly documented experiments with the mysterious force, and a collection of his papers describing these experiments was widely read by the 18th century cognoscenti – including Joe Priestley and Ben Franklin. He employed the newly-invented air pump (simply a pump for pushing out air, as in a common bike pump), popularised in England by Robert Hooke some decades before. Hauksbee made his own improvements, enabling the pump to create a vacuum.

Jacinta: Yes Hauksbee was a more interesting figure than The story of electricity presents. He didn’t ‘lose interest’ but worked on his experiments and reflected on them until his final illness in 1713 – and I’m thinking that illness, since he was only in his late forties – may have been due to mercury poisoning. Hauksbee was ‘lower class’ so few details of his life are documented. However, in these experiments he wasn’t thinking so much of electricity as of ‘attractive forces’. Also as an experimenter who must always have seen himself as an underling (in his book he mentions his ‘want of a learned education’), he doubtless felt obliged to follow the guidance of his Royal Society ‘master’, Newton, which took him into different fields of research….

Canto: The term ‘electricity’ was possibly not in common use then? You’re right, though, about Hauksbee, who rose from obscurity to become a member of the Royal Society, probably under the auspices of Newton. In late 1705, as a result of some spectacular effects displayed to the Society he became intrigued by ‘mercurial phosphorus’. The fact that mercury, in a vacuum, glowed when shaken, had already been noted by Jean Picard, a 17th century French astronomer, and the Swiss mathematician Johann Bernoulli.

Jacinta: And this has to do with electricity?

Canto: We shall see. Hauksbee wanted to work out the conditions under which this mercurial light was produced. He found that the more air in the container, the weaker the light. Also the light’s intensity depended on the movement of the mercury. He concluded that the friction of the mercury against the glass was the major cause. But was it only mercury that had this property, and was it only glass that brought it out? He experimented with other materials, finding a means of rubbing them together in a section of his air pump, Amber rubbed with wool produced a light, brightened in the absence of air. By contrast metal on flint only produced sparks when air was present. Remember, oxygen wasn’t known about at the time. In late 1705 Hauksbee presented one of his most spectacular experiments for the Society. Ingenious instrument-maker that he was, he created a glass globe, from which air could be pumped in and out, on a rotating spindle. The spinning globe came into contact with woollen cloth, and the contact created a weird purple light inside the evacuated globe, which reduced as air was let in. It was a fantastic mystery.

Jacinta: I’m hoping you can solve it.

Canto: Great expectations indeed. He experimented further, and found that when he pressed his own hands against a spinning evacuated globe, the same bright purple glow was produced, which again faded when air was let in to the globe.

Jacinta: Okay, what Hauksbee was exploring in these experiments are what we now call triboelectric effects. I remember playing around with this in schooldays by rubbing a plastic pen along the sleeve of my jersey and watching the fibres stand on end as the pen passed, and hearing the prickling sound of static electricity. The pen was then capable of lifting scraps of paper from the desk, for a time. But I didn’t see any purple lights and I’m not sure how the presence or absence of air relates to it all.

Canto: Yes, triboelectricity is about the exchange of electric charge between different materials – the build-up and discharge of electrical energy. It seems that some materials have a more or less positive charge and some have a more or less negative or opposite charge (because positive and negative are really arbitrary terms, the key point is their relation to each other), and we know that like charges repel and opposite charges attract.

Jacinta: You’ve brought up the word ‘charge’ here, and I’m wondering if that’s just an arbitrary word too – like degree of positive charge just means degree of being repulsed by its opposite, negative charge. In other words, different materials are attracted to or repulsed by each other to varying degrees under various conditions, and that degree or ‘amount’ of attraction or repulsion is referred to as ‘charge’. So ‘charge’ is a relational term…

Canto: Ummm. Maybe. In any case, if you take these different materials down to the atomic level, and I’m not sure how you take plastic and wool down to that level – I mean I know plastic is a petrochemical product, but wool, which I’ve just looked up, has a very complex chemistry – but the fact that the plastic pen, after some rubbing, pulls the fibres of your woollen sleeve towards it is because there’s an attractive force operating between opposite charges. In fact there’s a movement of electrons between the materials, from the wool to the plastic. This electron transfer leaves those woollen fibres with a net positive charge, which is attracted to the now negatively charged plastic due to the electron flow. I think.

Jacinta: Mmm. None of this was understood in the early eighteenth century, obviously. But before we go back there, we’ll stay with this concept of charge, which is nowadays calculated as a fundamental or base unit, based on the electron or its opposite, charge-wise, the proton. These elementary particles have the same but opposite charge, though they’re very different in mass (something which seems suspect to me). Anyway, taking things on trust, a unit of charge is ‘defined’ in standard macro terms as a coulomb, named for the 18th century French physicist Charles-Augustin de Coulomb. One coulomb equals approximately 6.24 x 1018 protons (or electrons). We’ll come back to this later, no doubt. Returning to Hauksbee’s experiments, he soon realised that it was the glass, not the mercury inside it, that was the agent of electrical effects. His experiments with glass globes were written down in great detail, a boon to later researchers.

Canto: Interestingly, I’ve discovered that, more or less exactly at the same time, one Pierre Polinière was conducting and presenting experiments on electroluminescence in Paris:

A closer examination of these experiments reveals not only that Polinière had personally presented them before the French Academy of Sciences, but that Polinière and Hauksbee, starting from a common interest in the ‘mercurial phosphor’, had conducted similar investigations and had in fact simultaneously announced their independent discoveries of the luminescence of evacuated glass containers.

Pierre Polinière, Francis Hauksbee and electroluminescence: a case of simultaneous discovery.
David Corson, 1968.

Jacinta: So we might finish by trying to explain our current understanding of electroluminescence (EL) and its applications. It’s a sort of combo of electricity and light, as you can imagine, or electrons and photons on the level of particles. For example, semiconductors emit light when subjected to a strong electric field or current….

Canto: Is that the basis of LED lighting?

Jacinta: Absolutely. Electrons in the semiconductor material recombine with electron holes, emitting energy in the form of photons. So it has taken us three centuries to really effectively harness the electroluminescent effects demonstrated by Hauksbee in the early days of the Royal Society.

Canto: What are electron holes? I’m thinking not ‘holes in electrons’ but holes left by electrons as they’re displaced in an electric current?

Jacinta: Yes, or almost. It’s like the lack of an electron where you might expect an electron to be. These holes where you might expect an electrically charged particle (an electron) to be, act like positively charged particles – a positron, say – and move through a lattice like an electron does. We could get into very complicated electronics here, if we had the wherewithal, but these holes are examples of quasiparticles, which mostly exist within solids. Fluid movement within solids (not apparently a contradiction in terms) is extremely complicated. Who would’ve thunk it? This movement of electrons and protons within solids is ‘regulated’ by Coulomb’s Law. Remember him? We’ll be getting to that law very soon, as it’s essential to the field of electromagnetism. And that’s our topic don’t forget.

towards James Clerk Maxwell: 1 – a bit about magnetism

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the terrell, or model globe, with which Gilbert conducted experiments

Canto: So what do you know about magnetism?

Jacinta: Well not a lot but I’m hoping to learn a lot. Some metals – but perhaps it’s only iron – appear to be attracted by other metals – or other bits of iron – so that they’re pulled together and are hard to pull apart, depending on the strength of the magnetism, which is apparently some kind of force. And I believe it’s related to electricity.

Canto: We shall learn more together. All this enquiry stems from a perhaps vague interest in James Clerk Maxwell, who famously connected electricity and magnetism in an equation, or a series of equations, or laws, with a great deal of mathematical sophistication, which I don’t have. Maxwell is hardly a household name in the way that Newton and Einstein are, but he’s undoubtedly revered among mathematical physicists. My own interest is twofold – I’d like to understand more about physics and maths in general, and – I’m Scottish, sort of. That is, I was born there and grew up among Scottish customs, though I’ve lived in Australia since I was five, and I always like to say that I haven’t a nationalist cell in my body. I’ve never waved a flag or sung any of those naff national anthems, and I have dual British/Australian citizenship only as a matter of convenience – and I suppose the more nations I could become a citizen of, the more convenient it would be. And yet. I’ve always felt ‘something extra’ in noting the Scottish contribution to the sciences and the life of the mind. James Hutton, Charles Lyell, James Watt, Adam Ferguson, David Hume and Adam Smith are names I’ve learned with a glimmer of unwonted or irrational pride over the years, though my knowledge of their achievements is in some cases very limited. And that limitation is perhaps most extreme in the case of Maxwell.

Jacinta: So we’ll get back to him later. There are good, easily available videos on all matters scientific these days, so I’ve looked at a few on magnetism, and have learned a few things. Magnetism apparently occurs when the atoms in a block of material are all aligned in the same direction, because atoms themselves are like tiny magnets, they’re polarised with a north and south pole, which I think has something to do with ionisation, maybe. Most materials have their atoms aligned in an infinity of orientations, with a net effect of no magnetism. Don’t quote me on that. The Earth itself is a gigantic magnet with a north and south pole. If it wasn’t, then the solar wind, which is a plasma of charged particles, would strip away the ozone that protects us from UV radiation. Because that field is sucked in at the poles, we see that plasma in the northern and southern latitudes, e.g. the northern lights. We now know that magnetism is essential to our existence – light itself is just a form of electromagnetic radiation (I think). But what we first learned about this stuff was pretty meagre. There were these rocks called lodestones, actually iron ore (magnetite), which attracted iron objects – swords and other tools of the iron age. What was this invisible force? It was named magnetism, after the region of Magnesia in what’s now modern Greece, where presumably lots of these lodestones were to be found. Early discoveries about magnetism showed that it could be useful in navigation…

Canto: But that wasn’t too early – there’s something of a gap between the discussions in Aristotle and Hippocrates and the 12th century realisation that a magnetic needle could be used for navigation. At least in Europe. The Chinese were well ahead in that regard. But I should stop here and say that if we’re going to arrive at Maxwell, it’s going to be a long, though undoubtedly fascinating road, with a few detours, and sometimes we might move ahead and turn back, and we’ll meet many brilliant characters along the way. And, who knows, we may never even arrive at Maxwell, and of course we shouldn’t assume that Maxwell is at the summit of all this.

Jacinta: So the first extant treatise on magnets was the Epistola de Magnete, by Petrus Peregrinus, aka Pete the Pilgrim, in 1269. It was described as a letter but it contained 13 chapters of weighty reading. The first 10 chapters apparently describe the laws of magnetism, a clear indication that such laws were already known. He describes magnetic induction, how magnetism can be induced in a piece of iron, such as a needle, by a lodestone. He writes about polarity, being the first to use the term ‘pole’ in this way – in writing at least. He noted that like poles repel and unlike poles attract, and he wrote of a south pole and a north pole. That’s to say, one end of a needle points north when given its head – for example when suspended in water. He also describes the ‘dry’ pivoted compass, which was clearly well in use by that time.

Canto: What he didn’t know was why a needle points north – actually magnetic north, which isn’t the same as the north pole – but close enough for most navigational purposes. He didn’t know that the Earth was a magnet.

Jacinta: On compass needles, there’s a neat essay online on how compasses are made. I’m not sure about how GPS is making compasses obsolete these days, but it’s a bit of a shame if it’s true…

Canto: So the next name, apart from the others, to associate with work on magnets was William Gilbert, who published De Magnete in 1600. This gathered together previous knowledge on the subject along with his own experimental work. One of the important things he noted, taken from the 1581 work The Newe Attractive, by Robert Norman, was magnetic inclination or dip, probably first noted by the Bavarian engineer and mathematician Georg Hartmann in the mid sixteenth century. This dip from the horizontal, either upward (steepest at the south pole) or downward (north pole) is a result of the Earth’s magnetic field, which doesn’t run parallel to the surface. Inspired by Norman’s work, Gilbert conducted experiments with a model Earth he made, concluding that the Earth was a magnet, and that its core, or centre, was made of iron…

Jacinta: Just how did he he work that out? Did he think that a bar magnet passed through the centre of the Earth from north to south pole?

Canto: I don’t think so, it’s probably more like he thought of Earth as a gigantic spherical lodestone with iron at its centre. It’s understandable that he would infer iron to be inside the Earth to make it magnetic, but he was the first to give a geocentric cause for the behaviour of compass needles – others had thought the attractive force was celestial. Interestingly, Gilbert was also a Copernican, in that he thought it absurd that the stars, which he believed to be vastly distant, revolved around the Earth. So he argued that the Earth turned, a view that got Galileo into so much trouble a few decades later.

Jacinta: Useful to be a Protestant in those times. Thank Dog for Henry VIII.

Canto: He also took an interest in what was later called electricity, though he didn’t consider it connected to magnetism. He built a versorium, the first electroscope, used to detect static electric charge. It was simply a metallic needle pivoted on a pedestal, like a compass needle but not magnetised. The needle would move towards a statically charged object, such as rubbed amber. In fact, Gilbert’s experiments strove to prove that static electricity was distinct from magnetism, which was an important development in early modern science.

Jacinta: I suppose we’re going to learn exactly what ‘static’ electricity is and how it fits in the over-all picture?

Canto: We shall try, though I shudder to think about what we’re embarking on here.

Jacinta: And I shudder to think about what cannot possibly be avoided – mathematics.

Canto: Well, yes, as we enter the 17th century, we’ll be encountering some great mathematical developments – with figures like Descartes, Pascal, Fermat, Liebniz and Newton all adding their weighty contributions to Galileo’s claim that nature is a book written in the language of mathematics.

Jacinta: Shit, I’m having a hard enough time trying to understand this stuff in English.

Canto: Hopefully it’ll be a great and rewarding adventure, and on the way we’ll learn about Coulomb’s inverse-square law, which is central to electrostatics. Meanwhile, it seems not much was added to our understanding of magnetism for a couple of hundred years, until Hans Ørsted’s more or less accidental discovery in 1819 that an electric current could create a magnetic field, by noting that a compass needle moved when placed near an electrified wire. Alessandro Volta had invented the voltaic pile, or battery, twenty years earlier, leading to a pile of electrical experiments in subsequent years.

Jacinta: But we’ll have to go back to the eighteenth century or beyond to trace developments in electricity before Ørsted’s finding brought the two fields together. And maybe we’ll look at the mathematics of
Charles-Augustin de Coulomb and others in the process. Let’s face it, we can’t progress towards Maxwell without doing so.

Canto: Tragic but true.

Written by stewart henderson

March 31, 2019 at 1:37 pm