# an autodidact meets a dilettante…

‘Rise above yourself and grasp the world’ Archimedes – attribution

## an interminable conversation 8: eddy currents, Ampere’s Law and other physics struggles

easy peasy

Canto: So we were talking about eddy currents, but before we get there, I’d like to note that, according to one of the various videos I’ve viewed recently, this connection between electricity and magnetism, first observed by Faraday and Henry, and brilliantly mathematised by James Clerk Maxwell, has transformed our human world perhaps more than any other discovery in our history. I think this is why I’m really keen to comprehend it more thoroughly before I die.

Jacinta: Yeah very touching. So what about eddy currents?

Canto: Okay, back to Wikipedia:

Eddy currents (also called Foucault’s currents) are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday’s law of induction or by the relative motion of a conductor in a magnetic field. Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field. They can be induced within nearby stationary conductors by a time-varying magnetic field created by an AC electromagnet or transformer, for example, or by relative motion between a magnet and a nearby conductor.

Jacinta: Right. All is clear. End of post?

Canto: Well, this ‘perpendicular’ thing has been often referred to. I’ll steal this Wikipedia diagram, and try to explain it in my own words.

So, the eddy currents are drawn in red. They’re induced in a metal plate (C)…

Jacinta: What does induced actually mean?

Canto: That’s actually quite a difficult one. Most of the definitions of electrical induction I’ve encountered appear to be vague if not circular. Basically, it just means ‘created’ or ‘produced’.

Jacinta: Right. So, magic?

Canto: The fact that an electric current can be produced (say in a conductive wire like copper) by the movement of a magnet suggests strongly that magnetism and electricity are counterparts. That’s the central point. That’s why we refer to electromagnetism, and electromagnetic theory, because the connections – between the conductivity and resistance of the wire and the strength and movement of the magnet (for example it can be made to spin) will determine the strength of the electric field, or the emf, and all this can be calculated precisely via an equation or set of equations, which helps us to use the emf to create useful energy.

Jacinta: Okay, so this metal plate is moving, and I’m guessing V stands for velocity. The plate is a conductor, and the nearby magnet (N – that’s the magnet’s north pole) produces, or induces, a magnetic field (B) – or it just has a magnetic field, being a magnet, and this creates a current in the plate.

Canto: Which is perpendicular to the magnetic field, because what causes the current in the plate is the movement of electrons, which can’t jump out of the plate after all, but move within the plane of the plate. And the same would go for a wire. There’s also the matter of the direction, within the plane, of the current – clockwise or anticlockwise? And many other things beyond my understanding.

Jacinta: Would it help to try for a historical account, going back to the 18th century – Franklin, Cavendish, even Newton? The beginning of the proper mathematisation of physical forces? I mean, all I wanted to know was how an induction stovetop worked.

Canto: That’s life – you wonder why x does y and you end up reflecting on the origin of the universe. I’ve looked at a couple of videos, and they explain well enough what happens when a magnet goes inside an electrified coil, but never really explain why. But let’s just start with Faraday. He was a great experimenter, as they all tell me, but not too much of a mathematician. Faraday wasn’t the first to connect electricity with magnetism, though. H C Ørsted was the first, I think, to announce, and presumably to discover, that an electric current flowing through a wire produced a magnetic field around it. That was around 1820, which dates the first recognised connection between electricity and magnetism. The discovery was drawn to the attention of Andre-Marie Ampère, who began experimenting with, and mathematising, the relationship. Here’s a quote from Britannica online:

Extending Ørsted’s experimental work, Ampère showed that two parallel wires carrying electric currents repel or attract each other, depending on whether the currents flow in the same or opposite directions, respectively. He also applied mathematics in generalizing physical laws from these experimental results. Most important was the principle that came to be called Ampère’s law, which states that the mutual action of two lengths of current-carrying wire is proportional to their lengths and to the intensities of their currents.

Jacinta: That’s interesting – what does the mutual action mean? So we have two lengths of wire, which could be flowing in the same direction, in which case – what? Do they attract or repel? Presumably they repel, as like charges repel. But that’s magnetism, not electricity. But it’s both, as they were starting to discover. But how, proportional to the lengths of the wire? I can imagine that the intensity of the currents would be proportional to the degree of attraction or repulsion – but the length of the wires?

Canto: You want more bamboozlement? Here’s another version of Ampère’s law:

The integral around a closed path of the component of the magnetic field tangent to the direction of the path equals μ0 times the current intercepted by the area within the path.

Jacinta: Right. Why didn’t you say that before? Seriously, though, I do want to know what an integral is. I’m guessing that ‘tangent to’ means ‘perpendicular to’?
Canto: Not quite. Forget the above definition, though it’s not wrong. Here’s another definition:
The magnetic field created by an electric current is proportional to the size of that electric current with a constant of proportionality equal to the permeability of free space.
Jacinta: No, sorry, that’s  meaningless to me, especially the last bit.

Canto: The symbol in in the equation above, (μ0), is a physical constant used in electromagnetism. It refers to the permeability of free space. My guess is that it wasn’t defined that way by Ampère.

Jacinta: I understand precisely nothing about that equation. Please tell me what an integral is, as if that might provide enlightenment.

Canto: It’s about quantifying areas defined by or under curves. And a tangent – but let’s not get into the maths.

Jacinta: But we have to!

Canto: Well, briefly for now, a tangent in maths can sort of mean more than one thing, I think. If you picture a circle, a tangent is a straight line that touches once the circumference of the circle. So that straight line could be horizontal, vertical or anything in between.

Jacinta: Right. And how does that relate to electromagnetism?

Canto: Okay, let’s return to Ampère’s experiment. Two parallel wires attracted each other when their currents were running in the same direction, and repelled each other when they were running in the opposite direction. It’s also the case – and I don’t know if this was discovered by Ampère, but never mind – that if you coil up a wire (carrying a current), the inside of the coil acts like a magnet, with a north and south pole. Essentially, what is happening is that the current in a wire creates a magnetic field around it, circling in a particular direction – either clockwise or anti-clockwise. The magnetic field is ‘stronger’ the closer it is to the wire. So there’s clearly a relationship between distance from the wire and field strength. And there’s also a relationship between field strength and the strength of the current in the wire. It’s those relations, which obviously can be mathematised, that are the basis of Ampère’s Law. So here’s another definition – hopefully one easier to follow:

The equation for Ampère’s Law applies to any kind of loop, not just a circle, surrounding a current, no matter how many wires there are, or how they’re arranged or shaped. The law is valid as long as the current is constant.

That’s the easy part, and then there’s the equation, which I’ll repeat here, and try to explain:

So, that first symbol represents the integral, and B is the magnetic field. Remember that the integral is about the area of a ‘loop’, so the area of B, multiplied by the cosine of theta (don’t ask) with respect to distance (d), is equal to a constant, (μ0), multiplied by the current in the loop (I).
Jacinta: Hmmm, I’m almost getting it, but I’ve never really met trigonometry.
Canto: Well the video I’m taking this from simplifies it, perhaps: ‘the total magnetic field along the loop is equal to the current running through the loop times a constant number’. So, it’s an equation of proportionality, I think. And the constant – mu0, aka the magnetic constant – has a numerical value which I won’t spell out here, but it involves pi and newtons per amps squared.
Jacinta: So you’ve used a ‘crash course physics’ video for the last part of this conversation, which is useful, but assumes a lot of knowledge. Looks like we may have to start those videos almost from the beginning, and learn about trickonometry, and integers, and so much els
Canto: ……..
References
https://en.wikipedia.org/wiki/Integral
https://www.sciencefacts.net/amperes-law.html

Written by stewart henderson

August 30, 2022 at 7:56 pm

## An interminable conversation 6: trying to understand inductive cooking.

the guts of an induction cooker, I believe

Canto: So, with all the fuss and excitement about renewables, we should continue the near impossible task of trying to get our heads around electricity, never mind renewable sources of electricity. It’s still electrickery to me. For example, Saul Griffith in The Big Switch recommends inductive electric stoves as a replacement for gas, which many swear by because they appear to heat your pot immediately, or at least very quickly compared to those old ring electric heaters…

Jacinta: Yes, but as Griffith says in that book, you can tell the gas isn’t too efficient because you feel yourself getting hot when you’re near the stove. That’s heat that isn’t going into the pot. Apparently that doesn’t happen with inductive electricity, which heats the pot just as rapidly if not more so, but almost nothing’s ‘wasted’ into the surrounding air.

Canto: Unless you like to feel toasty warm in the kitchen. Anyway we’re talking about induction cooktops,to give them their proper name, apparently. The old electric cooktops had those coils, and they’re what we grew up with. Here’s a summary from the Forbes website:

Also known as radiant cooktops, electric cooktops offer centralized heat. Electric cooktops have an electrical current that flows through a metal coil underneath the glass or ceramic surface. The coil becomes hot and starts glowing due to the electrical resistance. It will transfer its heat through the glass using infrared energy. This means the burner holding your pot or pan is the one that gets hot. Your food is then cooked by the transfer of heat between the cooktop and the pot. There is residual heat for an undetermined amount of time with electric cooktops, which is why these ranges tend to have an indicator light letting you know that the burner is still warm.

Jacinta: Metal coils under glass or ceramics…? As I recall, they were just coils, not under anything. They were grey. But maybe they were ceramic, with metal embedded within, or on the underside. I wish I was the type who pulled things apart to see how they worked, like geeky kids. And wtf is ‘infrared energy’? As far as I remember, the coils turned visible red when hot, not invisible infrared.

Canto: You see the red light but you feel the infrared heat. The heat you feel from the sun is in the non-visible part of the spectrum – the infrared and beyond. On the other side of the visible spectrum is the ultraviolet and beyond. I think.

Jacinta: So which side has the long wavelengths and which side has the short? – not that this would mean much to me.

Canto: Infrared radiation is about longer wavelength, lower frequency waves than visible light, and ultraviolet radiation is higher frequency and shorter wavelengths. So they bookend invisible light, if you will. But the longest wavelength, lowest frequency waves are radio waves, followed by microwaves, while the highest frequency, shortest wavelength radiation is gamma rays. Whether there are forms of radiation beyond these ends of the spectrum, I don’t know.

Jacinta: I’ve heard of gravitational waves, which were only detected recently. What about them?

Canto: They can have almost infinitely long wavelengths apparently. So to speak. Obviously if they were ‘infinitely’ long, if that’s even meaningful, they’d be undetectable. But let’s get back down to earth, and the most useful energy. Here’s how the Red Energy website describes induction cooktops:

Basically, a standard electric or gas cooktop transfers heat (or conducts heat) from the cooktop to the pot or pan. Whereas, an induction cooktop ‘switches on’ an electromagnetic field when it comes into contact with your pot or pan (as long as the cookware contains a ferrous material like iron or steel). The heat comes on fast and instantly starts cooking the contents.

Jacinta: Okay that explains nothing much, as I don’t know, really, how an electromagnetic field works (still stupid after all these years). As to ferrous cookware, I didn’t realise you could use anything else.

Canto: Well the same website says that, given the speed of heating, you might need to upgrade to cookware that can take the stress, so to speak. As to the electromagnetic field thing, Red Energy doesn’t really explain it, but the key is that an electromagnetic field doesn’t require the heating of an element – those coily things.

Jacinta: They’ve eliminated the middle man, metaphorically speaking? I’m all in for eliminating men, even metaphorically.

Canto: Thanks. So I’m trying to get my head around this. I need to delve further into the meaning of this magical, presumably infrared, heat. The essential term to explore is electromagnetic induction, and then to join that understanding to the practical aspects, yer everyday cooking. So this goes back to the working-class hero Michael Faraday, and the Scottish hero J C Maxwell, which will be fun, though of course I’m not at all nationalistic, but…

Jacinta: Canto isn’t a particularly Scottish name is it?

Canto: My real name is Camran Ciogach Ceannaideach, but I prefer a simpler life. Anyway electromagnetic induction has a great variety of applications, but this is the ultimate, i.e Wikipedia, definition:

Electromagnetic or magnetic induction is the production of an electromotive force across an electrical conductor in a changing magnetic field.

Jacinta: None the wiser. What’s an electromotive force?

Canto: Called emf, it’s ‘the electrical action produced by a non-electrical source, measured in volts’. That’s also Wikipedia. So a non-electrical source might be a battery (which is all about chemistry) or a generator (all about steam in industrial revolution days -creating mechanical energy).

Jacinta: So the infernal combustion engine somehow converts petrol into mechanical energy? How does that happen?

Canto: Off topic. This is really difficult stuff. Here’s another Wikipedia quote which might take us somewhere:

In electromagnetic induction, emf can be defined around a closed loop of conductor as the electromagnetic work that would be done on an electric charge (an electron in this instance) if it travels once around the loop.

Jacinta: Right, now everything’s clear. But seriously, all I want to know is how to get rid of that middle man. We were talking abut cooking, remember?

Canto: So emf is also called voltage, or measured in volts, which I seem to recall learning before. Anyway, nowadays electromagnetic induction is everywhere – for example that’s how money gets removed from your bank account when you connect those cards in your wallet to those machines in the shop.

Jacinta: So they’re zapping your card, sort of?

Canto: I’ve looked at a few sites dealing with electromagnetic induction, and they all give me the same feel, that it’s like weird magic. I suppose because they explain how it works but not why.

Jacinta: Shut up and calculate?

Canto: Anyway, induction cooking has been around for more than a century, but it’s really catching on now. They always say it’s more direct, because it doesn’t involve heating an element.

Jacinta: Don’t you know it’s magic?

Canto: No, it’s magnetic. Which explains nothing. But let me try another website, this time Frigidaire:

Induction cooktops heat pots and pans directly, instead of using an electric or gas-heated element. It boils water up to 50 percent faster than gas or electric, and maintains a consistent and precise temperature. The surface stays relatively cool so spills, splatters and occasional boil-overs don’t burn onto the cooktop, making clean-up quick and easy…. Induction cooking uses electric currents to directly heat pots and pans through magnetic induction. Instead of using thermal conduction (a gas or electric element transferring heat from a burner to a pot or pan), induction heats the cooking vessel itself almost instantly….. An electric current is passed through a coiled copper wire underneath the cooking surface, which creates a magnetic current throughout the cooking pan to produce heat. Because induction doesn’t use a traditional outside heat source, only the element in use will become warm due to the heat transferred from the pan. Induction cooking is more efficient than traditional electric and gas cooking because little heat energy is lost. Like other traditional cooktops, the evenly heated pots and pans then heat the contents inside through conduction and convection…. Important: For induction to work, your cookware must be made of a magnetic metal, such as cast iron or some stainless steels.

Jacinta: So I’m not sure if that gets closer to an explanation, but what’s surely missing is how magnetism, or a magnetic current, creates heat. It doesn’t use an ‘element’, but it must use something. I know that heat is energy, essentially, and presumably an electric current is energy, or force, like emf, which is also energy…

Canto: Yes it’s very confusing. The Wikipedia article gets into the maths fairly quickly, and when it describes applications it doesn’t mention cooking… Hang on, it takes me to a link on induction cooking. So here’s a definition, similar to the Frigidaire one, but a little more concise. Something to really zero in on:

In an induction stove (also “induction hob” or “induction cooktop”), a cooking vessel with a ferromagnetic base is placed on a heat-proof glass-ceramic surface above a coil of copper wire with an alternating electric current passing through it. The resulting oscillating magnetic field wirelessly induces an electrical current in the vessel. This large eddy current flowing through the resistance of a thin layer of metal in the base of the vessel results in resistive heating.

I’ve kept in the links, which I usually remove. For our further education. So it’s the resistance of the metal base of the pan that produces heat. Something like incandescent light, which is produced through the resistance of the tungsten filament, which makes it glow white (this was a light bulb moment for me). So you really have to use the right cookware.

Jacinta: Thanks for the links – yes, the key is that ‘resistive heating’, also called Joule heating. James Joule, as well as Heirnrich Lenz, independently, found that heat could be generated by an electric current, and, by experimental testing and measurement, that the heat produced was proportional to the square of the current (which is basically the emf, I think), multiplied by the electrical resistance of the wire. So you can see that the wire (or in cooking, the pot) will heat more readily if it has a high electrical resistance. This can be stated in a formula: , where P is the heating power generated by an electrical conductor (measured usually in watts), I is the current, and R is the resistance.

Canto: So we’ve made progress, but it’s the relation of magnetism to electricity – that’s what I don’t get, and that’s the key to it all. I think I understand that an electric current creates a magnetic field – though not really – and I get that an alternating current would induce an oscillating magnetic field, I think, but is this just observation without understanding? That electricity and magnetism are connected, so just shut up and calculate as you say?

Jacinta: So how, and why a high frequency alternating current creates a dynamic field, that’s what we’re trying to understand. And what’s an eddy current?

Canto: I think we’ve had enough for now, but we’re getting there….

Written by stewart henderson

August 27, 2022 at 5:20 pm

## what is electricity? part 8: turning DC current into AC, mostly

Canto: So before we go into detail about turning direct current into alternating current, I want to know, in detail, why AC is better for our grid system. I’m still not clear about that.

Jacinta: It’s cheaper to generate and involves less energy loss over medium-long distances, apparently. This is because the voltage can be varied by means of transformers, which we’ll get to at some stage. Varying the voltage means, I think, that you can transmit the energy at high voltages via power lines, and then bring the voltage down via transformers for household use. This results in lower energy loss, but to understand this requires some mathematics.

Canto: Oh dear. And I’ve just been reading that AC is, strictly speaking, not more efficient than DC, but of course the argument and the technical detail is way beyond me.

Jacinta: Well let’s avoid that one. Or…maybe not. AC isn’t in any way intrinsically superior to DC, it depends on circs – and that stands for circuits as well as circumstances haha. But to explain this requires going into root mean square (RMS) values, which we will get to, but for now let’s focus on converting DC into AC. Here’s a quote from ‘all about circuits’:

If a machine is constructed to rotate a magnetic field around a set of stationary wire coils with the turning of a shaft, AC voltage will be produced across the wire coils as that shaft is rotated, in accordance with Faraday’s Law of electromagnetic induction. This is the basic operating principle of an AC generator, also known as an alternator

The links explain more about magnetic fields and electromagnetic induction, which we’ll eventually get to. Now we’ve already talked about rotating magnets to create a polarised field…

Canto: And when the magnet is at a particular angle in its rotation, no current flows – if ‘flow’ is the right word?

Jacinta: Yes. This same website has a neat illustration, and think of the sine curves.

Canto: Can you explain the wire coils? They’re what’s shown in the illustration, right, with the magnet somehow connected to them? And the load is anything that resists the current, creating energy to power a device?

Jacinta: Yes, electric coils, or electromagnetic coils, as I understand them, are integral to most electronic devices, and according to the ‘industrial quick search’ website, they ‘provide inductance in an electrical circuit, an electrical characteristic that opposes the flow of current’.

Canto: OMG, can you explain that explanation?

Jacinta: I can but try. You would think that resistance opposes the flow of current – like, to resist is to oppose, right? Well, it gets complicated, because magnetism is involved. We quoted earlier something about Faraday’s Law of electromagnetic induction, which will require much analysis to understand. The Oxford definition of inductance is ‘the property of an electric conductor or circuit that causes an electromotive force to be generated by a change in the current flowing’, if that helps.

Canto: Not really.

Jacinta: So… I believe… I mean I’ve read, that any flow of electric current creates a magnetic field…

Canto: How so? And what exactly is a magnetic field?

Jacinta: Well, it’s like a field of values, and it gets very mathematical, but the shape of the field is circular around the wire. There’s a rule of thumb about this, quite literally. It’s a right-hand rule…

Canto: I’m left-handed.

Jacinta: It shouldn’t be difficult to remember this. You set your right thumb in the direction of the current, and that means your fingers will curl in the direction of the magnetic field. So that’s direction. Strength, or magnitude, reduces as you move out from the wire, according to a precisely defined formula, B (the magnetic field) = μI/2πr. You’ll notice that the denominator here defines the circumference of a circle.

Canto: Yes, I think I get that – because it’s a circular field.

Jacinta: I got this from Khan Academy. I is the current, and μ, or mu (a Greek letter) stands for the permeability of the material, or substance, or medium, the wire is passing through (like air, for example). It all has something to do with Ampere’s Law. When the wire is passing through air, or a vacuum, mu becomes, or is treated as, the permeability of free space (μ.0), which is called a constant. So you can calculate, say, with a current of 3 amps, and a point 2 metres from the wire that the current is passing through, the magnitude and direction of the magnetic field. So you would have, in this wire passing through space, μ.0.3/2π.2, or μ.0.3/4π, which you can work out with a better calculator than we have, one that has all or many of the constants built in.

Canto: So easy. Wasn’t this supposed to be about alternating current?

Jacinta: Okay forget all that. Or don’t, but getting back to alternating current and how we create it, and how we switch from AC to DC or vice versa…

Canto: Let’s start, arbitrarily, with converting AC to DC.

Jacinta: Okay, so this involves the use of diodes. So, a diode conducts electricity in one direction only…. but, having had my head spun by the notion of diodes, and almost everything else electrical, I think we should start again, from the very beginning, and learn all about electrical circuits, in baby steps.

Canto: Maybe we should do it historically again, it’s more fun. People are generally more interesting than electrons.

Jacinta: Well, maybe we should do a bit of both. It’s true that we’re neither of us too good at the maths of all this but it’s pretty essential.

Canto: Okay, let’s return to the eighteenth century…

References

Alternating Current vs Direct Current – Rms Voltage, Peak Current & Average Power of AC Circuits (video – the organic chemistry tutor)

Written by stewart henderson

January 16, 2022 at 6:19 pm

## towards James Clerk Maxwell: 1 – a bit about magnetism

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