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An interminable conversation 6: trying to understand inductive cooking.

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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

resetting the electrical agenda

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the all-electric la jamais contente, first car to break the 100 kph barrier, in 1899

In his book Clearing the air, Tim Smedley reminds us of the terrible errors we made in abandoning electric vehicles in the early 20th century. Smedley’s focus was on air pollution, and how the problem was exacerbated, and in fact largely caused, by emissions from car exhausts in increasingly car-dependent cities like Beijing, Delhi, Los Angeles and London. In the process he briefly mentioned the electric tram systems that were scrapped in so many cities worldwide in favour of the infernal combustion engine. It’s a story I’ve heard before of course, but it really is worth taking a deeper dive into the mess of mistakes we made back then, and the lessons we need to learn. 

A major lesson, unsurprisingly, is to be suspicious of vested interests. Today, the fossil fuel industry is still active in denying the facts about global warming and minimising the impact of air pollution on our health. Solar and wind power, and the rise of the EV industry – which, unfortunately, doesn’t exist in Australia – are still subject to ridiculous attacks by the heavily subsidised fossil fuel giants, though at least their employees don’t go around smashing wind turbines and solar panels. The website Car and Driver tells a ‘funny story’ about the very earliest days of EVs: 

… Robert Davidson of Aberdeen, built a prototype electric locomotive in 1837. A bigger, better version, demonstrated in 1841, could go 1.5 miles at 4 mph towing six tons. Then it needed new batteries. This impressive performance so alarmed railway workers (who saw it as a threat to their jobs tending steam engines) that they destroyed Davidson’s devil machine, which he’d named Galvani.

If only this achievement by Davidson, before the days of rechargeable batteries, had been greeted with more excitement and wonder. But by the time rechargeable batteries were introduced in the 1860s, steam locomotives were an established and indeed revolutionary form of transport. They began to be challenged, though, in the 1880s and 90s as battery technology, and other features such as lightweight construction materials and pneumatic tyres, started to make electric transport a more promising investment. What followed, of course, with the development of and continual improvements to the internal combustion engine in the 1870s and 80s, first using gas and then petrol – the 1870s into the 90s and beyond was a period of intense innovation for vehicular transport – was a serious and nasty battle for control of the future of private road transport. Electricity wasn’t widely available in the early twentieth century, but rich industrialists were able to create a network of filling stations, which, combined with the wider availability of cheap oil, and the mass production and marketing capabilities of industrialists like Henry Ford – who had earlier considered electric vehicles the best future option – made petrol-driven vehicles the eventual winner, in the short term. Of course, little thought was given in those days to fuel emissions. A US website describes a likely turning point: 

… it was Henry Ford’s mass-produced Model T that dealt a blow to the electric car. Introduced in 1908, the Model T made gasoline [petrol]-powered cars widely available and affordable. By 1912, the gasoline car cost only $650, while an electric roadster sold for $1,750. That same year, Charles Kettering introduced the electric starter, eliminating the need for the hand crank and giving rise to more gasoline-powered vehicle sales.

Electrically-powered vehicles quickly became ‘quaint’ and unfashionable, leading to to the trashing of electric trams worldwide. 

The high point of the internal combustion engine may not have arrived yet, as numbers continue to climb. Some appear to be addicted to the noise they make (I hear them roaring by nearly every night!). But surely their days are numbered. What shocks me, frankly, is how slow the public is to abandon them, when the fossil fuel industry is so clearly in retreat, and when EVs are becoming so ‘cool’. Of course conservative governments spend a fortune in subsidies to the fossil fuel industry –  Australia’s government  provided over $10 billion in the 2020-21 financial year, and the industry in its turn has given very generously to the government (over $1.5 million in FY2020, according to the Market Forces website).

But Australia is an outlier, with one of the worst climate policies in the WEIRD world. There will be a federal election here soon, and a change of government is very much on the cards, but the current labor opposition appears afraid to unveil a climate policy before the election. The move towards electrification of vehicles in many European countries, in China and elsewhere, will eventually have a knock-on effect here, but the immediate future doesn’t look promising. EV sales have risen markedly in the past twelve months, but from a very low base, with battery and hybrids rising to 1.95% of market share – still a paltry amount (compare Norway with 54% EVs in 2020). Interestingly, Japan is another WEIRD country that is lagging behind. China continues to be the world leader in terms of sheer numbers. 

The countries that will lead the field of course, will be those that invest in infrastructure for the transition. Our current government announced an infrastructure plan at the beginning of the year, but with little detail. There are issues, for example, about the type of charging infrastructure to fund, though fast-charging DC seems most likely.

In general, I’ve become pessimistic about Australians switching en masse to EVs over the next ten years or so – I’ve read too many ‘just around the corner’ articles with too little actual change in the past five years. But perhaps a new government with a solid, detailed plan will emerge in the near future, leading to a burst of new investment…. 

References

Tim Smedley, Clearing the air, 2019

https://www.caranddriver.com/features/g15378765/worth-the-watt-a-brief-history-of-the-electric-car-1830-to-present/

https://www.energy.gov/articles/history-electric-car

https://www.marketforces.org.au/politicaldonations2021/

 

Written by stewart henderson

February 27, 2022 at 1:07 pm

what is electricity? part 10 – it’s some kind of energy

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je ne sais pas

Canto: We’ve done nine posts on electricity and it still seems to me like magic. I mean it’s some kind of energy produced by ionisation, which we’ve been able to harness into a continuous flow, which we call current. And the flow can alternate directionally or not, and there are advantages to each, apparently.

Jacinta: And energy is heat, or heat is energy, and can be used to do work, and a lot of work has been done on energy, and how it works – for example there’s a law of conservation of energy, though I’m not sure how that works.

Canto: Yes maybe if we dwell on that concept, something or other will become clearer. Apparently energy can’t be created or destroyed, only converted from one form to another. And there are many forms of energy – electrical, gravitational, mechanical, chemical, thermal, whatever.

Jacinta: Muscular, intellectual, sexual?

Canto: Nuclear energy, mass energy, kinetic energy, potential energy, dark energy, light energy…

Jacinta: Psychic energy… Anyway, it’s stuff that we use to do work, like proteinaceous foodstuff to provide us with the energy to get ourselves more proteinaceous foodstuff. But let’s not stray too far from electricity. Electricity from the get-go was seen as a force, as was gravity, which Newton famously explained mathematically with his inverse square law.

Canto: ‘Every object or entity attracts every other object or entity with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres’, but he of course didn’t know how much those objects, like ourselves, were made up of a ginormous number of particles or molecules, of all shapes and sizes and centres of mass.

Jacinta: But the inverse square law, in which a force dissipates with distance, captured the mathematical imagination of many scientists and explorers of the world’s forces over the following generations. Take, for example, magnetism. It seemed to reduce with distance. Could that reduction be expressed in an inverse square law? And what about heat? And of course electrical energy, our supposed topic?

Canto: Well, some quick net-research tells me that magnetism does indeed reduce with the square of distance, as does heat, all under the umbrella term that ‘intensity’ of any force, if you can call thermal energy a force, reduces in an inverse square ratio from the point source in any direction. As to why, I’m not sure if that’s a scientific question.

Jacinta: A Khan Academy essay tackles the question scientifically, pointing out that intuition sort of tells us that a force like, say magnetism, reduces with distance, as does the ‘force’ of a bonfire, and that these reductions with distance might all be connected, and therefore quantified in the same way. The key is in the way the force spreads out in straight lines in every direction from the source. That’s how it dissipates. When you’re close to the source it hasn’t had a chance to spread out.

Canto: So when you’re measuring the gravitational force upon you of the earth, you have to remember that attractive force is pulling you to the earth’s centre of mass. That attractive force is radiating out in all directions. So if you’re at a height that’s twice the distance between the earth’s surface and its centre of mass, the force is reduced by a particular mathematical formula which has to do with the surface of a sphere which is much larger than the earth’s sphere (though the earth isn’t quite a sphere), but can be mathematically related to that sphere quite precisely, or to a smaller or larger sphere. The surface of a sphere increases with the square of the radius.

Jacinta: Yes, and this inverse square law works for light intensity too, though it’s not intuitively obvious, perhaps. Or electromagnetic radiation, which I think is the technical term. And the keyword is radiation – it radiates out in every direction. Think of spheres again. But we need to focus on electricity. The question here is – how does the distance between two electrically charged objects affect the force of attraction or repulsion between them?

Canto: Well, we know that increasing the distance doesn’t increase the force. In fact we know – we observe – that increasing the distance decreases the force. And likely in a precise mathematical way.

Jacinta: Well thought. And here we’re talking about electrostatic forces. And evidence has shown, unsurprisingly, that the decreased or increased force is an inverse square relationship. To spell it out, double the distance between two electrostatically charged ‘points’ decreases the  force (of attraction or repulsion) by two squared, or four. And so on. So distance really matters.

Canto: Double the distance and you reduce the force to a quarter of what it was. Triple the distance and you reduce it to a ninth.

Jacinta: This is Coulomb’s law for electrostatic force. Force is inversely proportional to the square of the distance –     F = k \frac{q_1q_2}{r^2}. Where F is the electric force, q are the two charges and r is the distance of separation. K is Coulomb’s constant.

Canto: Which needs explaining.

Jacinta: It’s a proportionality constant. This is where we have to understand something of the mathematics of variables and constants. So, Coulomb’s law was published by the brilliant Charles Augustin de Coulomb, who despite what you might think from his name, was no aristocrat and had to battle to get a decent education, in 1785. And as can be seen in his law, it features a constant similar to Newton’s gravitational constant.

Canto: So how is this constant worked out?

Jacinta: Well, think of the most famous equation in physics, E=mc2, which involves a constant, c, the speed of light in a vacuum. This speed can be measured in various ways. At first it was thought to be infinite, which is crazy but understandable. It would mean that that we were seeing the sun and stars as they actually are right now, which I’m sure is what every kid thinks. Descartes was one intellectual who favoured this view. It was ‘common sense’ after all. But a Danish astronomer, Ole Roemer, became the first person to calculate an actual value, when he recognised that there was a discrepancy between his calculation of the eclipse of Io, Jupiter’s innermost moon, and the actual eclipse as seen from earth. He theorised correctly that the discrepancy was due to the speed of light. Later the figure he arrived at was successively revised, by Christiaan Huygens among others, but Roemer was definitely on the right track…

Canto: Okay, I understand – and I understand that the calculation of the gravitational force exerted at the earth’s surface, about 9.8 metres per sec per sec, helps us to calculate the gravitational constant, I think. Anyway, Henry Cavendish was the first to come up with a pretty good approximation in 1798. But what about Coulomb’s constant?

Jacinta: Well I could state it – that’s to say, quote it from a science website – in SI units (the International System of units), but how that was arrived at precisely, I don’t know. It wasn’t worked out mathematically by Coulomb, I don’t think, but he worked out the inverse proportionality. There are explanations online, which invoke Gauss, Faraday, Lagrange and Maxwell, but the maths is way beyond me. Constants are tricky to state clearly because they invoke methods of measurements, and those measures are only human. For example the speed of light is measured in metres per second, but metres and seconds are actually human constructions for measuring stuff. What’s the measure of those measures? We have to use conventions.

Canto: Yes, this has gone on too long, and I feel my electric light is fading. I think we both need to do some mathematical training, or is it too late for us?

Jacinta: Well, I’m sure it’s all available online – the training. Brilliant.org might be a good start, or you could spend the rest of your life playing canasta – chess has been ruined by AI.

Canto: So many choices…

 

Written by stewart henderson

February 20, 2022 at 2:34 pm

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

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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

https://www.allaboutcircuits.com/textbook/direct-current/chpt-15/magnetic-fields-and-inductance/

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

what is electricity? part 5: volts, amps, currents, resistance and final acceptance, almost

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A vintage Edison carbon filament light bulb – I stole this from Amazon.com, which every decent person should do

Jacinta: So the struggle continues, but I do feel we’re making progress, after having perused our previous posts. We’re perhaps being too hard on ourselves.

Canto: Yes, we’re geniuses actually, asking all the smart questions, not taking anything for granted. Anyway, we posted an image with part 4 of this series, which might help us to understand volts, watts and so forth. It tells us that volts are ‘a force that makes electricity move’, and that voltage measures ‘the potential difference between two points in a circuit’. I don’t fully understand this. It also tells us that watts are the product of voltage and current, P = VI, which we’ve already stated. I’m worried that we’ll be able to make calculations without really understanding the forces involved.

Jacinta: I suspect that our lack of hands-on experimental experience is hindering us. Even brilliant.org won’t really give us that.

Canto: This ‘potential difference’ concept is hard to grasp. Here’s another, apparently very different definition:

Voltage is the pressure from an electrical circuit’s power source that pushes charged electrons (current) through a conducting loop, enabling them to do work such as illuminating a light.

This takes us back to the safe ground of comparing electricity with water. But how does ‘pressure’ equate with ‘potential difference’?  Fluke.com goes on to introduce another headache. Voltage can come in two forms, alternating current (ac) and direct current (dc). We’re definitely not ready for that complication.

Jacinta: But further on this site gives an explanation of potential difference, again using the water analogy. Like water in a tank, voltage is more powerful (has more potential energy) the more water is stored, the bigger the tank etc. When the valve to the tank is opened, that’s like switching on the current, but there will always be resistance (ohms) in the dimensions of the valve or the pipe (the conductivity of the wire). And of course we’re talking of the ‘flow’ of electrons, but I seem to recall it’s more like the electrons are bumping against each other rapidly, a sort of knock-on effect. I may be wrong about that though.

Canto: Voltage is a measure of the potential capacity to do work – to push electrons into activity, whatever the detail of that activity is. I think that’s right. I don’t understand why it’s called potential difference, though, rather than potential energy, say.

Jacinta: Okay, I’ve just asked the internet that question. On Quora, someone with a PhD in theoretical physics says that it’s not actually potential energy, though somewhat related. There’s an equation, U = qV, in which U is potential energy, q is charge, and V is potential, or voltage.

Canto: Right, so voltage is very close to potential energy, because it’s the next letter in the alphabet.

Jacinta: Haha, your knowledge has always been too alphabetical. But apparently it has something to do with fields, and scalar and vector properties. Let’s not go there.

Canto: We might not be able to avoid it. Another Quora answer gives voltage the symbol E, apparently due to Ohm’s Law, I think because in Ohm’s day voltage was described as electromotive force.

E (or V) = IR (I being the current, R the resistance).

Jacinta: We haven’t really talked about electrons thus far, because we’ve been treating the subject historically and we’ve not got past the 18th century, but let’s jump to a modern understanding for a while. We now know that metals and other materials that can pass electrons from atom to atom easily are called conductors. Or rather, we now know that the reason metals are good at conducting electric currents is because of their atomic structure, where valence electrons, the electrons in the outer or valence shell, are loosely bound and can move or bounce from atom to atom within the atomic lattice. I think. Materials like glass and rubber are insulators for the opposite reason – tightly bound electrons.

Canto: So wires of good conducting material, such as copper, are insulated with rubber, to contain and direct the current. If these conducting materials don’t have a current connected to them, the valence electrons will move about randomly. Attaching an electric current to these materials pushes the electrons in a particular direction. Which raises the question – how does this happen? Where exactly does this force come from? 

Jacinta: It apparently comes from the voltage – but that sounds like magic. Of course, the source is a battery or some kind of electrical grid which is connected to households – a  sort of power storehouse. The source is a force.

Canto: Nice. But how does an electrical current move these electrons? For example, we know how water in a stream flows from the mountains to the sea. That’s the force of gravity. And I know how that works, sort of.

Jacinta: What is gravity? Will that be our next 50-part series?

Canto: In yet another intro to electricity I get the analogy of voltage and water pressure, which sort of explains how the force works, like water released from a tank, but it doesn’t explain what the force is. That’s the question – what actually is electricity.

Jacinta: But surely it actually is electrons flowing in a circuit, in a particular direction. Or in lightning. And here’s another definition – of a volt. It’s a joule per coulomb. A joule, in this definition, is a unit of energy or work, and a coulomb is a ‘group of flowing electrons’.

Canto: Fluids again. Anyway, the direction of the current seems to be described as positive to negative (though I’m wondering if the ac/dc distinction comes into play here), as in a small circuit connecting to those terminals in a battery. But why does a current ‘flow’ in this direction, assuming it does? Or are these just arbitrary designations, made up by Franklin?

Jacinta: And here comes another problem thrown up by one of these ‘explanations for dummies’. It distinguishes between a closed circuit, which enables ‘flow’, and an open circuit which prevents the electrons from flowing. I’ve never heard these terms before. Sounds counter-intuitive, but no explanation is given.

Canto: The meaning seems to be that you have to close the circuit to make the flow happen, between one battery terminal and the other for example. And that circuit might include light bulbs, heaters etc. Switching the bulb off means opening the circuit and stopping the flow, at least to that particular bulb. If it’s really a flow.

Jacinta: Well it does seem to be, according to this explainer. The claim is that electron flow is measured in coulombs or amps, because one coulomb equals one amp, though why they confuse us with two measures for the same thing is as yet a mystery. Apparently we can measure the flow of electrons as easily as we can measure the flow of water in a pipe. Which is surely bullshit. The explainer goes on to tell us that this electron flow is called current, and the unit of measure is an amp, or a coulomb.

Canto: Aren’t we going to find out about Monsieur Ampère and Monsieur Coulomb?

Jacinta: Not for a while. Our explainer tells us that one amp or coulomb equals the flow of 6242 plus fifteen more zeroes of electrons over a single point in the circuit in one second.

Canto: Hmmm. I’d hate to be the one counting that, especially within the time limit. Not so easy-peasy. But this is called a unit of electric charge, or electron charge, or elementary charge, and Britannica tells us this about it:

In 2018 the General Conference on Weights and Measures (CGPM) agreed that on May 20, 2019, the ampere would henceforth be defined such that the elementary charge would be equal to 1.602176634 × 10−19 coulomb. Earlier the ampere was defined as the constant current which, if maintained in two straight parallel conductors of infinite length of negligible circular cross section and placed one metre apart in a vacuum, would produce between these conductors a force equal to 2 × 10−7newton per metre of length.

Jacinta: Clarity at last! I need a drink. Anyway, our previous explainer seems to distinguish the group of electrons (a coulomb) from their passing one point in a second (an amp). I think. But let’s move on to something else to be confused about. Electrical currents don’t have to pass through wires of course but they do in our everyday electric circuits. And all these wires have a certain level of resistance.

Canto: Ohm, I think I know where you’re going with this.

Jacinta: The longer the wire, the more the resistance. The thicker the wire, the less the resistance. So in everyday circuits we have to find a compromise. And resistance is also temperature-dependent. Our circuits often incorporate resistors to deliberately restrict electron flow, which seems to be essential for lighting. Resistance within materials occurs when electrons collide with atoms, apparently.

Canto: And ‘conduction’ involves dodging atoms?

Jacinta: Well, it’s just electrons, not a game of Red Rover. Incandescent lights work by incorporating resistors, because the collisions release energy, which heats up the resistant tungsten wire in the bulb, producing light.

Canto: Ahh, that’s a real light bulb moment for me. And that’s not even a joke, though it also is.

Jacinta: Sounds like a great note to finish on. We’ll camp here for the night. For the road is long and winding, and I fear has no end….

References

https://www.fluke.com/en-au/learn/blog/electrical/what-is-voltage

https://www.quora.com/Why-is-voltage-sometimes-called-potential-Its-not-potential-energy-so-what-is-it-the-potential-of-The-electric-field

How electricity works – working principle (video – the engineering mindset)

https://www.britannica.com/science/ampere

https://www.qrg.northwestern.edu/projects/vss/docs/thermal/3-whats-a-resistor.html

Written by stewart henderson

December 23, 2021 at 10:58 pm

what is electricity? part 4: history, hysteria and a shameful sense of stupidity

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to be explored next time

Canto: So we’re still trying to explore various ‘electricity for dummies’ sites to comprehend the basics, but they all seem to be riddled with assumptions of knowledge we just don’t have, so we’ll keep on trying, as we must.

Jacinta: Yes, we’re still on basic electrostatics, but perhaps we should move on, and see if things somehow fall into place. Individuals noted that you could accumulate this energy, called charge, I think, in materials which didn’t actually conduct this charge, because they were insulators, in which electrons were trapped and couldn’t flow (though they knew nothing about electrons, they presumably thought the ‘fluid’ was kind of stuck, but was polarised. I presume, though, that they didn’t use the term ‘polarised’ either.

Canto: So when did they stop thinking of electricity as a fluid?

Jacinta: Well, a French guy called du Fay postulated that there were two fluids which somehow interacted to cause ‘electricity’. I’m writing this, but it doesn’t make any sense to me. Anyway this was back in 1733, and Franklin was still working under this view when he did his experiments in the 1740s, but he proposed an improvement – that there was only one fluid, which could somehow exist in excess or in its opposite – insufficiency, I suppose. And he called one ‘state’ positive and the other negative.

Canto: Just looking at the Wikipedia article on the fluid theory, which reminds me that in the 17th and early 18th century the idea of ‘ether’, this explain-all fluid or ‘stuff’ that permeated the atmosphere somehow, was predominant among the cognoscenti – or not-so-cognoscenti as it turned out.

Jacinta: Yes, and to answer your question, there’s no date for when they stopped thinking about ether or electrical fluid, the combined work of the likes of Coulomb, Ørsted and Ampère, and the gradual melding of theories of magnetism and electricity in the eighteenth and nineteenth centuries led to its fading away.

Canto: So to summarise where we’re at now, Franklin played around with Leyden jars, arranging them in sets to increase the stored static charge, and he called this a battery but it was really a capacitor.

Jacinta: Yes, and he set up a system of eleven panes of glass covered on each side by thin lead plates, a kind of ‘electrostatic’ battery, which accumulates and quickly discharges electric – what?

Canto: Electrical static? Certainly it wasn’t capable of creating electrical flow, which is what a battery does.

Jacinta: Flow implies a fluid doesn’t it?

Canto: Oh shit. Anyway, there were a lot of people experimenting with and reflecting on this powerful effect, or stuff, which was known to kill people if they weren’t careful. And they were starting to connect it with magnetism. For example, Franz Aepinus, a German intellectual who worked in Russia under Catherine the Great, published a treatise in 1759 with translates as An Attempt at a Theory of Electricity and Magnetism, which not only combined these forces for the first time but was the first attempt to treat the phenomena in mathematical terms. Henry Cavendish apparently worked on very similar lines in England in the 1770s, but his work wasn’t discovered until Maxwell published it a century later.

Jacinta: Yes, but what were these connections, and what was the mathematics?

Canto: Fuck knows. Who d’you think I am, Einshtein? I suppose we’re working towards Maxwell’s breakthrough work on electromagnetism, but whether we manage to get our heads around the mathematics of it all, that’s a question.

Jacinta: To which I know the answer.

Canto: So let’s look at Galvani, Volta and Coulomb. Galvani’s work with twitching dead frogs pioneered the field of bioelectricity – singing the body electric.

Jacinta: Brainwaves and shit. Neurotransmitters – we were electrical long before we knew it. Interestingly, Galvani’s wife Lucia was heavily involved in his experimental and scientific work. She was the daughter of one of Galvani’s teachers and was clearly a bright spark, but of course wasn’t fully credited until much later, and wouldn’t have been formally educated in those Talibanish days. She died of asthma in her mid-forties. I wish I’d met her.

Canto: So what exactly did they do?

Jacinta: Well they discovered, essentially, that the energy in muscular activity was electrical. We now recognise it as ionic flow. Fluids again. They also recognised that this energy was carried by the nerves. It was Alessandro Volta, a friend and sometime rival of the Galvanis, who coined the term galvanism in their honour – or rather in Luigi’s honour. Nowadays they’re considered pioneers in electrophysiology, the study of the electrical properties of living cells and tissues.

Canto: So now to Volta. He began to wonder about Galvani’s findings, suspecting that the metals used in Galvani’s experiments played a much more significant role in the activity. The Galvanis’ work had created the idea that electricity was a ‘living’ thing, and this of course has some truth to it, as living things have harnessed this force in many ways throughout their evolution, but Volta was also on the right track with his skepticism.

Jacinta: Volta was for decades a professor of experimental physics – which sounds so modern – at the University of Pavia. But he was also an experimenter in chemistry – all this in his early days when he did all his practical work in physics and chemistry. He was the first person to isolate and describe methane. But here’s a paragraph from Wikipedia we need to dwell on.

Volta also studied what we now call electrical capacitance, developing separate means to study both electrical potential (V) and charge (Q), and discovering that for a given object, they are proportional. This is called Volta’s Law of Capacitance, and for this work the unit of electrical potential has been named the volt.

Canto: Oh dear. I think we may need to do the Brilliant course on everyday electricity, or whatever it’s called. But, to begin – everyday light bulbs are designated as being 30 amps, 60 amps and so forth, and our domestic circuits apparently run on 240 volts. That latter is the electric potential and the amps are a measure of electrical output? Am I anywhere close?

Jacinta: I can’t pretend to know about that, but I was watching a video on neuroanatomy this morning…

Canto: As you do

Jacinta: And the lecturer informed us that the brain runs on only 20 watts. She was trying to impress her class with how energy-efficient the human brain is, but all I got from it was yet another electrical measure I need to get my head around.

Canto: Don’t forget ohms.

Jacinta: So let’s try to get these basics clear. Light bulbs are measured in watts, not amps, sorry. The HowStuffWorks website tells us that electricity is measured in voltage, current and resistance. Their symbols are V, I and R. They’re measured in volts, amps and ohms. So far, so very little. They use a neat analogy, especially as I’ve just done brilliant.org’s section on the science of toilets. Think of voltage as water pressure, current as flow rate, and resistance as the pipe system through which the water (and effluent etc) flows. Now, Ohm’s Law gives us a mathematical relationship between these three – I = V/R. That’s to say, the current is the voltage divided by the resistance.

Canto: So comparing this to water and plumbing, a hose is attached to a tank of water, near the bottom. The more water in the tank, the more pressure, the more water comes out of the hose, but the rate of flow depends on the dimensions of the hose, which provides resistance. Change the diameter of the hose and the outlet connected to the hose and you increase or reduce the resistance, which will have an inverse effect on the flow.

Jacinta: Now, to watts. This is, apparently, a measure of electrical power (P). It’s calculated by multiplying the voltage and the current (P = VI). Think of this again in watery terms. If you increase the water pressure (the ‘voltage’) while maintaining the ‘resistance’ aspects, you’ll produce more power. Or if you maintain the same pressure but reduce the resistance, you’ll also produce more power.

Canto: Right, so now we’re adding a bit of maths. Exhilarating. So using Ohm’s Law we can do some calculations. I’ll try to remember that watts are a measure of the energy a device uses. So, using the equation I = P/V we can calculate the current required for a certain power of light bulb with a particular voltage – but using the analogy of voltage as water pressure doesn’t really help me here. I’m not getting it. So let me quote:

In an electrical system, increasing either the current or the voltage will result in higher power. Let’s say you have a system with a 6-volt light bulb hooked up to a 6-volt battery. The power output of the light bulb is 100 watts. Using the equation I = P/V, we can calculate how much current in amps would be required to get 100 watts out of this 6-volt bulb.

You know that P = 100 W, and V = 6 V. So, you can rearrange the equation to solve for I and substitute in the numbers.

I = 100 W/6 V = 16.67 amps

I’m having no trouble with these calculations, but I’ve been thrown by the idea of a 6-volt light bulb. I thought they were measured in watts.

Jacinta: Okay, so now we’re moving away from all the historical stuff, which is more of our comfort zone, into the hard stuff about electrickery. Watts and Volts. Next time.

References

https://www.britannica.com/biography/Charles-Francois-de-Cisternay-Du-Fay

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

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

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

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

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

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

https://science.howstuffworks.com/environmental/energy/question501.htm

https://byjus.com/physics/difference-between-watts-and-volts/

Written by stewart henderson

December 19, 2021 at 8:33 pm

what is electricity? part 2 – the mystery gets murkier

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Canto: So we were trying to comprehend early ideas about electricity as a fluid, which led Franklin to define two ‘states’ of the fluid, ‘negative’ for having a deficiency, and ‘positive’ for having an excess. He also called the negative state ‘resinous electricity’ and its opposite ‘vitreous electricity’. Presumably he thought the fluid was in a balanced state before these different elements started rubbing against each other.

Jacinta: And they were trying to regain this balanced state, which made the sparks fly?

Canto: Dunno, but let’s return to Britain, where Francis Hauksbee (1660-1713), a lab assistant to Isaac Newton, was being inventive with air pumps and pneumatic engines, decades before Franklin’s 1840s experiments.

Jacinta: I’d ask you what a pneumatic engine is, but I suppose that’d take us way off topic?

Canto: Probably. It apparently has something to do with compressed air, and some kind of energy derived from un-compressing it, or something. Anyway, air pumps were used to create vacuums, or relative vacuums. Apparently, Hauksbee, an ingenious instrument maker, noted that glass was a really good material for viewing experiments, and in 1705 he performed a remarkable experiment with one of his air pumps and that mercurial, and very dangerous element, mercury (though ‘elements’ in the modern sense, weren’t known or at least defined at the time).

Jacinta: I suppose elements wouldn’t have been defined until the atomic theory became a thing.

Canto: Anyway I’m betting that his experiments with mercury shortened Hauksbee’s poor life (he was accepted into the Royal Academy in 1703, just as Newton became its president with the aim of reinstating its grandeur, but he was given special ‘low class’ status). He’d created a version of Otto von Guericke’s electrical machine, made of glass, with air pumped out, and some mercury inside. He rubbed the sphere to create a charge, and the mercury glowed when he put his hand on it (the globe, not the mercury). Fantastical, but nobody knew what it meant, except that it could be used as a source of night-light, which actually happened, but much later.

Jacinta: But nobody had much idea about whys and wherefores at this time.

Canto: They presumably speculated. A similar phenomenon, in large, was St Elmo’s fire (he was the patron saint of sailors), a bluish glow around a sailing ship, or more recently, around an aircraft. We know now this is a form of plasma, the ionised state of matter. During thunderstorms the voltage differentials are greatest – it requires a particular differential for it to happen, and the shape of the body around which the light is seen is an important factor. Pointy objects create a more intense field (Franklin realized this). The violet-blue light is caused by the nitrogen and oxygen in the atmosphere.

Jacinta: Are you sure you know what you’re talking about?

Canto: I’m never certain about anything, that’s my vocation, or just my fate.

Jacinta: Pneumatic tyres are filled with compressed air, or gas. So that helps to understand what a pneumatic engine might be, maybe.

Canto: So Hauksbee had found a way to accumulate an electric charge, and in 1745, in Leyden, Holland, they found a way to store this charge – an instrument that came to be known as a Leyden jar. Let me quote from the scientific historian, Thomas Crump:

The so-called Leyden jar was simply a substantial glass chamber, with separate layers of metal foils on the inside and outside surfaces. The inside was charged by a metal chain connecting it to a charged body, which then lost its charge to the air.

And this was apparently the first capacitor. We’ve talked about capacitors and supercapacitors before, but of course we barely understand them. In any case this Leyden jar device allowed a lot of electrostatic potential to build up between the inner and outer surfaces – enough to kill small birds who came in contact. Nice.

Jacinta: Or were forced to come into contact. I know they tried it on monks too. Presumably they couldn’t find the nuns.

Canto: Anyway they now had some control over this electricity thing, even if they hadn’t a clue what it was. They had some idea as to how to create and release this electrical charge thingummy.

Jacinta: So now we come to Coulomb?

Canto: No, Alessandro Volta (1745-1827) first. I’m following Crump, for better or worse. But more importantly than people, it’s batteries we’re going to focus on now. And I’m not sure where to begin.

Jacinta: It was a term – battery I mean – first used by Franklin in 1749, but what he actually created were capacitors, devices that accumulated charge, until they were discharged. Batteries – I’m kind of guessing here – are devices that store charge more or less permanently, and can release charge in a controlled way, and be recharged in a controlled way.

Canto: And what is this thing called charge?

Jacinta: Well let’s continue to grope toward an understanding. So I’ll return to Franklin. He wrote a book, Experiments and observations on electricity, made at Philadelphia in America, published in 1751. His researches led him to believe that everything contained charge, positive and negative, but that they were almost always in equilibrium, a neutral state. Or the fluid, which could be ‘negativised’ or ‘positivised’ by friction, could be returned to balance by ‘discharging’ it.

Canto: And surely therein lay a mystery. How or why did this build-up of negativity or positivity get discharged? I just don’t understand it. Not just the discharge but the creation of the charge.

Jacinta: I suppose they – Franklin, Hauksbee and the rest – just made the observation and called it ‘charge’. From whence, ‘discharge’. Maybe you’re just overthinking it. They certainly didn’t know what was going on, they just noted this reliable cause-and-effect behaviour and sought to utilise it, and find out more about it. Anyway, keep on overthinking, it might be a good thing.

Canto: Okay, Franklin was exercised by the discharge side of things. He found that pointy objects – we now call them lightning conductors – were most effective at discharging this build-up of charge, and recreating neutrality, the safe, ‘natural’ condition. A great, practical solution for buildings. But he developed a theory of sorts, of zero-sum conservation of this thing called charge. Whatever was accumulated in, say, a Leyden jar, was restored on discharge, nothing gained and nothing lost. I think.

Jacinta: Well, here’s a quote from Crump’s book, which might unenlighten us further:

Franklin succeeded in giving Leyden jars both positive and negative charges, and showed that the force itself was stored in the glass of the jar with the charge being proportional to its surface area.

Canto: Yeah, that needs unpacking, if possible. The ‘force’ being stored, is that the charge? If so, why does he use different terms? Charge is either negative or positive, isn’t it? So he was able to give these jars either a negative or a positive charge/force, but not both at the same time, though it’s ambiguous in this quote.

Jacinta: What I think he’s saying is there’s this force, which we now call electricity, which can either be negatively or positively charged, and its strength will be proportional to the surface area of the glass jar. I don’t think he was giving the jar different charges at the same time, but how he knew that the charge was sometimes positive, sometimes negative, or what that even means, I’ve no idea.

Canto: Yes, I’m more confused than ever. Let’s try to understand Leyden jars a bit more. Apparently it was invented in 1745 by one Pieter van Musschenbroek as a ‘cheap and convenient source of electric sparks’. That’s from Britannica on electromagnetism. So, to be more precise about this first jar, it was a glass vial partially filled with water, which ‘contained a thick conducting wire capable of storing a substantial amount of charge’.

Jacinta: Presumably that ‘thick conducting wire’ corresponds to the ‘metal chain’ in Crump’s description. I don’t know what the water’s for.

Canto: And Britannica makes no mention of the ‘separate layers [how many???!!] on the inside and outside surfaces’.

Jacinta: Okay, here’s a simplified picture, which might help.

So, in this one there’s no water, but I’ve seen other pics that indicate a jar more than half-filled with water, so who fucking knows. Note that there’s one layer of tin foil on the outside and another on the inside. Note the metal rod passing through a cork into this evacuated jar, and then a wire, presumably of some kind of metal, connecting to the tin foil.

Canto: Is tin a good conductor?

Jacinta: Apparently so. Not as good as silver or copper, but better than lead. And please don’t ask me why some metals are better conductors than others. It’s so frustrating trying to learn from the internet, even when you know which sites to avoid. For example, take this statement on what I’d expect to be a reliable site:

Although Leyden Jars allowed the storage and dissipation of electricity, there were still issues present. One issue was the lack of energy from the charge. While it could only attract small objects like a bit of paper, that was all it could basically do. Also, it could only perform that function after the jar was charged, which also took lots of time.

And then this, from Britannica:

The Leyden jar revolutionized the study of electrostatics. Soon “electricians” were earning their living all over Europe demonstrating electricity with Leyden jars. Typically, they killed birds and animals with electric shock or sent charges through wires over rivers and lakes. In 1746 the abbé Jean-Antoine Nollet, a physicist who popularized science in France, discharged a Leyden jar in front of King Louis XV by sending current through a chain of 180 Royal Guards. In another demonstration, Nollet used wire made of iron to connect a row of Carthusian monks more than a kilometre long; when a Leyden jar was discharged, the white-robed monks reportedly leapt simultaneously into the air.

Canto: Hmmm. One of these descriptions is not like the other. Where’s Micky Faraday when you need him?

Jacinta: I can but do my best. Let’s get back to batteries, again. Franklin’s ‘battery’ was really a capacitor, as mentioned, a way of accumulating more electric charge, and temporarily storing it, until it was required for a sort of ‘big bang’ release, I think. You can do this with Leyden jars linked together:

The above ‘device’ was used for demonstration purposes back in the day. Franklin’s electrostatic machine, though, didn’t look anything like this. It was a mammoth device of cranks and pulleys, created with much help from his friends. The mechanisation was presumably for creating as great an accumulation of charge as possible. Crump writes that Franklin built a glass and lead battery consisting of eleven condensers connected in series – which is clearly not his electrostatic machine. And apparently it wasn’t a battery, either, at least not in the modern sense. And WTF is a condenser? Anyway, this confusion has gone on long enough. We’ll try to clear some of it up next time.

References

Thomas Crump, A brief history of science

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

https://en.wikipedia.org/wiki/St._Elmo%27s_fire

https://www.britannica.com/science/electromagnetism/Invention-of-the-Leyden-jar

https://www.bluesea.com/resources/108/Electrical_Conductivity_of_Materials

https://en.wikipedia.org/wiki/Franklin%27s_electrostatic_machine

 

Written by stewart henderson

December 6, 2021 at 10:57 pm

What is electricity? part 1 – static electricity, mostly

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'Ben Franklin acquiring electricity', filched, methinks, from Reddit

Canto: So it seems we’ve been here before but we’re back at the beginning again, because we’re still largely ignorant. And sadly, even if we finally get a handle on this complex phenomenon, we’ll be likely to forget it again through disuse, and then we’ll die.

Jacinta: So let me begin as naively as possible. Electricity is this energy source, or comes from this energy source, which travels through a wire by some kind of force that excites the electrons in the wire, which then oscillate and create an energy transfer along the wire, to a connector to a light bulb or a toaster, and when a switch connects the wire to the toaster it heats up your bread. But electricity doesn’t have to travel though a wire because I think lightning is electricity, but it needs a conducting material, which in the case of lightning is probably water vapour. I’ve heard somewhere that water is quite a good conductor of electricity.

Canto: Well, all that may or may not be true but what is voltage, what is current and why are certain materials conductors, and superconductors, electrically speaking, and what is an electric field? And I’ve heard that electrons really do flow in a wire, rather than just oscillating, though I’ve no idea what to make of that. 

Jacinta: My next step is to look for experts, and to try to put their explanations into my own words, for ownership purposes. So I went to the ‘expert site’, Quora, and found quite a few contradictory or confusing responses, but assuming that the response that comes up first is some kind of popularly selected ‘best’ response, I’ll focus on Anthony Yeh’s answer. Oh by the way, the question is something like ‘what do electrons actually do in an electrical circuit?’ – though even that requires prior knowledge of what an electrical circuit actually is. 

Canto: So let’s see if we can bed down the concept of an electrical circuit. So a website called ‘all about circuits’ gives us the basics, starting with static electricity. This was probably woman’s first discovery relating to the electrickery thing. Two different materials rubbed together – glass and silk, wax and wool – created this stickiness, this attraction to each other. And then it was noticed that, after the rubbing, the identical materials, such as two glass rods, exerted a force against each other. And another observation was that the wax, after rubbing with the wool, and the rod after rubbing with the silk, attracted each other.

Jacinta: Yes, this must’ve seemed quite bizarre to first discoverers. And they found that it worked as a sort of law. If the item was attracted by glass it would be repelled by wax – that’s to say, two rubbed wax cloths would always repel each other, as would the two rubbed glass rods. Which led to speculation about what was going on. The materials didn’t appear to be altered in any way. But they behaved differently after rubbing. Seemed like some invisible, quasi-magic force was in operation. 

Canto: One of the earliest speculators that we know about was Charles du Fay (1698-1739). Note the dates – we’re really into the period inspired by Galileo, Newton and Huygens, the early days of theoretical and experimental physics. He separated the force involved into two, which he called vitreous and resinous. They were at first thought to be caused by invisible attractive and repulsive fluids. They later came to be known as positive and negative charges. 

Jacinta: But when Benjamin Franklin (1706-90) came to experiment with what became known as electricity, it was still thought of as a fluid…

Canto: But hang on – this static electricity stuff must go back way earlier. Sparks fly, and you feel the energy on your skin when you remove, say, a piece of nylon clothing. And you see the sparks in the dark. I get it from metal door-handles quite regularly, and you can actually see it – it ain’t no fluid. Surely they noticed this way more than a couple of hundred years ago. 

Jacinta: Okay let’s go back thousands of years, to Thales of Miletus, about 600 BCE. I’m using Quora again here. He noticed that rubbed amber was able to attract stuff, like leaves and other ground debris. Theophrastus, a student of Plato and Aristotle, who took over Aristotle’s Lyceum, also left some notes on this phenomenon, but this didn’t get any further than observation. William Gilbert (1544-1603), a much under-rated genius whom I read about in Thomas Crump’s  A brief history of science, wrote a treatise, On the magnet, which compared the attractive, magnetic properties of lodestones with the properties of rubbed amber. He called this property ‘electric’, after elektron, the Greek word for amber. He also built the first electroscope, a simple needle that pivots toward an electrically charged body. Gilbert was able to distinguish between a magnet, which always remained a magnet, that’s to say, an attracter of metals, and an electrically charged material, which could easily lose its charge. So we’re now into the 17th century, and very far from understanding the phenomenon. The first electrical machine was constructed by Otto von Guericke (1602-86), another interesting polymath, in 1660. It was a rotating globe of sulphur, which attracted light material, creating sparks. Nothing new of course, but a useful public demonstration model.

Canto: So we’re now getting to a period when a few enlightened folks were set to wondering. And this was when they must’ve noted the phenomenon’s small-scale similarity to lightning.

Jacinta: Yes, and so experiments with lightning were undertaken in the eighteenth century, generally with disastrous results. The fact is, though Ben Franklin did do some experimentation with kites and lightning, he mainly focused on glass and amber rods. He noted, as before, that there were two different forces, or charges, attractive and repulsive. When a rubbed amber rod was brought toward another rubbed amber rod they repulsed each other. When the same amber rod was brought toward a glass rod, they were attracted. He considered there were two opposite aspects of the same fluid (for some reason investigators – at least some of them – was still thinking in terms of fluids). The identical aspects of the fluid repelled, while the opposite aspects attracted. He decided, apparently quite arbitrarily, to name one (glass) positive, the other (amber) negative. And we’ve been stuck with this designation ever since..

Canto: Yes, I’ve heard that it would have been much better to name them the other way round, but I’ve no idea why. And also, why is all this called static electricity? Obviously that name came later, but what does it mean? We hear people saying ‘I’m getting a lot of static’, which seems to mean some kind of interference with a signal, but I’ve no idea why it’s called that. 

Jacinta: Oh shite, we’ll never get to the bottom of all this. Here’s a Wikipedia definition, which might help:

Static electricity is an imbalance of electric charges within or on the surface of a material. The charge remains until it is able to move away by means of an electric current or electrical discharge. Static electricity is named in contrast with current electricity, which flows through wires or other conductors and transmits energy

Canto: Okay, that helps. Static electricity ‘remains’ – it has to be discharged. So lightning is a discharge of static electricity? 

Jacinta: I believe so, and that spark you get from the car doorhandle is a discharge of the static electricity built up in your body. Now let’s return to the online textbook ‘All about Circuits’. It points out that Ben Franklin did have a reason for his positive-negative designation. Here’s a quote: 

Following Franklin’s speculation of the wool rubbing something off of the wax, the type of charge that was associated with rubbed wax became known as “negative” (because it was supposed to have a deficiency of fluid) while the type of charge associated with the rubbing wool became known as “positive” (because it was supposed to have an excess of fluid). Little did he know that his innocent conjecture would cause much confusion for students of electricity in the future!

Canto: Okay, I’m not sure whether this is a headfuck. When wax is rubbed with wool they attract each other. Franklin thought in terms of fluids, and he conjectured that, in the rubbing, the wool removed fluid from the wax – so wool had an excess of the fluid, and wax had a deficiency. The deficiency, which of course wasn’t really a deficiency, he termed ‘negative’ and the excess was ‘positive’. Sort of makes sense. Though why people since have felt this is the wrong way round, I don’t get at this stage. 

Jacinta: So now we come to Charles-Augustin de Coulomb (1736-1806), and I suspect we’ll be dwelling on him for a while, because ‘All about circuits’ deals with him rather cursorily, methinks. It tells us that Coulomb experimented with electricity in the 1780s using a ‘torsional balance’ (wtf?) to measure the force generated between two electrically charged objects. 

Canto: Exquisitely meaningless at this stage. Anyway, onward and downward…

References

https://www.quora.com/How-do-electrons-flow-in-a-circuit-Do-the-electrons-literally-move-or-is-there-just-a-transfer-of-energy-I-read-somewhere-that-the-direction-of-the-electrons-is-generally-unknown-Is-this-true

https://www.allaboutcircuits.com/textbook/direct-current/chpt-1/static-electricity/

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

https://www.quora.com/What-were-static-electricity-shocks-believe-to-be-during-antiquity-and-the-Middle-Ages

Thomas Crump, A brief history of science, 2001

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

Written by stewart henderson

November 28, 2021 at 8:52 pm

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 lightning, 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: 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