an autodidact meets a dilettante…

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

Archive for the ‘electrons’ Category

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

leave a comment »

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 6: ohm’s law, electron flow and ac/dc, not explained

leave a comment »

got it?

Canto: So we were getting into the behaviour of electrons in electrical field or currents, and the different ways electrons behave when voltage or electromotive force is applied to them, depending on the materials in which they’re embedded, whether that material is more or less conductive/resistant.

Jacinta: Which led to our light bulb moment. But we really need to look at electrons and their behaviour more closely, methinks.

Canto: I’ve noticed Quora questions such as ‘Why do electrons move against the electric field?’ and ‘Why do electrons experience force in direction opposite to electric field?’ Amongst other confusing things, responders note that there is simply a convention, created by Franklin. The convention being, I think, that electric fields/currents flow from positive to negative. This isn’t entirely clear to me, though I get the idea of conventional designations.

Jacinta: A number of responders point out, in different ways, that an electric current, say from a battery, flows from the positive terminal to the negative terminal. Electrons, being negatively charged, are repelled by the negative terminal and attracted to the positive terminal, due to the rule that like charges repel and opposite charges attract. So electrons flow in the opposite direction of the current/field. Which raises the question of why currents flow from positive to negative (presumably that’s just the convention).

Canto: So if the convention was turned around and we describe the flow as being from negative to positive, then we’d recognise the flow of electrons as going in that direction? I mean, which way do electrons flow really?

Jacinta: This might be a non-issue. A circuit attached to a voltage generator, such as a battery, sends the electrons in the direction of the current, which is arbitrarily designated as from the positive terminal to the negative one. Sounds like the electrons, negatively charged, are being pushed to the negative terminal, which would be expected to repel them, but that isn’t what’s happening. The electrons are just flowing in the direction of the current. Better to call the terminals A and B.

Canto: But if that was so, there’s an easy fix – we’d stop referring to those terminals as positive and negative. But I don’t think it is so. In one video I’ve watched, a battery is described as something which has two terminals, positively and negatively charged points, with a charge imbalance between them. The electrons are definitely described as being ‘pushed’ by the current from the negative point or terminal to the positive one, as you’d expect with opposite charges attracting. Though it also says that the flow of the charge is opposite to the flow of electrons, something to ponder. It also describes the negative point as a source, and the positive point as an attractor. The two-pronged electrical plugs use this system, one being the source, the other the attractor. And a ‘short circuit’ involves wires burning out because there is no resistance in the circuit – that’s to say, no appliances which work by applying resistance, which creates energy to run the appliance, as we saw with an incandescent bulb. Fuses act to prevent short circuits, cutting the current when the wire overheats.

Jacinta: Well, we seem to be learning something. This is better than a historical account it seems. But there are still so many problems. The ‘electricity explained’ video you’ve been describing says that the negative point is the source. So it’s saying negative to positive, simply ignoring the positive to negative convention. Perhaps we should too, but the video makes no mention of the convention, which confuses me.

Canto: Well, let’s push on. We’ll need to understand electrical fields, and of course the difference between ac and dc, and probably a host of other things, before we return to the historical discovery stuff, which of course is fascinating in its own quite different way.

Jacinta: Absolutely. And the relationship between electricity and magnetism, and Maxwell’s equations, haha. All without ever doing anything hands-on.

Canto: So I’m watching the apparently somewhat notorious recent Veritassium video on the subject, and I’ve learned in the first minute or so that a battery uses dc electricity whereas the grid connected to our homes uses ac. Though I knew that about the grid. Not that I know what it means exactly.

Jacinta: Yes, and he then says that in ac the electrons are just wiggling back and forth – as ‘alternating current’ suggests. But as mentioned earlier, I thought that was always the case – or, no, the electrons don’t flow, they just bump each other along, which obviously isn’t the same as ‘wiggling’. Each electron has moved, but only slightly. And I never thought of this in ac or dc terms.

Canto: So I’ve just watched the whole video, and I think I’ll pass on commenting at this stage. Obviously I don’t understand it all, nor do I understand the comments, many of them highly detailed.

Jacinta: Yes I think we should get our heads around the ac/dc stuff, and fields, then maybe get back to it.

Canto: This’ll probably take a lifetime, but we’ll start with direct current, dc. Your basic AA or AAA battery is a source of direct current. I’m looking at a typical AA 1.5 volt battery. It will provide 1.5 volts of, errr, voltage constantly in a circuit. Until it doesn’t. But also the circuit will have a resistance, measured in ohms, and we need to remember Ohm’s Law, from part 5, V (or E) = IR. That’s to say, the voltage is the current (I, in amps) multiplied by the resistance. I don’t know why that is, of course, but in any case a circuit connected by a certain voltage of battery will produce a particular current depending on the size of the resistance.

Jacinta: Like the dimensions of a pipe through which water flows. If you have one part of the pipe with a narrowed channel, that will effect the whole flow. The same with a resistor. And of course any wire will have resistance, depending on its conductivity. So why do we multiply the current by the resistance?

Canto: Ohm’s Law can be expressed as I = V/R. Here’s an elaboration of this:

This equation, i = v/r, tells us that the current, i, flowing through a circuit is directly proportional to the voltage, v, and inversely proportional to the resistance, r. In other words, if we increase the voltage, then the current will increase. But, if we increase the resistance, then the current will decrease.

I think it means that voltage will need to be increased to overcome the resistance, which reduces the current. It would be worthwhile to think of this in the brilliant.org way, to solve some simple problems. I’ve used study.com here, a site for engineers and such. Suppose you have a 10 volt battery connected to a light bulb with a resistance of 20 ohms. What is the current in the circuit?

Jacinta: So we have an equation with three variables. The current, in amps, is the voltage divided by the resistance, in this case 10/20, so the current should be 0.5 amps? Wow, I think I done some maths!

Canto: So if we double the voltage in this circuit, we double the current. Now, the great Khan, of Khan Academy fame, describes voltage as electric potential, as we’ve described before, or even energy potential. Think of a closed tap with potential energy. Open it, and you release kinetic energy in the flow. Current is measured as the flow of ‘electricity’, or electrical charge, per unit of time, I = Q/t.  But then he confuses me with coulombs, which I’m not ready for. Q means charge (possibly measured in coulombs), and I’m not sure of its relation to V.

Jacinta: We’re equally confused. Let’s focus briefly on ac electricity. Alternating current involves this ‘wiggling’ of electrons mentioned before. Apparently electrons can be made to wiggle back and forth at particular rates, measured in cycles. Each cycle involves the electrons moving forward and then back to their starting points. In some grids, the electrons wiggle like this at 50 cycles/second, in others, e.g in the US, at 60 cycles/ second, or 60 hertz. How electrons can be made to do this I’m not sure – it presumably involves pulses of force? From both ends? Anyway, this form of electricity is apparently safer because it doesn’t heat up the wires so much. I can’t clearly see why though. But then you need transformers to connect the wires to your house, which uses direct current, I think. And as far as I know, a transformer is, like – here, a miracle happens.

Canto: So, more questions than answers here. What, exactly, is a transformer? How does it work? Why doesn’t ac electricity heat up the wires so much? How exactly is ac electricity created? Does every home need a transformer, or is it one transformer per street, or district….? it just goes on and on…

References

https://www.quora.com/Why-do-electrons-move-against-the-electric-field

What is electricity? – Electricity Explained – (1) , video from Into the Ordinary

https://study.com/academy/lesson/ohms-law-definition-relationship-between-voltage-current-resistance.html

Introduction to circuits and Ohm’s law | Circuits | Physics | Khan Academy

Alternating current, direct current & what is frequency? | Physics | Khan Academy

 

Written by stewart henderson

January 2, 2022 at 11:02 am

What is electricity? part 1 – static electricity, mostly

leave a comment »

'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