an autodidact meets a dilettante…

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

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

Leave a Reply

%d bloggers like this: