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Posts Tagged ‘electromagnetism

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

on electrickery, part 2 – the beginnings

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William Gilbert, author of De Magnete, 1600

Canto: So let’s now start at the beginning. What we now call electricity, or even electromagnetism, has been observed and questioned since antiquity. People would’ve wondered about lightning and electrostatic shocks and so forth.

Jacinta: And by an electrostatic shock, you mean the sort we get sometimes when we touch a metal door handle? How does that work, and why do we call it electrostatic?

Canto: Well we could do a whole post on static electricity, and maybe we should, but it happens when electrons – excess electrons if you like – move from your hand to the conductive metal. This is a kind of electrical discharge. For it to have happened you need to have built up electric charge in your body. Static electricity is charge that builds up through contact with clothing, carpet etc. It’s called static because it has nowhere to go unless it comes into contact with a positive conductor.

Jacinta: Yes and it’s more common on dry days, because water molecules in the atmosphere help to dissipate electrons, reducing the charge in your body.

Canto: So the action of your shoes when walking on carpet – and rubber soles are worst for this – creates a transfer of electrons, as does rubbing a plastic rod with wooden cloth. In fact amber, a plastic-like tree resin, was called ‘elektron’ in ancient Greek. It was noticed in those days that jewellery made from amber often stuck to clothing, like a magnet, causing much wonderment no doubt.

Jacinta: But there’s this idea of ‘earthing’, can you explain that?

Canto: It’s not an idea, it’s a thing. It’s also called grounding, though probably earthing is better because it refers to the physical/electrical properties of the Earth. I can’t go into too much detail on this, its complexity is way above my head, but generally earthing an electrical current means dissipating it for safety purposes – though the Earth can also be used as an electrical conductor, if a rather unreliable one. I won’t go any further as I’m sure to get it wrong if I haven’t already.

Jacinta: Okay, so looking at the ‘modern’ history of our understanding of electricity and magnetism, Elizabethan England might be a good place to start. In the 1570s mathematically minded seamen and navigators such as William Borough and Robert Norman were noting certain magnetic properties of the Earth, and Norman worked out a way of measuring magnetic inclination in 1581. That’s the angle made with the horizon, which can be positive or negative depending on position. It all has to do with the Earth’s magnetic field lines, which don’t run parallel to the surface. Norman’s work was a major inspiration for William Gilbert, physician to Elizabeth I and a tireless experimenter, who published De Magnete (On the Magnet – the short title) in 1600. He rightly concluded that the Earth was itself a magnet, and correctly proposed that it had an iron core. He was the first to use the term ‘electric force’, through studying the electrostatic properties of amber.

Canto: Yes, Gilbert’s work was a milestone in modern physics, greatly influencing Kepler and Galileo. He collected under one head just about everything that was known about magnetism at the time, though he considered it a separate phenomenon from electricity. Easier for me to talk in these historical terms than in physics terms, where I get lost in the complexities within a few sentences.

Jacinta: I know the feeling, but here’s a relatively simple explanation of earthing/grounding from a ‘physics stack exchange’ which I hope is accurate:

Grounding a charged rod means neutralizing that rod. If the rod contains excess positive charge, once grounded the electrons from the ground neutralize the positive charge on the rod. If the rod is having an excess of negative charge, the excess charge flows to the ground. So the ground behaves like an infinite reservoir of electrons.

So the ground’s a sink for electrons but also a source of them.

Canto: Okay, so if we go the historical route we should mention a Chinese savant of the 11th century, Shen Kuo, who wrote about magnetism, compasses and navigation. Chinese navigators were regularly using the lodestone in the 12th century. But moving into the European renaissance, the great mathematician and polymath Gerolamo Cardano can’t be passed by. He was one of the era’s true originals, and he wrote about electricity and magnetism in the mid-16th century, describing them as separate entities.

Jacinta: But William Gilbert’s experiments advanced our knowledge much further. He found that heat and moisture negatively affected the ‘electrification’ of materials, of which there were many besides amber. Still, progress in this era, when idle curiosity was frowned upon, was slow, and nothing much else happened in the field until the work of Otto von Guericke and Robert Boyle in the mid-17th century. They were both interested particularly in the properties, electrical and otherwise, of vacuums.

Canto: But the electrical properties of vacuum tubes weren’t really explored until well into the 18th century. Certain practical developments had occurred though. The ‘electrostatic machine’ was first developed, in primitive form, by von Guericke, and improved throughout the 17th and 18th centuries, but they were often seen as little more than a sparky curiosity. There were some theoretical postulations about electrics and non-electrics, including a duel-fluid theory, all of which anticipated the concept of conductors and insulators. Breakthroughs occurred in the 1740s with the invention of the Leyden Jar, and with experiments in electrical signalling. For example, an ingenious experiment of 1746, conducted by Jean-Antoine Nollet, which connected 200 monks by wires to form a 1.6 kilometre circle, showed that the speed of electrical transmission was very high! Experiments in ‘electrotherapy’ were also carried out on plants, with mixed results.

Jacinta: And in the US, from around this time, Benjamin Franklin carried out his experiments with lightning and kites, and he’s generally credited with the idea of positive to negative electrical flow, though theories of what electricity actually is remained vague. But it seems that Franklin’s fame provided impetus to the field. Franklin’s experiments connected lightning and electricity once and for all, though similar work, both experimental and theoretical, was being conducted in France, England and elsewhere.

Canto: Yes, there’s a giant roll-call of eighteenth century researchers and investigators – among them Luigi Galvani, Jean Jallabert, John Canton, Ebenezer Kinnersley, Giovanni Beccaria, Joseph Priestley, Mathias Bose, Franz Aepinus, Henry Cavendish, Charles-Augustin Coulomb and Alessandro Volta, who progressed our understanding of electrical and magnetic phenomena, so that modern concepts like electric potential, charge, capacitance, current and the like, were being formalised by the end of that century.

Jacinta: Yes, for example Coulomb discovered, or published, a very important inverse-square law in 1784, which I don’t have the wherewithal to put here mathematically, but it states that:

The magnitude of the electrostatic force of attraction 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.

This law was an essential first step in the theory of electromagnetism, and it was anticipated by other researchers, including Priestley, Aepinus and Cavendish.

get it?

Canto: And Volta produced the first electric battery, which he demonstrated before Napoleon at the beginning of the 19th century.

Jacinta: And of course this led to further experimentation – almost impossible to trace the different pathways and directions opened up. In England, Humphrey Davy and later Faraday conducted experiments in electrochemistry, and Davy invented the first form of electric light in 1809. Scientists, mathematicians, experimenters and inventors of the early nineteenth century who made valuable contributions include Hans Christian Orsted, Andre-Marie Ampere, Georg Simon Ohm and Joseph Henry, though there were many others. Probably the most important experimenter of the period, in both electricity and magnetism, was Michael Faraday, though his knowledge of mathematics was very limited. It was James Clerk Maxwell, one of the century’s most gifted mathematicians, who was able to use Faraday’s findings into mathematical equations, and more importantly, to conceive of the relationship between electricity, magnetism and light in a profoundly different way, to some extent anticipating the work of Einstein.

Canto: And we should leave it there, because we really hardly know what we’re talking about.

Jacinta: Too right – my reading up on this stuff brings my own ignorance to mind with the force of a very large electrostatic discharge….

now try these..

Written by stewart henderson

October 22, 2017 at 10:09 am