The Science of Everything Podcast - Episode 43: Electric Forces and Fields

Episode Date: December 30, 2012

An overview of the basics of electric charges, electric fields, and electric potential energy. I also discuss how objects become charged, how charged particles interact via Coulomb’s Law, how electroscopes work, and how batteries generate voltage. Recommended prerequisites are Episode 9: Matter and Molecules, and Episode 17: Energy, Work, and Momentum.

You're listening to The Science of Everything podcast, episode 43. Electric Fields and Forces. And I'm your host, James Fodor. In this episode, we're going to have a look at the basic concepts of electric charges, electric fields, and electric forces. I'll talk about how, what are charged particles, how charged particles interact with each other via something called Kulom's Law. I'll talk about electroscopes. I'll talk about batteries, potential difference, electric potential energy, and many other

important foundational concepts in understanding electricity. The recommended prerequisite for this episode is episode 9, Matter and Molecules. Without further ado, let's begin. So first of all, some basics on electricity and electric charge. The electromagnetic force, which is what we're going to be talking about throughout this episode, and also some sequels to this, is one of the four fundamental forces of nature. It's also the one that's most important for our sort of everyday existence and interaction. So of the four fundamental forces of nature, two of them, the strong and the weak nuclear forces,

are only relevant at subatomic scales, and so we don't really observe them directly. They're relevant to things like radioactivity and quantum mechanics, but apart from that, they don't really directly intervene in our sort of everyday life. The third is gravity, which is very important in terms of, you know, dropping objects and aircraft flying and the planets orbiting the sun and so forth. But by far the most important from sort of a human perspective is electromagnetism, because electromagnetism is, well, first of all, it's important for keeping atoms together, you know, the electrons bound to the positively charged nucleus.

But second of all, it's also crucial for how macro-scale objects interact. So, for example, the reason that you can't walk through a wall is actually because the electrons of the atoms in the wall are repelling the electrons in the atoms of your body, or out of skin and so on, when you push your hand close enough to the wall. The wall isn't preventing you in some direct sense, because the atoms in your hand never come into direct contact with the atoms in the wall. It's just that the electrons from the wall and hand come close enough together to repel each other. So really what's happening is the wall is repelling you rather than you're sort of directly touching it.

And that's the case for any macro objects, even if they're not charged in an aggregate sense. They're still repelling each other based on the electrons in the outer shells and the atoms. But anyway, some of those concepts I haven't introduced it, but I just wanted to illustrate the fact that electromagnetism is very important for everyday interactions, and it's the force that sort of dominates the human scale of existence. If you go up into looking at things in the size of stars and galaxies, then gravity begins to dominate. you go down to the subatomic level of the weak and strong nuclear forces dominate.

But at our scale, electromagnetism is king. So electromagnetism is so-called because it's sort of got two components or aspects to it, electricity and magnetism. Originally these were thought to be completely separate forces, but in the 19th century it was found that changing electric fields can give rise to magnetic fields, and changing magnetic fields give rise to electric fields. So it was found that they relate to each other.

But we won't really talk about that in this episode. It's just important to understand that the overarching force is called electromagnetism, and the aspect of that force that we're going to look at in this episode. is electricity. So, the first concept that we need to understand in regards to electricity is that of an electric charge. Now, I've mentioned this many times in this and previous episodes, but it's important that we have a clear idea of what it means. An electric charge, or just electric charge, is simply a physical property of matter that causes it to experience a force when it's near some other electrically charged matter. There's two types of electric charge,

positive and negative. There's also neutral, but that's not really a third type. It's just sort of the absence or cancelling out of positive and negative. Electric charge is something that basically fundamental particles have. So an electron is a fundamental particle. You can't break it up and do any smaller particles, as far as we know. It has one property, a fundamental property of an electron, is that it possesses a charge of negative one, an electric charge of negative one.

And that's just sort of intrinsic to an electron. A proton is not a fundamental particle. It's actually made up of even smaller particles called quarks, but for the moment we'll just think of it as fundamental, just to simplify things a bit. It has a charge of positive one, and that's sort of an intrinsic property of a proton. And there are many other particles as well that have their own

associated electric charges. But it's just a fact of the universe that these fundamental particles have charges. Then when you put them together, you can sort of aggregate charges. So, for example, if I bring two protons together, each proton has a charge of plus one. If I bring them both together, then the clump of two protons will now have a charge of plus two. If I bring a million protons together and have no electrons, then I've got a charge of plus a million. If I bring one proton and one electron together and, you know, bring them right sort of into contact with each other or as close as they'll get, then those charges cancel out. And the net charge, as we say, will be zero because plus one, minus one, cancels out to zero.

So there's essentially two ways you can be neutral. A particle or an object can be neutral. One is the complete absence of charge. So something like a photon is electrically neutral because it just doesn't have any intrinsic charge or a neutron is intrinsically neutral. Actually, it's made up of quarks that cancel each other out. But we can just think of it as being intrinsically neutral for our purposes.

But most of the time, that's not what happens. Most of the time, neutral objects, that is objects that have no net charge, are neutral because they have a balance or a close enough balance at least, it doesn't have to be literally exactly the same, but rough balance of protons to electrons. This is the case for most objects in the macro world, trees, cars, people, whatever. For the most part, these objects are neutral, electrically neutral,

because they have basically the same number of protons as electrons, and therefore the charges balance out. Okay, so electric charge just refers to that fundamental physical property. You've got positive charge or negative charge. How do they interact with each other, though? Well, positive charges repel other positive charges, and negative charges repel other negative charges. But, as you probably also know, positive and negative charges attract each other.

So you can remember that by saying, like, charges repel and opposite charges attract. Again, that's just a property of how electricity works. Also, it's important to understand there's no real point, there's no real significance to the words positive and negative. There's no, like, positives are not better than negative in some sense, and they don't really behave differently in any way. They really could just be called type 1 and type 2 of electricity, you know, up and down or left and right. Like, it doesn't make any difference. There's just two types. The yin and the yang, if you will.

Just a word on why electricity and gravity are so different, because this is important to understanding why electricity is dominant in our human-scale macro world. Essentially, the reason is because electricity has two types of charge, positive and negative, which can cancel each other out, and that tends to be what happens. At the very small scale, it's common to find, you know, charged ions or charged molecules, but as you get larger and larger, it's very rare to find a charged house or a charged person.

So the more atoms you tend to get, the more likely it is that charges will balance out. basically because if you had just a massive amount of charge, like if a person, something the size of a person was just completely comprised of protons that had no negative charge at all, say, their positive charge would be so great that the forces that they would exert on surrounding objects would be tremendous and, you know, that bad stuff would happen. Well, not bad stuff would happen, but it would just get crazy. So, in a sense, that sort of object would be unstable, and so we don't observe it.

Gravity, however, there is no possibility of charges cancelling out because there's only one type of gravity. It's always attractive. Massive objects always attract other massive objects. in a sense there's no negative gravity, contrary to what you might hear in some science fiction. And so as the objects that we're talking about get bigger and bigger, their gravitational effects just always increase because there's no way to detract from that, whereas electricity or the electric charge tends to decrease,

or at least it tends to trend towards zero. So something the size of a planet is almost certainly going to be basically electrically neutral, but it's going to have a big gravitational influence. So that's why electricity dominates the scale of humans, but gravity dominates the stellar scale once you get big enough objects that gravity has enough of a, that there's enough gravity, gravity to dominate electricity. And by the way, the reason that the strong and weak nuclear forces aren't dominant is simply that they don't act over a very long distance. They taper off very

quickly. Gravity and electricity taper off with distance as well, but not nearly as fast as the two nuclear forces do. Okay, so now that we've established what charges are and how they repel or attract each other, we'll talk a little about static electricity. So when people say static electricity, they're usually referring to things like shocks that you get by when you touch a car door sometimes after you've been driving or when, or if you pick up a woolen jumper after walking over carpet or stuff like that. Basically, those little shocks you get occasionally when you've been rubbing against something usually. The phenomenon of static electricity basically occurs because when certain materials are rubbed together, you can move charged particles, generally electrons,

so think of those electrons, you can move electrons from one material to the other. So as an example, if we rub a balloon with a piece of wool, both the wool and the balloon become charged, this is occurring because electrons are moving from the wool to the balloon. Or we can think of it as a rod as well. Rod's probably easier. So if we rub a plastic rod with a bit of wool, you probably see a physics professor doing this at some point in your education. At high school or uni, they like to do this. Rub, plastic rod with a piece of wool. Electrons are transferred just by the sort of action of friction, basically. The physical action of rubbing transfers electrons from the wall to the rod, and therefore both become charged. The rod becomes negatively charged because it's picked up a bunch of

extra electrons, and the wool becomes positively charged because it's lost a bunch of electrons. The wall hasn't gained any positive charge, but by, it already had plenty of positive charge to start with, remember all the protons it had. Previously, it was neutral because it had roughly a balance of protons and electrons, but now a bunch of electrons have been rubbed off onto the plastic, and so there's an excess of protons now, and so the wool becomes positively charged, and the rod becomes negatively charged. Now, the significance of this is that if you were to go and, say, touch the rod, or touch the wool, the electrons in the rod would flow into your hand very quickly and immediately because essentially, remember, the electrons that

are bunched up on the rod are trying to repel each other, or they're tending to repel each other because that's what light charge do repel. And so the electrons are pushing each other away, but they can't move very far apart from each other because they're confined to the plastic rod. Essentially, that's because electrons have a hard time traveling through air. Air is a fairly good electrical insulator, which means electrons can't travel through air very easily. And so they're basically confined to the rod. Once you take your hand and touch the rod, however, your hand is a much better conductor than air, and so the electrons can much easily, more easily move onto your hand,

and they do so because it's essentially energetically favorable, because the electrons are all pushing each other apart, repelling each other, and your hand is neutral. If your hand was negatively charged as well, then the electrons wouldn't have a tendency to move there, but your hand is neutral, so there's, you know, a zero charge in your hand versus a high negative charge on the rod, the electrons are going to move

onto your hand, and that happens very rapidly, and you feel that as a sort of a small electric shock. So that's just charge moving from one place or another. It could be vice versa, as well, if you touch the wood, which is positively charged, then the electrons would do the reverse. They'd move from your hand to the wool, but you feel basically the same thing. So I've just been talking about the different between conductors and insulators. Conductors are substances that allow electricity to

flow through them, and electricity is just the movement of charged particles, generally electrons, whereas insulators are materials that don't allow charged to move through them, so that don't allow electrons to move freely through them. The difference between whether a substances are conductor and insulated essentially depends upon how tightly bound are the electrons. If the electrons are very tightly bound to the atoms, they can't move very freely, and therefore the substances and insulated. So ionic substances tend to be like this because the electrons are all tightly bound up in the ionic structure. Whereas metallic substances, because they have that sea of free electrons surrounding all the atoms, can conduct electricity very easily because

the electrons can move around. See some of the chemistry of those that I've done. I can't specifically remember which one we talked about this, but we've definitely covered some of the properties, conduction and insulator properties of different materials in the past. So that's effectively what determines. And there are other complicating factors as well, but that's basically what determines whether substances is a conductor or an insulator, how tightly bound the electrons are to the nucleus. So, for example, if you charge a metal rod by rubbing it with the wall, it's much easier for you to discharge the metal rod. In fact, it's basically impossible for you to charge the metal rod if you're holding it, because as soon as the charge starts to rub off from the wall onto the metal,

it just flows right into your hand, whereas a plastic rod is an insulator, whereas metals are a conductor. So the insulator, it's much harder for the charge to be transferred. Maybe if you wet your hand and touch the plastic rod, that would help because wet skin conducts electricity better than dry skin. But anyway, so it's harder to discharge a plastic rod just by touching it because it's an insulator much easier to discharge a metal rod because the charge flows so easily through it. But in either way, fundamentally the same thing is happening. You're building up charge by the rubbing action, and the charge can be dispersed again

by coming into contact with a neutral object or an object of the opposite charge. Now, here's another interesting thing that happens. If I charge this plastic rod by rubbing it with the wool again, and then bring it near some small pieces of paper, the rod will actually attract the small pieces of paper. And small pieces of metal, it's not intrinsic to paper, it's just relatively small objects, because large objects have a larger mass, and so it's harder for the relatively weak electromagnetic force, at least on these scales, to have much of an effect on large objects.

So it's not going to pick up a car, but you can observe it by the fact that it will literally pull up small pieces of paper, and the paper will stick to it. The reason this is happening is by what's called induced charge. Now the pieces of paper themselves are electrically neutral because pretty much all objects by default are electrically neutral. The rod we know is negatively charged. What's happening is that the negative charges in the rod are essentially, they're exerting a repulsive force on all negative charges around them.

Not just the negative charges in the rod, but the negative charges in the air and also the negative charges in the pieces of paper. So it's pushing all of these negative charges away. Within the piece of paper, remember that the electrons can't really get out of the piece of paper and move into the air because the air is an insulator. What they can do, however, is move from one side of the piece of paper to another. I'm not sure how good a conductor or a piece of paper is, but it's good enough so that the electrons can be forced to move to the other side, or at least move some distance toward the other side. It's not necessarily the case that each electron literally moves to the very far other side of the paper,

but at least on average, the electrons in the paper tend to move somewhat away from the rod, because they're being repelled by the excess of electrons in the rod. Now, when that happens, we set up something that is called an induced dipole. A dipole is just when we have two sides of an object that are differentially charged. So in this case, the piece of paper will have a negatively charged side, the positively charged side. The piece of paper as a whole is still neutral, because it's still got the same number of electrons and protons. What's happened is that the electrons and protons have been rearranged,

such that the electrons are bunching up on the side furthest away from the rod, and the protons are sort of bunching up on the side closest to the rod, because the protons are being pulled to the rod, because remember a negative and positive charge attract, whereas the electrons in the paper are being pushed away from the rod because the negative charges in the excess negative charges in the rod are pushing them away. And so we've got a positive and a negative side to the piece of paper, and this is called a dipole.

Now, this dipole is what allows the piece of paper to be attracted to the charged rock, because although the absolute charges on the positive in the negative side of the paper are the same, and remember we know they have to be the same because we started off neutral and all we've done is rearranged charges, so, you know, they still have to add up to zero in a sense. However, the positive charge, the positive dipole, is closer to the rod than the negative side is. And we know this is the case, because the whole point of the dipole

is that the negative charges have been pushed further away from the rod because of the repulsive force. So, as a result of that, the positive charge side is closer to the rod. And this is crucial because the electromagnetic force, or the electric force in this case, decreases in intensity with distance. So that means, although the positive charge is the same as the negative charge on the piece of paper,

the force that's exerted, the attractive force between the negative rod and the positive end of the piece of paper, is greater than the repulsive force between the negative rod and the negative side of the paper. There is still a repulsive force there, but it's less than the attractive force between positive side of the paper and negatively charged rod because of the difference in distance. The positive side of the road, sorry, the positive side of the paper is closer to the rod, and therefore its attractive force overcomes the repulsive force of the negative dipole of the paper. And so overall, there's a net positive force on the piece of paper. And therefore the piece of paper is brought towards and is attracted towards it so literally will move towards the negatively charged rod.

And so this basic story is the same for anything. It's called, it doesn't have to be just pieces of paper, it's just they're a good example. And it's called induced charge. Essentially what happens is that if you have a charged object and move it near a neutral object, the charged object will induce a dipole in the neutral object and then generate an attractive force between the formerly neutral object and still like overall neutral object and the charged object. And this induced force is always attractive, because it'll always be the case that the charges of the same type, as the charged object you're dealing with, whether it's positive or negative charge, will always be pushed further away from the object, and therefore always sort of reduced in their strength. So, if I have a positively charged rod, it will push away the positive charges, and therefore the attractive force between positive and negative charges will be greater than the attractive force between positive and negative charges will be greater than the attractive force between positive and negative. It's the same either way.

Now you might be wondering, what if the neutral object, say the pieces of paper are insulators? Pieces of paper, I don't know how good insulators there are, but say we could use something that's an exceptionally good insulator like certain crystallized structures, for example, where the electrons are very closely bound to their nuclei. Even here, we can still get an induced charge effect, because effectively what happens is, and the details of this are more complicated than we need to go into, but essentially it's because the molecules themselves are rotating around such that the positive ends of the molecules are located. So if we have a negative rod, the positive ends of the molecules are rotating so that they're closer to the negative charge rod and the negative ends of the molecules are further away from the negative charge rod. So it's the same story as before, except that instead of the charges within the object, say within the piece of paper, instead of the charges themselves moving, the molecules inside the object are rotating around. And so instead of one big dipole, you've sort of got many tiny molecular dipoles that are each exerting their own tiny little force, which then add up to to produce a large force. So even if the object that you're inducing the charge unit is an insulator, you'll still have that attractive effect. And it's not just molecules as well.

The same thing can actually happen to individual atoms. You can polarize individual atoms so that there's sort of a negative and a positive charge to the atom by essentially biasing the electron shells, the electron clouds, so that the electrons are more likely to spend time in one side of the atom than another and so on. But if you've listened to the episode on Matter and Molecules, and I think the history of the atom, then you're not talking about there. But the details of that are not crucial. The important thing to understand is that regardless of the type of material, induced charge will still work, and therefore, charged objects can pretty much always attract neutral objects.

And, of course, we know they'll always attract other charged objects that are of the opposite charge, and always repel charged objects that are of the same charge, because that's the nature of electric charge. Now, I mentioned before that the magnitude of the force between two charged objects decreases with distance. This kind of makes sense. It's the same as with gravity, and the same as with the weak nuclear force.

The strong nuclear force is actually kind of weird, but we won't get into that. The actual law, the mathematical law that describes exactly how much the force decreases with distance is called Kulom's law. And it's modeled after Newton's Law of Gravitation. Newton's Law of Gravitation says that the force between two massive objects is equal to, is proportional to, so there's a proportionality constant. But aside from that, is proportional to the product of their masses

divided by the square of the distance between them. So that means as the objects get more massive, the force between them increases with the product of those masses, and as the two objects get further apart, the gravitational force between them decreases with the square of that distance. So that's Newton's law of gravitation. Kulam's law is pretty much exactly the same, except instead of the mass of the object,

we have, into the equation, we put the charge of the objects. So charge is sort of analogous to mass. This harkens back to what I said before, whereby mass aggregates on a large scale, and it never detract from itself. It never cancels out because there's no negative mass, and so that's why gravity is dominant in the large-scale universe, whereas charge does not aggregate because it cancels out,

positive and negative cancel. And so at the large scale, we tend to have neutral objects, and so electromagnetism tends to fade away. So we can see there, in that analogy alone, that charge is sort of analogous to mass. They both refer to how much a given object interacts with the relevant force, charge, the electromagnetic force, and mass, the gravitational force. So in the case of Kulom's law, you multiply the charge of the two objects you're considering together, and then divided by the square of the distance between the charges, and that gives you, and multiplied by a constant, and that gives you the force between them. Now, you might be wondering how this multiplication of the charges

works given that there are two different types of charges. All you have to do is you put a positive in for the positive charge and a negative in for the negative charges. The constant K that we use for the electric force is negative, and so that means that essentially we have a triple negative, which turns into a negative, and therefore the force is negative. That means there's a repulsive force between the objects. The force acts in the opposite direction to the line connecting the two objects, essentially.

If we have one negative and one positively charged object, then we've got a positive times a negative, which leaves a negative, and then we multiply that negative again by the negative on the constant, so a negative times a negative. So essentially we've got a double negative here instead of a triple negative before. That leaves us with the positive sign, so the overall force is positive, and therefore the charges attract each other. So it all works out.

Kulom's all still allows, it was consistent with the fact that positive charges repel and like charges, that like charges repel and unlike charges attract. It just gives us a more precise mathematical way of describing how that happens. Okay, so that's some of the basics we need to understand, about electric charges and induced charge and how they interact with that. Now we're going to talk about the electric field, which is a little bit more abstract, but also very important. So before we talk about the electric field, we need to understand what a field is in general. Now, I have mentioned the concept of a field way back in episode 11 on the origin of the universe

when I talked about scalar fields. The electric field is not a scalar field, is actually a vector field, which is slightly different, but the concept of a field is the same. So a field is an abstract mathematical concept basically, which all it does is it takes all the space around an object, so a three-dimensional space you can think about it, takes the three-dimensional space surrounding an object in all directions, and assigns a number to each point in that space. A vector field is a little bit more than that, because instead of assigning a number to every point in that space, it assigns a vector to each point in that space. And a vector is just like a little arrow. It has a direction and a magnitude. So the larger the magnitude of the vector essentially the longer the arrow is. And the arrow here we can think about as the force that's being exerted, and I'll explain that a little more in detail in a moment. But just think about all these little arrows.

Each little point in space surrounding an object has an arrow associated with it. The arrows are in different directions, and there may be an overall patent to the directions, or they could even be random. And electric field, they won't be random, but just in general, the arrows in a vector field could well be random. There's no rule about what directions they have to point in. It just depends on the particular vector field. So they have a direction and a magnitude. And every point in space has its own little arrow associated with it. That's literally all the vector field is.

It's an abstract mathematical phenomenon. What we can do is we can take this abstract mathematical thing and apply it to understanding how electricity works. It turns out that we can describe the interactions between charged particles as if every charged particle changes the space around it or exert some sort of influence on the space around it. So when I say space, I literally mean like three-dimensional space, and changes the space such that the space around it has an electric field.

So in other words, we can say that each charged particle exerts it's an electric field on the space around it. And what the electric field represents is basically the force that will be exerted on a particular point charge, a tiny positive charge located at that point. So remember, force is a vector. We talked about this in the Newtonian mechanics episode, I think, which means force has a direction and a magnitude. So that sort of makes sense in this concept because the electric field represents a force,

and we know the electric field is a vector field, so it needs to have a vector field needs to have a direction, a little arrow, and a magnitude, so that fits. So each of these arrows represents a force. And what force is it? It's the force that the particle that creates the field exerts on an imaginary tiny positive charge located at that point in the field. So remember, every different point in the field

has its own arrow, and so it has its own force associated with being at that point. Now, you could have different points in the field could happen to have the same magnitude in the same direction, but they needn't have. Every point can have a different vector or a different force associated with it. And this tiny positive charge that I've talked about,

that's a purely imaginary charge. It's not actually there. It's just we're imagining if you put a tiny positive charge at this point, what force would be exerted on this charge and how large would it be and what direction would it be in. And once we know what that is, that is the direction we sort of draw the force line in. It's a little bit hard to explain this without a diagram. I say that rather a lot. But just imagine a particle in the center. This is our particle that creates the electric field. You always have to start with a particle that creates the electric field. Without something to create the electric field, there's just no electric field and nothing happens, and it's very boring.

Once we have something to create the electric field, then a whole bunch of arrows appear. And generally the arrows are the point towards the charge, if it's a negative charge, or away from the charge if it's a positive charge. And the reason for that is, remember, the arrows point in the direction of the force on an imaginary positive charge located at that point. If the particle creating the magnetic field is positively charged, we know that it's going to repel our imaginary positive test charge, and so the arrow should point away from the originating charge.

However, if the originating charge is a negative charge, then the imaginary test particles that we're thinking of will be attracted towards the negative originating particle and therefore the arrow should point towards the negative particle. So this means that electric fields always point away from positive charge and towards negative charges. As I said before, each individual charge creates its own electric field. So technically what we have to do is if we had a bunch of charges,

which is normally what we have if anything interesting is going to happen, then we have to calculate the electric field for each charge separately, and then you can add them up. Electric fields are additives. If I have one charge on the left and one charge on the right, and they're each generating electric fields, then somewhere in the middle of the two particles, I just work out contribution of the electric field from left particle, contribution of electric field from right particle, and add them to each other. And there's a way you can add vectors together.

We need to get into that, but you can do that. And that produces the sort of net electric field at that point. And so if we had three particles, then you just add the contributions to the electric field of each of the three, and so on. And so basically by building up, taking the electric field particle by particle and combining them together, we can work out the electric field for large objects. And there are many, you know, simplifying rules of thumb, such that if you have a big ball of charge, you can usually just treat that as if all of the charge

were located at the central point and just pretend it's all there and calculate the electric field on that basis. So we don't, in practice, we don't have to calculate the electric field for each charge individually. We can sort of use these simplifying rules to just calculate it for this clump of charge

and this clump of charge over here and so on. But conceptually, each charge does produce its own contribution to the electric field. And remember, it's a very important emphasize, these test charges that we are imagining, the positive test charges, they are purely imaginary, so they don't actually exist. If they did actually exist, we would have to then work out their own contribution to the electric field because any charge, you know, has its own electric field. So if we actually put a positive charge in the electric field, that would change the

electric field because the positive charge would generate its own electric field, and therefore you'd have to add the two together. So the positive charge we're imagining is like, if we could just sort of plop a positive charge here, and somehow the positive charge did not exert its own electric field. Now, of course it would, but supposing that it somehow didn't, what force would be exerted on it? And that might sound like it's sort of an old thing to do, but it's just really useful conceptually to be able to do that. Essentially what it's doing is it's just pulling apart the effect on forces and charges of just this one particular source charge or this other particular source, and not worrying about all the other ones. So it's being able to separate the effects

of the electromagnetic force, basically, of different charges, and then you put him together, rather than having to consider everything at once. To emphasize, the electric field only depends upon the positioning and the magnitude, so the charge, of the source charges. It doesn't depend upon what the force is being exerted on, so it's not dependent like on the test charges, because this is purely imaginary. So I've said before that the electric field is a vector field, so it's basically just a bunch of arrows located at different points in space surrounding the source charge, and the arrows point in the direction that force axon, on the positive charge, on the imagining positive test charge. Another way that electric fields are often represented is by lines. Essentially, the reason for that is because if you put lots of arrows near each other,

it starts getting really messy, and it's basically hard to see what's going on. So instead, we draw lines. The lines, you can generally put arrows on them as well, to be clear about which direction it's going on. But it's sort of like instead of having separate arrows, we just combine them together into one big, long line, which we put arrow heads along. And I'll post some diagrams up on this.

You probably know what I'm talking about, because you've likely seen these diagrams before, where it just has lots of sort of, well, not exactly circular, but curves that go out from a single point and the curves move apart from each other and there's arrows along them and they sort of bend around. They kind of look like. They can look spidery or, yeah, it's a bit hard to describe them. Hopefully you know what I'm talking about. If you've ever seen a representation of a magnet or anything like that, or if you've seen someone put iron filings around a magnet, while those are actually magnetic field lines, but they look basically the same as electric field lines.

Anyway, that's what it looks like. So the line representation is not different from the vector representation from the arrows. it's just a different way of representing it. Conceptually, each point has its own arrow, but drawing the lines is just a bit easier. Another important thing to understand about the electric field is that the direction of the arrows, or the direction of the lines,

does not tell you the direction the particle, a particle place that that point is going to move in. It tells you the direction of the force that's going to be exerted. So, for example, imagine that I had an electric field that points east, it just always points east, regardless of, this would be called a static electric field. It's just, you know, if I move 10 metres forward along the electric field, it's still pointing east.

I'd have to give a magnitude as well, but imagine it's a fairly small electric field that's just pointing east. Now imagine I have a proton that comes whizzing in from the south and is going, it's traveling north. And it's traveling north, say, very close to the speed of light. Maybe this is a linear particle accelerator or something. We have a very weak eastward electric field and the positively charged proton is whizzing north, very close to the speed of light. In this case, the proton most definitely will not travel east. In other words, it will not travel in the direction of the electric field, even though that's the direction the arrows are pointing. What will happen is that the electric field will exert a force on the particle shore as it's moving through the electric field.

That's what an electric field does. The arrows tell you the direction the force is going to be exerted in. So that means the proton will be deflected towards the east, because that's the direction than the electric field's pointing in. But because it's traveling north so fast, the degree of deflection is going to be very small. So it's not going to move much to the east at all. It's mainly just zipping north, and that's going to mostly continue. If it was traveling much slower, then the degree of deflection will. would be much greater, because although the force is the same, essentially, the forces are going

to be applied for much longer time, because it takes a lot longer for the electron to pass through the electric field, whereas if it's going near the speed of light, then the proton just zips through and has hardly any time to feel the effect of the force acting on it. So the overall motion of a particle in an electric field, or a charged particle in an electric field, depends upon the existing motion of the particle. So if it's already traveling, you know, substantially fast in one direction, then the the electric field might not change its velocity very much, but if it doesn't have much existing motion,

then the electric field might actually substantially change its motion. The degree to which the motion of a particle is affected by an electric field doesn't just depend on the charge of particle, and the speed of the particle also depends upon the mass of particle, because remember, force equals mass times acceleration, the electric field only tells you the force, and so if a really massive particle won't be accelerated by very much, whereas a small particle that has the same charge will be accelerated much more.

And this is actually how particle accelerators work. Essentially, they exert a known electric or magnetic force. Magnetic fields act sort of similarly, as we'll see in a future. So they exert a known electric or magnetic force on an unknown particle. They see how much it's deflected, and by that they can determine its charge and mass and other things. So that's kind of an interesting application. One final topic that I'd like to talk about before we move on to electric potential is electroscopes. An electroscope is simply a device that detects the electric charge of an object.

So it allows you to tell when something is charged. How does it work? Well, an electric scope is essentially a metal rod suspended vertically with a metal ball at the top and two light metal strips hanging underneath. So you've got a ball on the top, a metal rod, two strips hanging underneath, sort of hanging vertically down under the influence of gravity initially. Now, what we do is we bring a charged object and we touch it on the metal ball on the top of the electroscope, because metal is a conductor of electricity, the charges from the charged objects are going to flow into the metal ball and then down through the metal rod, and onto the small light metal strips. So saying that the initial object we have is positively charged, it doesn't really matter, but it could be negative charge.

We'll do the same thing, but we'll just imagine it's positively charged for this example. The positive charges move onto the metal ball, down the metal rod, and onto the metal strips. Actually, it could well be the other way. It could be negative charges moving from the metal rod and strips and so on onto the positively charged object, which then sort of gets diminished the electric. the negative charges coming onto it diminish the degree of the positive charge, and it sort of becomes more neutral, but it doesn't really matter.

Positive charges are moving one direction, or negative charges moving the opposite direction, it has the same net effect, in that the electroscope becomes charged. Now, because the two metal strips are fairly light, when they become charged, so when the charge comes and settles on the light metal strips, because they're fairly light, they will actually exert a substantial repulsive force on each other, because the strips are separate from each other, and, but they will nevertheless acquire the same charge, whether it be positive or negative, because they're both connected to the same metal rod in the electroscope.

So, say they both become positively charged, the two metal strips become positively charged, and therefore, you know, two positively charged objects that repel each other. So the metal strips repel each other and push each other apart. And the way we see that is the metal strips, instead of hanging down vertically, they start to rise. And at the very extreme, they could be completely horizontal, because that would essentially represent the metal strips being as far away from each other as they could be. You can imagine the ends of the metal strips being as far away from each other as they could be, whereas if the metal strips were hanging down, the tips or the ends of the metal strips would be quite close to each other. If they're horizontally pointing in opposite directions, the ends of the two metal strips are as far away from each other as they can be.

So the greater the degree of charge on the electroscope, the further away, or the more the electric strips, sorry, the metal strips repel each other, and the closer they get to the horizontal. That is how an electroscope allows us to measure the degree of electric charge. We take our object that we want to determine the charge of, touch it on the electroscope, or even just move it close enough to the electroscope for a current flow, but generally we touched on the metal ball on the top, charge flows down through the rod, onto the strips at the ends, and the more the ends move up and push away from each other, then the more highly charged was the original object.

If they don't move up at all, like there's literally no movement, then the initial object wasn't charged. It was neutral because nothing happened. So that's an electroscope. Again, that's something you may have seen demonstrated before. It's sort of similar in its basic obloration to a vandergraph, generator, which uses a band which spins around rubbing off electrons, and the electrons move onto a top metal ball, which then you can put your hands on, and your hair will stand on end.

The reason for that is essentially the charge is flowing from the metal ball through your hands into your hair. Your hair is becoming charged, whether it be negative or positive charge. I think it's negatively charged. The strands of your hair are then repelling each other, and so the way they can sort of best repel each other is to rise up and point away from each other. So it's a very similar effect where basically you're transferring charge from one region to another to small object which then sort of begin to repel each other.

And if the charge on the Vandigraph generator becomes sufficiently large, then you can get sparks flying off. The spark itself is just a visual manifestation of charge very rapidly moving from the Vandigraph generator to say your hand or a rod held near the Vandigraph generator or wherever else the spark is moving towards. And that's essentially the Vandigraph generator discharging, the negative charges, pushing away from each other

and moving to something that's more neutrally charged, so as to balance out that charge. Finally, to finish up the episode, we'll talk a little bit about electric potential and electric potential energy. So, so far we've talked about electric charges and electric fields, but electric potential is something different again, although it's closely related. Electric potential energy is a form of potential energy, so it's measured in joules, which is the main unit of measurement of energy. And electric potential energy results from electric forces, from the potential energy that objects could gain from moving down an electric field. Probably the easiest way to understand electric potential energy is to imagine, is to gravitational potential energy, and indeed it is very similar.

Gravitational potential energy is essentially the energy that an object has as a result of its position relative to another massive object. If I'm located far above the surface of the Earth, then I have the potential to sort of fall down to earth, and in fact I will do that unless something is prevent me from doing it. That's because I have gravitational potential energy. I'm located away. I'm a massive object, because I have mass, located far away from another massive object. and so the force of gravity would tend to pull us together.

If I'm prevented from doing that by something else, say I'm standing on something, then I still have the potential energy to make that fall, to essentially move to a level of lower potential energy inside the gravitational field or the gravitational well of the earth. The same thing happens with electric charges. If I have a positive and a negative charge, and I separate them, the charges have potential energy, because essentially if I let them go, if I allowed the charges to attract each other,

they would move towards each other. One way we could think about it is if I had the two charges and somehow held them, maybe I'm trapping them in some other electric field or something, or a magnetic field even, if I held them apart from each other, and then all of a sudden let them go, they would accelerate towards each other and essentially come together. As they did that, they would gain kinetic energy. Where has that kinetic energy come from?

We know that energy has to be conserved, so the kinetic energy can't have just come out of thin air. Well, the source of the kinetic energy is the conversion of the electric potential energy that the two charges had when they were held far apart from each other, As the charges move towards each other, that electric potential energy is converted into kinetic energy. And when the two charges collide, well, the kinetic energy might be converted into a different, well, might stay kinetic energy, because maybe the particles will rebound, or maybe it'll be converted into heat or light or something like that.

But the energy will be conserved in any case. But the main point is that the electric potential energy, we know it exists, because if you let the particles go, they move towards each other and gain a kinetic energy, while that kinetic energy has to come from somewhere. So the potential energy is that the store that you have, by sitting uphill from another particle. If I'm a negatively charged particle and I'm held at some distance from a positively charged particle,

that's like sitting uphill in an abstract sense. In this case, it's an electric potential energy sense instead of a gravitational potential energy sense, but in both cases, it's sort of sitting uphill from the other particle. If I let it roll down the hill, then it loses electric potential energy, but gains kinetic energy as it rolls down. So if I have a positive charge and a negative charge,

and I separate them, you can think about the positive charges being at the bottom of a valley and the negative charges being at the top of a hill, or vice versa, it doesn't really matter which one's which, as long as one's on the top and one's on the bottom. And if I allow them to come to each other, then the electric charge rolls down from the top of the hill into the valley, and reaches the sort of low energy situation where both the charges are right next to each other, because opposite charges attract. However, if I had two positively charged particles, and I put them next to each other,

that would be a representation of that would sort of be that both of them were located at the top of a hill. And if I let them, you know, if I let them go and allow them to move naturally, they would be repelled from each other, and so they would both sort of, you can think of it as rolling down on opposite sides of the hill into moving further apart from each other and therefore moving into a lower energy position. Like charged particles tend to push away from each other and so their electric potential energies are shaped such that they tend to do that. You know, so if they're both near each other, that's actually the top of a hill. They have high electric potential energy when they're near each other because they tend to push each other apart. Whereas opposite charges have high electric potential energy when they're far apart from each other because they tend to come together. Another way of thinking about it is, if I I started with these two charged particles right next to each other. How could I get them far apart from each other? In the case of the two charged particles that had the same charge, I wouldn't have to do anything. I'd just have to let them move apart from each other.

In fact, I'd have to do work in order to stop them. Well, I wouldn't have to do work, but I'd have to exert a force in order to stop the particles from moving apart from each other. So that tells me that they actually lose energy, like it's energetically favorable for the particles to move apart from each other. Whereas if the particles were oppositely charged, I would have to actively do work.

Like, I'd have to physically pull them apart. I'd have to do work, expend energy in order to do that. So that tells me that it's energetically unfavorable for them to move apart. So essentially, I'm pushing the particle uphill in moving them away from each other, the positive and the negative charge. So that's what electric potential energy represents. Basically how far uphill you are in the energy level, a potential energy level sense of things.

The higher the hill, the greater the energy gain there would be in terms of allowing the two particles to come together or allowing you to push apart from each other, depending on whether they're the same or oppositely charged. Now we come to one of the more complicated or at least more confusing things about the electric force, which is electric potential. Electric potential in itself is not too hard to understand. It's just hard to understand because we just talked about electric potential energy. So electric potential and electric potential energy are different things.

They're closely related, but they are different. So basically one just has the word energy tacked on the end and the other one doesn't. The difference between them is that electric potential is basically just electric potential energy, so that's in jules. of any charged particle at a given location, because of course we know that the electric potential energy depends on the charge of the particle, and depends on where you put that particle, it depends on the location of the particle, just like my gravitational potential energy depends on my mass and the mass of the earth, and it depends on where I am relative to the earth. If I'm right on top of the earth, I have low gravitational potential energy, because I can't really fall anywhere.

If I'm high up, I have high gravitational potential energy because there's a long distance I go fall. Same thing with charged particles. So the electric potential energy of a given charge particle at a given location is equal to the electric potential energy of that particle of that location divided by the charge of that particle. And this is the extra bit. So when we have, to get from electric potential energy to just plain old electric potential, we take the electric potential energy at a given point and divide by the charge of that particle. So because we are dividing by the charge of the particle, electric potential is only a property of the electric field itself, not of the particle we have there.

So, to take our gravity example again, the sort of gravitational version of this, it would be like taking the gravitational force between me and the earth and dividing it by my mass. So doing that would cancel out my mass, and so my mass wouldn't be a factor anymore. Because remember, the magnitude of the force between me and the earth, depends on the Earth's mass

and on my mass. If I then divide out my mass, the only factor left is the, well, the distance between us, but crucially, the mass of the Earth. Same thing with electric particles. If I have a positive charge and a negative charge, say the positive charge I'm going to call my source charge and the negative charge, my test charge. The force between positive and negative charges,

or in other words the electric potential energy, because they're very closely related, will depend upon the distance between the source and the test charges and also on the relative sizes of their charges, depending on how positively or how negatively charged they are. However, the electric potential of those charges would only depend upon the magnitude of the positive source charge and the distance between them, but it doesn't depend upon the magnitude of the negative test charge,

because to get from the electric potential energy to the electric potential, I had to divide by the charge of the test charge. That's the whole point of electric potential. It cancels out or divides out the effect of the charge of the test particle, just leaving the effect of the source particle. Now, of course, it's kind of arbitrary. Which charge do I treat as the source and which charge do I treat as the test charge? So which one do I divide out?

It doesn't really matter. It just depends on what you're interested in. Am I interested in the electric potential of the positive particle, or am I interested in the electric potential of the negative particle? So you can do it either way. It just depends on what your reference is, what you're looking at. So this means that the electric potential is a property of only the source charge. So it's the property of that particular charge, whereas the electric potential is a property of a system of charge particles, because electric potential energy is only relevant when you have more than one particle.

To take the example of gravity again, if I just had Earth and no other objects anywhere near it, then there's no gravitational forces, You can only have gravitational forces when you have two massive objects. Similarly, you can only have electric forces when you have two or more charged particles. If you just had one charge particle, nothing happens. So there's no electric potential energy if there's only one charge particle. You can only have electric potential energy if there are two or more charged particles. And so that's why we say electric potential energy is the property of a system of particles,

so a bunch of particles, and not just a single particle. However, electric potential is just the property of one charge, because it's canceling out. It's like electric potential energy, except that it cancels out the effect or the charge of the test charges. So it's just looking at one charge at a time. So electric potential is very similar to the concept of the electric field. Remember, electric field too is only a property of the source charge that are being affected by the field, just the source charge. Same with electric potential potential, it only depends upon the source charge. I said before that electric potential energy

is measured in joules because of this type of energy. We know that to get from electric potential energy to electric potential, you have to divide by the charge of the test particle. So charge is measuring in couloms, that's just a measure of charge, coulons all, same thing. So if we divide measuring joules by measuring coolums, we get a measure of joules per coulomb. So therefore, the electric potential is measured in joules per coulom.

Another word for that is the vault, which you've probably heard of before, volts. This is a measure of electric potential. A vault is just equal to 1 jule per coulom. The amount of energy per unit of charge basically. So if something has a high voltage, it basically means there's a lot of energy for each unit of charge there. So this

is what leads to a big misconception, because people often think that if it's something has a high voltage, be it an electrified fence or a battery or whatever, that must mean it has a lot of energy. Not necessarily, because voltage is energy per charge. If you have a very small amount of charge, then the total amount of energy is very small. This is why something like a Vandigraph generator can have an immensely high voltage, but, you know, you touching it's not going to hurt you. Well, it might give you a bit of it, may give you a little bit of pain, but it's not going to cause you any damage. The reason is because, well, among other things, the main reason is that the amount of charge is very small.

the total amount of energy is very small too, and so therefore you're not really in any danger. It's the total amount of energy that is going to affect, you know, heart rhythms and other things like that, not just the amount of charge, the amount of energy per unit of charge, or in other words, not just the voltage. So, understanding the difference between electric potential energy and electric potential is crucial to understanding why voltage alone is not the source indication of whether a given source of electricity is dangerous or not. You need to know both the voltage and the total amount of charge. or, as we'll talk about later, the current. Now, I've been using the term voltage and electric potential, as if they're synonymous.

They're almost synonymous, but not quite. Electric potential is measured in volts, but voltage, I mean voltage, but I'm saying it Voltage, because that's how it's spelled V-O-L-T-A-G-E. Voltage, or voltage, is not the same thing as electric potential, and it's not the same thing as a vault. Voltage is potential difference, which is simply the electric potential of a given point or a given charge located at a particular point minus the electric potential at some other point.

So you can imagine as like a starting line almost. At the starting line, we take the electric potential here, then we take the electric potential at the finishing line, of whatever system we're interested in. It could be an electric circuit or a battery or whatever. We take the electric potential, not the energy, the potential at start and finish and subtract the finish from the start.

And what we left with is just the difference in potential between these two points. This is called the potential difference, or the voltage. So voltage is just potential difference. it's electric potential 0.1 minus electric potential point 2. And it's measuring in volts. So, potential difference is measuring in volts. Electric potential is also measuring volts.

The reason we're interested in the concept of voltage or potential difference is because the potential difference is equal to the work that you would have to do per unit charge in order to move the charge between those two points. So if I've got point A and point B with a 10 volt potential difference, or a potential difference of 10 volts between point A and point B, that means I would have to do 10 joules of work for every coolum of charge I wanted to move from point A to point B. The work can be positive or negative, depending on exactly how you define things,

because you've got positive and negative charged, and you can define distances positive or negative. So I don't want to get into that, so don't worry about the science too much. Just conceptually, the voltage or the potential difference between two points represents the amount of work in jewels per unit charge I would have to do to move the charge from one point to another. So that's why voltage can be very useful. But again, it doesn't represent the total amount of energy, just per unit charge, which is crucial, because voltage only depends upon the source charges, not the charges that I'm putting there, that have a force exerted on them, just the source of the charge.

There are many sources of voltage or potential difference used in science, industry, and everyday life. Batteries are probably a most common example. Batcharies will have a voltage rating that tells you the potential difference they produce. The way a battery produces a potential difference is essentially by a chemical reaction within the battery, and refer back to our previous episode on electrochemistry for more details on how this works. A chemical reaction within the battery leads to an excess of positive charge on one terminal,

the battery and an excess of negative charge on the other terminal of the battery. And this therefore leads to a potential difference. There's a difference in the potential between the negative side and the positive side. And therefore, I can use that to basically generate a current between the negative and the positive side. And we'll talk more about the details of a current in a future episode, because so far we haven't talked too much about currents, mostly just static charges and fields and so on. In order to generate an electric current, basically, you need to start with the potential

difference or a voltage. And batteries are a good source of those. So finally, before we finish the episode, I, I just want to bring things together a bit by explaining how potential difference relates to the concept of the electric field. Potential difference and electric field are both just two different ways of looking at how a source charge affects the space around it, and particularly how it interacts with other charge particles around it. So there are two different ways of looking at it. A charged particle generates a potential difference in the space around it,

and it generates an electric field in the space around it. And, you know, those two things aren't separate from each other. They're the same phenomenon. They're just different ways of looking at it. specifically, and sort of mathematically, the potential difference between two charged particles, so say A and B, is equal to the electric field in that area, times the distance between the particles. Now, that's assuming the field is constant and it's directly pointed from one particle to another,

so technically the mathematics are slightly more complicated than this, but simplifying it, if we have a constant electric field and point A and point B, so with a charge particle at each point, the potential difference between these two points is equal to the distance between them times the field. This kind of makes sense because the potential difference represents the amount of energy per unit charge that you would have to exert in order to move the charges from point A to point B. The electric field represents the force at any given point that acts per unit charge. So both the potential difference and the electric field are per unit charge. The only difference is that to convert a potential difference to sort of the same units as an electric field, we just need to multiply by the distance.

because electric field refers to a force. Force times distance becomes energy. That's the principle of mechanics, basically, that the force times the distance applied is equal to work or energy, because work is just the type of energy. So basically, this takes us back to the idea that, as I said before, the principle that the potential difference between two charged particles is simply equal to the electric field between them

times the distance between the particles. So, that's all we have for this episode. We'll continue the discussion of electricity with a future episode on electric circuits and circuit components. and if some of the concepts of electric potential and voltage and so on haven't been made completely clear by this episode, I'll hope that they will be by the time we get through that one. So I'm hopefully you enjoyed this episode. If so, please go onto iTunes and give us a favorable rating for the podcast.

I've got about, I think, seven or eight ratings so far, but many of the more popular podcasts have dozens or hundreds of ratings, and so the more I can get, the more exposure of the show can get, the more listeners we can get, and therefore the more people will benefit from my wonderful podcast, because we all know how wonderful it is. Also, you can go onto the Facebook page of this podcast. Just type in The Science of Everything podcast into Facebook, and you should be able to find it. Give the podcast a like and share it with friends and family and so forth.

Again, thanks for listening, and I'll talk to you next time.