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24. Electric Force & Field; Gauss' Law

Electric Fields in Conductors


Electric Fields in Conductors

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Alright, guys. So in this video, I want to talk about conductors and electric fields. We've talked about them separately. So now I want to talk about what the electric field inside of conductor is. So let's check it out. So just remember when we're talking about electric conductors, these air things that allow electrons to move inside of them, all right. And when you have electrons, I'm gonna be using electrons for this video. By the way, these electrons, when they're inside of a conductor, they're freely able to move around. But they want to get this far away as possible from each other because they repel right like charges repel. Now, one of the consequences of this fact and this is the key part of this video is that the Net electric field inside of a conductor is always going to be equal to zero. So basically, what happens is that the electrons move around in such a way that they cancel out the electric field inside of them. We're going to see to specific examples of how that happens right down here. So to specific charge arrangements that you might see in your textbook or in tests or when you have a net charge conductor without an electric field anywhere outside of it. So if imagine, I take this neutral conductor that has the same amount of positive charges and negative charges and I start throwing some electrons at it, right? So I put some electrons on it, whether it's conduction or induction. Well, these things are allowed to move inside of the conductor, and so because they're like charges, they want to move away from each other. So what they're gonna do is they're gonna distribute themselves on the surface, right, because that's as far apart as they could get from each other. Well, imagine I put tomb or electrons on this thing. Well, these electrons also want to repel each other, so they but they also want to repel the charges that exists on the outside right here. So in other words, they have to get equally far away from each other in such a way where they sort of balance each other out. So these two electrons will appear right over here. This is the farthest distance that each one of these electrons can end up from the other on. So that's where they want to go. So now let's say I add four more electrons over here, so I've got form or now these four electrons again could move inside of the conductor and then want to separate as far as possible. Now, the only place that they could go is basically out to the diagonal points right here. They basically want to maximize the distance away from all of the other electrons as far as far as possible, so these electrons will distribute themselves on the surface right here. Now, what is the result of this? Well, what happens is that if you were to take a look at this point right here and try to calculate the electric field, you'd have to sum up what the electric fields, which, by the way, point towards the negative charges. They would point all the way. This way they would point towards each one of the respective charges. But what happens is that if the center of this conductor, all the electric field lines will end up canceling each other out. So you have all of these charges here. So if you have a net charge, Q. But the electric field inside is just equal to zero Justus we said before. So there's another kind of example that we can see. It's when you actually have an uncharged conductor, which means the same number of positive and negative charges. But now you have an external electric field that is on the outside. So let's take a look what happens here. We know that there's gonna be an equal number of positive and negative charges. But what happens is that positive charges wanna go with the flow and negative charges, like electrons wanna go against the flow. So what happens? It happening is these positive charges will start to pile up here on the right hand side, and these negative charges will start to pile up on the left hand side. You start to get this sort of polarization is very similar to how we talked about polarization before. So you basically have these negative charges and these positive charges. There's just a split apart from one another, and the result of this is we know that electric field lines will always point from positive charges to negative charges. So the electric field is basically gonna get set up inside of this conductor because you're polarizing all of these charges. You're moving them from one side to the other. So what ends up happening is that you end up with a new electric field that's inside of the conductor. Now you might be looking at me like I'm crazy because I said that electric electric fields have to be zero inside of conductors. But what ends up happening is that this electric field that's inside that gets set up inside of the conductor cancels out with one that's outside. And so what ends up happening is that the Nets electric field is equal to zero. Justus, we said before. All right, so this is another type of example that you might see with polarization and charge arrangements in which the electric field has to be zero. So one thing I want you to take away is that when you have cases like this, where you have a net charge on a conductor, the Net charges will always move and distribute themselves on the surface of the conductor. And again, that's because that's the farthest they could get away from each other. They basically have to go all the way out to the surface, and they'll always distribute themselves in a way that cancels out what the electric field is inside of that conductor. All right now, there's one thing I want. There's one last thing I want to talk about. So we've talked about the electric fields inside. Conductors have to be has to be zero. But what happens if you were to go outside of this electric of this conductor? Well outside of a conducting charged fear with Q. So, for instance, if you were to be outside like this and try to calculate the electric field, that's just going to be K Times Q Divided by R Squared, which is just the same exact thing as if it were basically just a point charge. So even large objects, if you're outside of them, will just act as if all of their charge was concentrated at the center right here. Alright. So with that being said, let's go ahead and take a look at an example. We've got a spherical conductor and has a radius of 0.5 m, so I've got this little actually let me go ahead and let's do that. So you've got a spherical conductor and I'm told that the radius of this conductor. So I'm gonna call that big R is equal to 0.5 m. I'm also told that this spherical conductor has a net charge of two micro columns. Now, I know that this net charge whether it's positive or negative, so I'm just gonna call him positives have to distribute themselves evenly on the surface. So now I have to feel. And now I have to figure out what happens to the electric field at certain distances from this conductor. So in part A, we're gonna be looking at 0.8 m, So let's go ahead and draw this out in the diagram. Well, 0.8 m is going to be a point that's gonna be outside of the conductor, right? Because the Radius 05 So I'm gonna call this little are, and that's equal to 0.8 m. So I know that the electric field right, the electric field is going to be outside of a conductor with some charge. It's gonna be K times Q divided by r squared. So I've got 8.99 times 10 to the ninth. Now I've got the two micro columns by the way. That's times 10 to the minus six, right, Because this is equal to 10 to the minus six. And then I've got divided by the distance between them. That's gonna be point. Oops, I've got 0.8 and I've got a square that so the electric field over here ends up being to 81 times 10 to the fourth. And that's Newtons Per cool. Um, all right, so that's the answer to part a. Part B is now asking us to look at the electric field at a 0.0 point m from the center of the conductor. So now, 0.4 m. Well, let's check that out in the diagram. At what point is 0.4 m uh, correspond to will? The radius of this thing is 0.5 m. So anywhere from the center of this conductor right here, that's 0.4 m away. You're gonna be inside of the conductor. And what do we say? The electric field inside of a conductor is equal to zero. So this is a very important fact that you need to know. And it's also the answer to our problem. Alright, guys, So this is a very, very important thing. You'll definitely need to know for future sections and chapters. So let me know if you guys have any questions. Watch the video a couple times. You didn't understand anything and just let me know the comments if you want to explain, all right.