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Anderson Video - Electric Fields in Metals

Professor Anderson
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One thing that we need to talk about is electric fields in metals. Okay, we mentioned this earlier in class but let's refresh our memory. The idea is this, electrons in metals are free to move, this is what makes it a metal. Later on we're gonna learn about resistance and resistance has to do with trying to not let them move so easily, so all conductors have a resistance associated with them unless it's a superconductor, okay? Then the resistance goes to zero. But for now let's not worry about any resistance, let's just pretend those electrons are basically free to move. So here is a material, Gold, which is a metal, and if I put an electric field on it everywhere then charge in the metal starts to move. The protons don't move, okay? The electrons are the ones that move, so the electrons that were on these atoms in the center suddenly start moving to the left until they pile up on the left side. And they do this very quickly, okay, on the order of Pico seconds. The positive charges that are left over here are missing an electron. You got a nucleus there and one of its electrons migrated away and so it's a net positive charge. And so now you have positive charge on the right, negative charge on the left, and that means there has to be an internal field that looks like this. Okay, there is some field that develops in the material, but remember E is everywhere, okay? E is not only outside, it's inside the material and so when we calculate the net e in there, we have to worry about not only the internal field, but that external field, and those are pointed in opposite directions. Okay and so if we just worry about the magnitudes at this point, we can write it like this and that's going to be zero. The e field in here is zero. You know it has to be zero, why? Because if it wasn't then charge would still be moving. So once the charge separates and we have the static case, which is you've reached equilibrium, then there's no more electric field in there, because if there was charge would still move. Okay and so we have rules for conductors, we have five separate rules that describe conductors in the static case. And I want you to make sure that you understand that this is the static condition because later on we're going to talk about things that are actually moving, charge is still moving. So the first rule is just what we said: e equals zero inside. If you are inside the metal the electric field is zero. Good. The second is any excess charge has to be on the surface. So we saw that all the negative charge went over to this side and all the positive charge stayed over on this side, if you sprinkled some more charge on there, it would all go to the surface. Okay, any excess charge that you put on a conductor goes to the surface. It doesn't have to be in an external electric field or not, if you took a ball, a metal ball, and you just sprinkled some electrons on it, which we know how to do now, right? You take a metal ball and you drag it across the carpet, that's gonna put electrons on it, they immediately go to the surface. And in fact in the case of a sphere, all those electrons will distribute themselves uniformly, okay, they'll all go to the surface. If it's a thin rod it's a little more interesting. If I have a thin metal rod and I drag it across the carpet and then I ask you where are the electrons on that rod? They are no longer uniformly distributed, they are bunched up around the ends. Okay. They are bunched near the ends and this is one of the reasons that carpet fibers tend to have a lot of electrons on the end of the carpet fiber, it's pushing all those electrons out to either end. So it's kind of weird but thin rods have more electrons on the ends than they have in the middle. Alright, there's also no net charge inside. So in the volume of the material every positive charge has a negative charge right next to it, those atoms in there are neutral It's the same voltage everywhere. We're gonna learn about voltage tomorrow and the next day but the idea is that voltage relates to electric field, we'll see how it relates, and you're familiar with voltage, right? If I have a battery that has 1.5 volts, if I connect wires to the battery and I look at the ends of those wires, that voltage is still 1.5 volts and it's because the voltage in that metal in that conductor is the same everywhere. And the last is that the electric field is perpendicular to the surface. This is external electric field, so if you have an object that have some complicated shape, this is a metal, and you did have some charge on it, it would make an electric field that is everywhere perpendicular to its local surface. Maybe that one doesn't look very perpendicular, let's change it. There we go. Okay, these are the five rules from-- for conductors, if you just start with e equals zero everything else falls out of that. Okay, all the other rules follow from e equals zero. Yeah Sam? >> (student speaking) So for the distribution of the electrons betweem the sphere and the rod, does it depend on the shape or the type of material? It depends on the shape. Yeah. So basically the shape is important because the charges are trying to redistribute themselves such that the electric field is zero inside. Okay, and it makes sense that if I had a thin rod, it couldn't just be distributed like that uniformly because if I was looking at a point right here, I've got one charge on my right, I've got four on my left, that would lead to an electric field, right? So that can't be right and it turns out to be a really exquisitely hard physics problem to determine the distribution of charge in a thin rod. It's very challenging, very difficult, okay? Well beyond what we're talking about in this course, but this simple example tells you it can't be uniformly distributed because that would make a point to the left and if E is pointing to the left then this electron is going to move to the right, but I can make the same argument over here and so this one would move to the left and what you end up with is a very complicated distribution. It's bunched up around the ends and then less in the middle. Yeah.