24. Electric Force & Field; Gauss' Law
Conservation of Charge
Conservation of Charge
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Hey, guys. So in this video, I want to talk about a very important conservation that you're going to see an electricity called the Conservation of Charge. There's not a lot of whole lot of problem solving that you're gonna do, but it's definitely important concept that you need to know. So let's check it out. Basically, what it says is that charge being a property of matter can't be created or destroyed. And that's known as charge conservation or the law of Conservation of charge, whatever you'll see expressed in multiple different ways. But it's basically like we studied energy. We said that energy can't be created or destroyed. It only moves from one thing to the other. So this means if you have a system of objects, if you have a lot of them and one object is gaining one, Coolum means that something else has lost one. Cool, Um, all right, and we saw how a couple ways of how that could happen through induction or conduction or polarization, things like that. There's another thing that you need to know about conservation of charge and how they move from one object to another, and that's when you bring conductors together. So whenever you bring conductors together and usually it'll be like to metal spheres or something like that, the charges will move until they reach something called equilibrium at a later time. And all that leaked equilibrium means is that if you have imbalanced charges on spheres like so, if you have two objects A and B and they have different amounts of charge, when you bring them together and you allow them to touch and reach equilibrium, the charges transfer until they finally are equal to each other. It's basically the way that they achieve balance. So let's go ahead and use this conservation law and these these conducting spheres that what we just talked about in order to answer some questions about these scenarios. So these following scenarios, each pair of these conducting spheres is brought into contact and allowed to eat reach equilibrium, we have to figure out, is the amount of charge that's transferred and the direction of transferred in each one of these three cases. So in case A, we have to conducting spheres and the charges are given for both of them Now what we do is if they're brought together and allowed to reach equilibrium. Then what happens is we have to figure out what the total amount of charges in each one of these cases now, in the in this first case, we have the total amount of charges, just the sum of three and negative one, which is just too cool arms. So that means when they reach equilibrium, both of them are gonna have the exact same amount. So you just take this number and you just cut it in half. So that means that equilibrium for each one of these things is gonna be one Coolum beach for one one. Cool. Um, and one Kula means a total of two. So that means what has to happen is that this guy over here has to give up to cool homes of charge. So you have to give two columns to the other one. Don't don't bother with the direction of like, which way the electrons air going. All you have to know really is which way the charges air moving. So don't concern yourself a whole lot with the with the way that the electrons are moving anyway. So that's basically the first example. Now we've got some negative numbers here. We've got negative five columns. Negative three columns, But we still approach it the same way. The total amount of charge in the before case is going to be a negative eight. Cool. Um, so that means when they're both had equilibrium, they're both gonna have the exact same amount of charge. You cut it in half and you get negative Four columns. So, in other words, this guy in this negative three here has to give up one, uh, cool. Um, in this direction. So this guy has to give up one. Cool, um, to become negative forces the minus one, and then this one has to gain one. Cool. Um, in order to become negative four. Right. So here we lost two and gains to All right, So this for this final example here, we've got a three Coolum and too cool. Um, negative. Too cool in charge. So you add these things up together and we get the total amount of charges one cool in between the both spheres. So now it has to happen. Is the equilibrium is gonna be 0.5 of a cool. Um, I want you to be very careful because I know you guys were looking at me like I'm crazy right now because I said a couple of videos that you can't have half charges. Here's the difference. This is a half of a cool, um, so you can have half of a cool, Um, because of cool, um, is an enormous amount of charges, so that's fine. And that's okay. But you cannot have is you cannot have half of an electron. That's different. Coolum is billions and billions. Billions of charges. You cannot have half of an electron. You can have half of cool. Um, anyways, so you've got this one Coolum here. Each one has toe have 0.5 columns at the end. So now it has to happen is from the three. Kulemin has to give up 2.5 columns into this, uh, this charge right here. So this one is gonna lose 2.5. This one's gonna gain 2.5, and then your equilibrium is gonna be 0.5. All right. Pretty straightforward. So now let's look at his second example, which we're actually gonna use that conservation of charge. So we're told that two charged metal balls. That means that they're conductors. Metal means of conductors are moving around an insulated box. What that means is that the walls of the box itself can't really pick up charges and they're colliding, and they're randomly exchanging these charges. But they're not necessarily reaching equilibrium. So at first we're told that the charges of each one of these metal spheres and then at some later time we're told that this charge has or this metal sphere has negative two columns were supposed to be figuring out how much this has. So we have an isolated system here and insulated box. So we're gonna have to use conservation off charge. And that means that the queue here before has to equal que here afterwards. So the total charge here, the total amount of charge is just one plus three, which is four cool homes. And then we write that out is that Q one plus Q two is equal just to one plus three in that equals four, right? So pretty straightforward. Well, what we're saying here is that the Q total in the after case also has to be for cool. Um, because we have to conserve that charge. So we write that equation out. Right? So we've got negative two. Plus, what is going to give me four columns? Go ahead and positive. You haven't figured it out yet, but in order for this thing to equal four columns, this guy has to be six columns over here. And that's the answer. So this is a six columns that we have that conservation of charge. Alright, guys, that's basically it. Let me know if you guys have any questions.