Hey, guys. So in this video, I want to talk about a very important conversation that you're going to see in electricity called the Conservation of Charge. There's not a whole lot of problem solving that you're going to do, but it's definitely an 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 Coulomb means that something else has lost one. Cool, um, alright, and we saw how a couple of 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 two 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 conducting spheres that 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 reach equilibrium, we have to figure out 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 two 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 this first case, we have a total amount of charges, just the sum of three and negative one, which is just two Coulombs. So that means when they reach equilibrium, both of them are going to 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 going to be one Coulomb each for one, one Coulomb, and one Coulomb means a total of two. So that means what has to happen is that this guy over here has to give up to two Coulombs of charge. So you have to give two Coulombs to the other one. Don't bother with the direction of like, which way the electrons are going. All you have to know really is which way the charges are moving.

So don't concern yourself a whole lot 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 Coulombs and negative three Coulombs., But we still approach it the same way. The total amount of charge in the before case is going to be a negative eight. So that means when they're both at equilibrium, they're both gonna have the exact same amount of charge. You cut it in half and you get negative four Coulombs. So, in other words, this guy in this negative three here has to give up one, uh, Couilomb in this direction. So this guy has to give up one, and then this one has to gain one. And Coulomb, in order to become negative four. Right? So here we lost two and gained two. Alright, So this for this final example here, we've got three Coulombs and negative two Coulombs in charge. So you add these things up together, and we get the total amount of charge as one Coulomb between both spheres. So now what has to happen is the equilibrium is gonna be 0.5 of a Coulomb each. 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 Coulomb, so you can have half of a Coulomb because a Coulomb is an enormous amount of charges, so that's fine. And that's okay. But what you cannot have is, you cannot have half of an electron. That's different. A Coulomb is billions and billions of charges. You cannot have half of an electron. You can have half a Coulomb, anyways, so you've got this one Coulomb here. Each one has to have 0.5 Coulombs at the end. So now what has to happen is from the three Coulombs has to give up 2.5 Coulombs into this, uh, this charge right here. So this one is gonna lose 2.5, this one is gonna gain 2.5, and then your equilibrium is gonna be 0.5. All right. Pretty straightforward. So now let's look at this 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 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 Coulombs we're supposed to be figuring out how much this has. So we have an isolated system here and insulated box. So we're going to have to use conservation of charge. And that means that the Q here before has to equal Q here afterwards. So the total charge here, the total amount of charge is just one plus three, which is four Coulombs. And then we write that out as that Q1 plus Q2 is equal to just one plus three 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 four 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 Coulombs? Go ahead and pause if you haven't figured it out yet, but in order for this thing to equal four Coulombs, this guy has to be six Coulombs over here. And that's the answer. So this is six Coulombs that we have that conservation of charge. Alright, guys, that's basically it. Let me know if you guys have any questions.