Electric Potential Energy

by Patrick Ford
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Alright, guys. So in the past couple videos, we've talked about electric forces how to charge is actually exert forces on one another through electric fields and forces things like that in this video, we're gonna cover electric potential energy. Let's check it out. So, basically, imagine I had these two identical charges and with a hold them in place, we know there's some electric force between them, so if I release them, they would both go flying opposite in opposite directions and they would gain some velocity, which means that in this process, they've gained some kinetic energy. Remember that kinetic energy is energy associate with objects motion. But this energy could have just come from nowhere. In fact, what happens is that these two charges, when they have some distance apart, they have some stored energy between them. We know that that's stored energy is called potential energy. Now, in the case of electricity, we're just gonna call this electric potential energy and what we're talking about charge conservation or start energy conservation. We know that anything that we lose in potential energy is gained in kinetic energy. So, for instance, if I have a charge that loses one Jule of Potential, and it gained 11 Jewell in kinetic energy assuming that we have non conservative, no non conservative forces involved. So I've been talking about two point charges. So, for instance, if we had Q one in Q two and they were separated by some distance are, then that means that the electric potential energy between them is just going to be simply K Q one Q two over our another way that you might see this is if you have, like a big charge, you might see this as big Q. Little Q Over are now. There's two differences I wanna point out here. So one we were talking about Coolum law, and this was always R squared. So we have to be very careful when we're talking about electric potential energy because this actually decreases as one over are not one over r squared like it does in Coolum slaw. You might be tempted just sort of like through habit to write one over r squared. So just be careful you're doing one over R with energy. Eso If you've actually seen our chapter on gravitation, it's very similar to how gravitation potential energy was always one of her are. But the force was one of our square. So just in case you've seen that before, the other difference is that the signs of the charges and energy actually do matter when we're talking about electric potential. Remember that that pro tip I gave you guys for columns law was that you were just going to calculate the magnitude and then worry about the direction later. Well, he were actually supposed to take the signs into accounts. So that's basically all we need to know about electric potential energy. Let's go ahead and take a look at a quick example. So how far apart must a three Coolum are? Three micro Coolum and negative to micro Coolum charge Visa. Their potential energy is something so we have a positive and negative point charge right here. Which means you gonna use our formula for electric potential energy. So we've got Let's see, we're looking for the our distance right the distance between these two charges. So now we're gonna use the potential energy, and that's just gonna be K Q one Q two divided by our. So let's just go ahead and make sure that I have everything else that I need to solve the problem. So I have the electric potential energy. This is the negative 100 mg rules. The negative actually does matter. And then I have K, which is just a constant That's the columns Constant, the two charges involved and now supposed to be finding what the distance between these charges has to be. So all you have to do is just rearrange this using some algebra. I'm gonna move this are up, and I have to move this you down. So basically, they're just trading places. So that means that the distance is just gonna be 8.99 times 10 to the ninth. Then I have three micro columns. That means 10 to the minus six. Remember that this means micro. And then I have negative to micro cool. Um, so that's 10 to the minus six. And now I have divided by negative 100. But remember, this is 100 million jewels. This Milly means 10 to the minus three. So I have to write negative 100 times 10 to the minus three. And now I can go ahead and plug all the stuff in. So if you go ahead and plug this in, you should get a distance of 0.54 m. So that's how far these things have to be apart from one another, so that their potential energy between them is this negative. 100 million jewels. All right, that's pretty much it. So now we've talked about two point charges in this example. So what if we have a collection of charges? So, for instance, what if I have an arrangement off three charges? Well, what happens is that for a group of charges, we know that there exists a potential energy between any two charges. So, for instance, these two charges Q one and Q two have a potential energy between them. And if they're distances, are 12 they're gonna have you want to between them. But there's also this pair right here. There's the pair between Q one and Q three that's gonna have a potential energy of you won three and likewise this Q three and Q two has the potential energy of you to three. So what happens is there exists this potential energy between all of the pairs of charges in this assembly here, So that means that the total amount of potential energy, it's just going to be the sum of all of those potential energy. So you want to Plus, you won three, plus you to three. Now, if you have Mawr and Mawr charges, you're just gonna ADM or and Mawr terms together basically, you know, adding all of the all of the pairs of charges together, all the potential energies between them most of the time, you only see about three or four in anyways, because and their interest in being a bunch of terms to the other way, you might also see this is that this is the energy required to separate each charge to out to infinity, or it's the energy to bring them in from infinity. So that's two ways you might actually see that written. So let's go ahead and work out this example how much potential energy is carried by this following system of charges. So first things first, we just wanna go ahead and label all of these charges. So this is one cool, um, negative. Two columns and three Cool. Um, so I'm just gonna call each one of these Q one Q two and then Q three. Just because that's gonna be easiest. Okay, so this pair right here has a potential energy, and this is gonna be you 12 and then this pair over here is you And then finally, I have a pair between you one and three, and all I have to do is just make sure that I'm dealing with each one of them separately. And then I need to know what this distance is as well. So the distance between you between one and three. Okay. So we know if we're trying to figure out what the total potential energy is, you total. We just have to add all these things up together. So you want to and then you won three. And then you 23 Okay, so let's see you want to is just gonna be 8. 99 times 10 to the ninth. Now we've got Let's see, we've got the charges involved, which is gonna be one Coolum and negative. Two columns and I have to write that negative sign divided by the distance between them. It's just just gonna be 4 m. Okay, so that's this term right here. Now you won three. I'm gonna have to figure this out. So let's see. I know that this distance right here is basically the high pot news of the triangle between this m and 3 m sides. So if I use the Pythagorean theorem So Pythagorean Theorem, then our 13 is just gonna be 5 m. Okay, So that means that I'm gonna you gonna you 8.99 times 10 to the ninth. Now, I have the two charges involved. So in this case, I'm gonna have one Cool, um, and three Coolum. And now I'm gonna divided by the distance, which is five. And now, lastly, all I have to do is just add this last term right here. This is gonna be 8.99 times 10 to the ninth. And now I've got let's see, negative to cool OEMs and three cool homes divided by the distance between them, which is three. You go ahead and plug all of these things in separately and then add them all up together. You should get a total potential energy of negative 1. times 10 to the 10th. And that's in jewels. All right, so that's how we work with this stuff with potential energies. It's basically just like cool looms law. Except we just have to add you have to do one over our instead of one over R squared. And the other difference is that we don't have to do any Vector edition or anything like that, because these things are energies and these air scaler is they're not vectors. We don't have to do any decomposition zehr, signing coastlines, anything like that. Okay, let's go ahead and do a couple more examples and let's keep going, let me know if you have any questions.