Coulomb's Law

by Patrick Ford
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Hey, guys. So in this video, we're gonna talk about Cool owns law, which is a really, really important law that you need to know for electricity. So basically gives us the electric force between two charges. So go ahead and watch this video as many times you need Thio. We're gonna be covering a lot of examples and practice problems in the videos after this. So basically, electric forces can be attractive or repulsive, and that's a direct consequence of what we talked about with, like, charges, you know, being attracted and or unlike charges attract ing and, like charges repel ing. So, unlike charges, if you have positive, negative or negative, positive will exert attractive forces on each other. Or is if you have to, like charges like two protons or two electrons, things like that. Those things want to fly away from each other so like charges will repel and exert repulsive forces on each other. Now the name for the force is called Columns Law or the Coolum Force, and that gives us the force between two charges. So if you have two charges Q one and Q two and they're separated by some distance, little are thin. The force that exerts between them is gonna be K Q one Q. Two. So both both the charges divided by r squared. It's very similar to how we studied the gravitational force between two masses. So you have some constant times, the two masses divided by the distance between them. Well, columns law, the electric force just as some constant times the two charges divided by the distance between them. So this K constant right here is called columns constant, and that has a number 8.99 times 10 to the ninth. It's really easy to remember, because it's like 899 10 9. So this is something you absolutely should commit to memory. It's very important a lot of times on tests you won't be given this number exactly. So go ahead and commit that to memory, and there's some units associated with that. It's Newtons meters squared per Coolum squared, although that's a lot less important. You probably won't need to know that. So basically, this equation right here gives us the force that exists between two charges and also acts on both of those charges because of action reaction. That's the magnitude of that force. As for the direction that force always points along ah line that connects the two charges. So line connecting to charges. And basically what I mean by that is if you have these two charges Q one and Q two and you know the distance between them, that's little are then, if it's a repulsive force and from Q one and Q two and that's gonna go in this direction, so that's gonna be a repulsive force. And if it's an attractive force, then it's just gonna point in the opposite direction. So that's gonna be, uh, yeah, yeah, that's Ah, that's attractive. And, um, yeah, so it always just exerts along the line that connects those two things. And again, the attractive or propulsion just has to do with whether the fact there are like or unlike charges like repel unlike attract. So I'm gonna give you guys a pro tip in order to figure out the magnitude and direction. So whenever we are trying to figure out cool OEMs law, we're always gonna find the magnitude of the Coolum force just by using positive numbers, and then we'll worry about the direction later. So find the direction by using the attracting and repelling rules. So whenever you're plugging in to this formula that we've given the Coolum force, you're always just gonna use positive numbers and then worry about the direction later. All right, so let's go ahead and take a look. A quick example. In this problem in this example here, we're gonna be calculating the ratio of the electric to the gravitational forces in a hydrogen atom. So in a hydrogen atom, we just have the proton. So we have the mass of the proton and we've got the mass of the electron. But there's electric forces because thes things also have charges. So we have the charge of a proton and the charge of an electron. Now we know that the charges for each of these things were just related to the elementary charge. So this is plus E and this is minus E. So basically, we're trying to figure out what the ratio of the electric force is to the gravitational force. So let's go ahead and solve each one of those separately. So we've got the electric force is gonna be, Let's see, we got K that constant times the product of the two charges. So we've got Q proton que electron and then divided by the distance between them. So that's gonna be r squared. And actually, I have all of these constants just in this nice little table right here. So we know this K constant is 8.99 times 10 to the ninth. Remember that. Now we've got the elementary charge. That's also something you should know. 1.6 times, 10 to the minus 19. And now that's for the proton. For the electron, it should be negative. But again, we're just gonna worry about the magnitude of the force. So we have to just plug in a positive number, right? Worry about the direction later and really were asked to find the ratio of, like, the magnitudes of these forces anyways, so we're just gonna use positive numbers. All right, so we've got the distance 5.3 times, 10 to the minus 11 and that is gonna be squared. So you go out and work this out. You should get 819 times 10 to the minus eight. That's a Newton's. So that's that one. So right, So actually going to use a different color for that. So that's the electric force. Now we just have to do the same exact thing for the gravitational force. So now, gravitational force. Well, and just in case you have you forgotten the gravitational forces capital G times the mass of both objects divided by little r squared. So we've actually have all of these constants over here. So I've got 6.67 times, 10 to the minus 11. That's the gravitational constant. The mass of the proton, 1.67 times 10 to the minus 27. And then all of that's an S. I, by the way and then 9.11 times 10 to the minus 31. And then we've got the same distance between them 5.3 times, 10 to the minus 11 uh, squared. So we work this out and you should get 3.61 times 10 to the minus 47 which is a huge I'm sorry, which is a very, very, very tiny number s so we're just gonna see how tiny that is in a second. So we've got the ratio of these things. Uh, the gravitational or to the electric and the gravitational force. That's just gonna be 8.19 times 10 to the minus eight. Divided by 3.61 times 10 to the minus 47 which is a very, very time number. If you work this out, you've actually plugging those numbers and divide them. You should get 2.27 Let me write that out. Two points to seven times 10 to the 39. And by the way, this is just a dimensional issue. No number because we're trying to basically figure out how much time, how many times stronger is this force than the gravitational force. So, in other words, this thing is trillions and trillions and trillions of times stronger than the gravitational force. Electric force is a very, very strong force, and this is our final answer. So again, there's no units. Alright, eso Let's go ahead and take a look at another example here. So we've got two identical charges and they're connected by five centimeters water wire. Now what's happening is we have two identical charges that are on the end of a string like this and because they're like charges they want to repel away from each other. But as they start to do that, there's some tension that's created in the wire. And using that we're supposed to figure out what the magnitude of these charges are. So the first thing is that we know that these two charges are identical. What that means is that we have. Q one is equal to Q two, so that means that we can just use Q in our equation, not have to worry about Q. One Q. Two. They're the same exact thing. So if we're trying to figure out what the charges are, then we just start off with cool OEMs law. So in other words columns, laws saying that we've got K Times Q one Q two divided by r squared. But again, if these two things are the same thing, this is just gonna turn into a K Q squared. Divided by R squared, right, because Q Times Q. If they're the same exact thing is just Q squared. So all we have to do is just figure out what this Q squared is. All right. So let's see. We've got these, like charges and they're trying to exert repulsive forces on each other like that, right? So cute one is trying toe push away Q two and Q two is trying to push away Q. One action reaction, and the reason that they're not flying apart is because there's some tension that exists between the wire that basically keeps these things together. So we know that the tension here is equal to 10 Newtons, and so if everything is in equilibrium, then the tension the tension is equal to the electric forces. So we've got the electric forces right here and here. And I know I just didn't draw them equally sort of to scale. But these things should be equal to each other. So in other words, the tension is equal to the electric force. That's why nothing is actually flying apart. All right, so let's see, we've got, um let's set up the equation If I wanted to Q squared. So I just have to do Q squared over r squared. Now I'm just gonna isolate Q squared by moving this over and then moving the K to the bottom. So we're gonna get that f e the electric force Times R squared, divided by K is equal to Q squared, All right. And if you go ahead and look through our numbers I have with the electric forces because I know it's just the tension. Now I've got r squared. Now, I just have to I just have to realize that this is in five centimeters, so I have to convert it to s I first. So I mean, I have that are, uh this distance right here is equal to 0. m. So I've got that's and then K is just the constant, right? So I'm ready to go. So I've got 10 Newtons times the R squared, which is 0.5 I've got a square that divided by 8.99 times 10 to the ninth. If you go ahead and work this out, you should get, um Let's see. I got some number. Oh, that's right. We have to square root this thing first. So all you have to do is for this number, you have to take the square roots of that. And that should equal Q. So I'm gonna write that you're gonna do that. And if you work this out and I'll take the square root. You should get a charge that is equal to 1.67 times 10 to the minus six. And that's in cool OEMs right there. So that is the answer. Let me know if you guys have any questions with this.