Hey, guys. So in this video, we're going to talk about Coulomb's law, which is a really, really important law that you need to know for electricity. It basically gives us the electric force between two charges. So go ahead and watch this video as many times as you need to. We're going to be covering a lot of examples and practice problems in the videos after this. Basically, electric forces can be attractive or repulsive, and that's a direct consequence of what we talked about with charges: unlike charges attract and like charges repel. So, unlike charges, if you have positive, negative, or negative, positive, will exert attractive forces on each other. Or if you have two like charges, like two protons or two electrons, 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 Coulomb's Law or the Coulomb force, and that gives us the force between two charges. So if you have two charges Q1 and Q2, and they're separated by some distance, little r, then the force that exerts between them is going to be:

K Q1Q2 r 2It'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, in Coulomb's law, the electric force is just some constant times the two charges divided by the distance between them. So this K constant right here is called Coulomb's constant, and that has a number: 8.99 × 10^{9}. It's really easy to remember, because it's like 899 times 10^{9}. 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 are some units associated with that. It's Newtons meters squared per Coulomb 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 a line that connects the two charges. And basically, what I mean by that is if you have these two charges Q1 and Q2, and you know the distance between them, that's little r, then if it's a repulsive force from Q1 to Q2, that's going to go in this direction, so that's going to be a repulsive force. And if it's an attractive force, then it's just going to point in the opposite direction. So that's going to be, uh, yeah, that's attractive. And, um, yeah, so it always just exerts along the line that connects those two things. And again, the attractive or repulsion just has to do with whether the fact they are like or unlike charges; like repel, unlike attract.

So I'm going to give you guys a pro tip in order to figure out the magnitude and direction. So, whenever we are trying to figure out Coulomb's law, we're always going to find the magnitude of the Coulomb 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 into this formula that we've given for the Coulomb force, you're always just going to use positive numbers and then worry about the direction later.

Alright, so let's go ahead and take a look at a quick example. In this problem, we're going to 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 are electric forces because these 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 are just related to the elementary charge. So this is +e and this is -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 going to be, let's see, we've got K, that constant, times the product of the two charges. So we've got:

K QprotonQelectron r 2And actually, I have all of these constants just in this nice little table right here. So we know this K constant is 8.99 × 10^{9}. Remember that. Now we've got the elementary charge. That's also something you should know, 1.6 × 10^{-19}. And now that's for the proton. For the electron, it should be negative, but again, we're just going to 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 we are asked to find the ratio of like, the magnitudes of these forces anyway, so we're just going to use positive numbers.

Alright, so we've got the distance 5.3 × 10^{-11}, and that is going to be squared. So you go ahead and work this out, you should get 8.19 × 10^{-8}. That's in Newtons. So that's the electric force.

Now we just have to do the same exact thing for the gravitational force. So now, the gravitational force, well, just in case you have forgotten the gravitational forces:

G mprotonmelectron r 2So we've actually have all of these constants over here. So I've got 6.67 × 10^{-11}. That's the gravitational constant. The mass of the proton, 1.67 × 10^{-27}. And then all of that's in SI, by the way, then 9.11 × 10^{-31}. And then we've got the same distance between them, 5.3 × 10^{-11}, squared. So we work this out, and you should get 3.61 × 10^{-47}, which is a very, very, very tiny number. So we're just going to see how tiny that is in a second.

So we've got the ratio of these things. The gravitational or to the electric and the gravitational force. That's just going to be:

8.19 × 10 ^ −8 / 3.61 × 10 ^ −47If you work this out, you've actually plugging those numbers and divide them. You should get 2.27 × 10^{39}. And by the way, this is just a dimension issue. No number because we're trying to basically figure out how much stronger 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. The electric force is a very, very strong force, and this is our final answer. So again, there are no units.

Alright, let's go ahead and take a look at another example here. So we've got two identical charges, and they're connected by a five-centimeter 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 Q1 is equal to Q2, so that means that we can just use Q in our equation and not have to worry about Q1 Q2. They're the same exact thing. So if we're trying to figure out what the charges are, then we just start off with Coulomb's law. So in other words, Coulomb's law is saying that we've got K times Q1 Q2 divided by r squared. But again, if these two things are the same thing, this is just going to 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. Alright. 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 Q1 is trying to push away Q2, and Q2 is trying to push away Q1, 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 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.

Alright, so let's see, we've got, let's set up the equation If I wanted to Q squared. So I just have to do:

Q2/r2Now I'm just going to isolate Q squared by moving this over and then moving the K to the bottom. So we're going to get that FE, the electric force times r squared, divided by K is equal to Q squared, alright. 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 realize that this is in five centimeters, so I have to convert it to SI first. So I mean, I have that r, this distance right here, is equal to 0.05 m. So I've got that, 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 0.05, I've got to square that divided by 8.99 × 10^{9}. 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 take the square root of this thing first. So all you have to do is for this number, you have to take the square root of that. And that should equal Q. So I'm going to write that you're going to 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 × 10^{-6}. And that's in Coulombs right there. So that is the answer. Let me know if you guys have any questions with this.