concept

## Magnetic Force Between Two Moving Charges

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Hey, guys. So in this video, we're gonna talk about the magnetic force between two moving charges. Let's check it out. So you may remember, parallel currents feel a mutual force. So if you have a current this way, I won. And then you have another wire this way with current I to, um they're going to feel a force. A mutual force given by this equation. You not I one I two l divided by two pi r. And you may even remember that if they are going the same direction, which is in the case, this case here, they're going to have on attractive force. We're gonna have an attractive force. Well, remember, realized that currents are really just charges that are trapped in a wire. So if charges trapped in a wire end up having a mutual force between the two wires, the charges that are moving by themselves will also have will also fewer mutual magnetic force to apply a force on each other. Okay, so you need to know this. This is a big deal, and you should know this. But before I go any any further, I wanna have a big disclaimer for this video, which is Ah, lot of professors and textbooks actually skip this part out and you may never need to know this equation. I'm gonna even equation for the mutual force. You may never need to use it. Now. I included this video. I'm including this video for all textbooks, even textbooks that don't particularly have things topic explicitly. Because I want you to know that these are, um that these things happen. But if you don't need to know this, you should probably stop here on not learn more equations. You don't need any more equations in your life. Eso if you haven't seen this, Um, if you haven't seen your professor covered this equation, then you probably don't need to know what you might want to ask him to just to clarify whether you need it or not. Eso for those of you that you needed Let's keep going in the force equation is gonna look very similar to this, but it's gonna be a little bit different. So mu not Q one Q two v one V two divided by four pi R square Where are is still the distance. So notice how here, instead of I one. I have key one view one, and instead of I too, I have Q two v tube Cool. That's the equation. Plug it in and you're done. Now. Directions are a little more complicated here. You had to possible directions. You keep going right and left. And then here you get going right and left here. You still have right and left. But the charges could be positive or negative, which throws things off. But I figure this out for you. There's actually 16 different combinations. There's 16 different combinations off positive, negative, right, left for all these different things. But I worked out everything for you. And all I need to know is that if the charges have the same direction in the same charge, So for example, here you have let's say this is a positive and a positive and they're both going to the right. Then they will be attractive. They will attract okay, which is actually very similar. This is very similar to this. Remember, currents, by definition, are positive. So in their two positives that are going to the right, this is identical situation to that. So it is attractive. But it turns out that if they're both opposite directions and opposite charges, it will also attract. Okay, so this is this situation and this is this situation here where you have a positive in one direction and a negative in a different direction, and they will also attract all other combinations you should know will repel. OK, one of the ways you could do this you can kind of figure this out is by looking at Q one. Q two v one V two. Okay, so let me show you this real quick. Q. One Q two v one V two. So let's look at this example here. The key ones air positive. And let's say that because you're going to the right, that's positive as well. So you have a positive times, a positive times, a positive times, a positive that's a positive in this situation. Here you have a key, one that is positive. Accu tune that is negative, a V one that is positive to the right and then a V one and V two that is negative to the left. If you multiply all these guys, you end up with a positive. That's why in these two situations, the positive here means that they will attract. That's another way that you can do it. But honestly, I think it's just best if you just remember these three things. And, by the way, all the other combinations that you have. If you were to multiplied, accusing V's, you end up with a negative, which means that it is repulsive. Okay, it's a repulsive force. Um, so let's look at this example real quick on Electron is moving right with one times 10 to the eighth when a proton passes moving left. And then it says here that they are three micro meters of parts. So let's put the electron up here so and the proton is up here. Remember, the charge of an electron is minus E and the charge of a proton is plus e andan. The electron is moving right with one times 10 to the eighth and the electron is and then the I'm sorry, the elections moving right and the proton is moving left with two times 10 to the negative Eighth. What is the magnetic force between them? So a magnetic force f B it's gonna be It's just the equation we wrote up here right, So it's just me. You knots key one Q two v one v two Divided by four pi r Squared the distance between them is three micro meters. So three times 10 to the negative six. So this is gonna be a gigantic number here, So let's start plugging in 44 pi times 10 to the negative seven. That's my mu, Not the charges of these guys. Air both 1.6 times 10 to the negative 19 columns. Remember almost all or maybe even all magnetism questions you always plug. Everything is a positive because your direction is always given by things like the right hand rule. Okay, So even though these two guys have different signs of charges, we're just gonna plug them in both as 1.6 times 10 to the negative 19th. And in fact, it's not twice. It's one time to the other. So I could just square this if I want to. Times of speeds, which are one times 10 to the eighth times, two times 10 to the eighth, divided by four pi. Four pi times the distance, which is three times 10 to the negative. Six. Don't forget that this whole thing is squared. OK, the four pipes cancel, which is cute. But you still got a lot of work here. And if you plug all of this into your calculator, you get 5.7 times 10 to the, um, times 10 to the negative. 18 Newton's okay. It's a tiny, tiny force. Cool. That's that's by the way, What is the direction of this force? What's the direction of this force? Well, they have. It's gonna be an attractive force. Hopefully, you thought that this would be an attractive force because they have opposite directions, right? And they have opposite charges, so this force will be an attractive force. Part B is actually old news part beats asking, What is the electric force between them? And I'm just adding this year because you might take this question as well. It's cute, Um, the electric force between two charges. Remember, it's just cake you won over Q two over our square. This is one of the first things you learned in electricity. Andi. I can plug in the numbers. K is a constant nine times 10 to the ninth. Key one is 1.6 times 10 to the negative 19. There's actually two of them, so that square divided by the distance, which is three times 10 to the negative six, also squared. And if you do all of this in the calculator, get 2.56 times 10 to the negative 17. And that's part B. By the way, if you divide, this one is a larger force, right? This is a larger force of the two because the negative exponents is smaller. But if you do like that, if you were curious of how much stronger one is versus the other, and you were to do a ratio of the electrical to the magnetic force, sometimes you see a question like this. Also, you would see that it's about 4.5. So even though the electric force is stronger than the magnetic force, it's only 4.5 times stronger. It's not like a million times stronger, so they're pretty close. They're both really, really weak in this situation. That's it for this one. Let's keep going