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Potential Due To Point Charges

Patrick Ford
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Hey, guys. So in the last video, we saw how charges that have put inside of potentials experience, um, electric potential energy. But we also said that charges produce their own potentials. So we're gonna check out what the potential of a point charges in this video. We're also going to see a very important quantity called potential difference. Let's check it out. So we've got this electric potential, which is mostly just called a potential and basically what it is. It's like an energy field. So if a charge basically produces some field that tells other charges around it, how much energy to experience we saw with the equation? For That was it was you equal to Q V. And one of the one of things we can dio is we can rearrange to actually solve for this potential right here. We just move the Q over, and we know that the potential is just you divided by Q. So, in other words, one way to think about this potential is it's basically the amount of electric potential energy per unit charge. It's basically how much potential energy something is going to give. Another charge divided by how many cool homes it is. That's kind of one way to think about this. So we saw that if you have a charge like this, So, for instance, you have a producing charge which will call Q. And you wanted to figure out what the potential is at a specific point. Let's say right over here, all you need to know is Q and you need to go the distance. And basically, what you'll be figuring out here is that at point A, for instance, and you'd be figuring out what the potential is at the specific location. But remember that this potential basically exists everywhere, which means I could drop another point like this. And basically, if I know that distance, I was gonna call this R R two and R one Then if I wanted to figure out what the potential is at Point B, then basically, all we just need to know is these two these quantities right here, and I'll be figuring out the potential at this location. Now its potential here has an equation, and it's basically K times. The magnitude of the producing charge Q. Divided by little are one of the ways we can see where that equation comes from is directly from this. V equals you over. Q. We know that you is equal to K times the two charges involved, in other words, big Q and little Q and then over our. So if what happens is if you divide this formula by the feeling charge, basically, you get back to this formula. So it's like the amount of energy that something is gonna produce per unit charge of that producing charge, if that makes sense. All right, now this potential is often referred Thio or is often associated with energy rights. Basically, how much energy something's gonna give another charge. And when we're talking about energy in physics, usually we're interested in the difference in energy because that tells us something about its motion. So that means that there is a an actual quantity here, which is basically the difference in the potentials at this location. And this potential difference, which is just the difference in the potential of two points, has a symbol, Delta V. And if things weren't already complicated enough, this symbol has a special name called Voltage, and that name just sucks because it's already sort of similar to something that we've seen before, which is volts. But remember that that volts is basically just the unit for potential. And what I want to point out is that these two things are not equal to each other. So you can't just say that the voltage is equal to volts. So I just want to reiterate that again, voltage is not the same thing as volts. Voltage is the difference in potential between two points and volts is just the potential at one location. Okay, so there's actually a difference. There literally there is a difference. And basically, this, uh, this potential difference is, if you want to measure it from point A to point B for a charge that was moving there, then this would just be VB minus V a. So it's In other words, it's basically final minus initial. So this potential difference right here is always gonna be the final minus. Initial. You'll normally see it like a charge is moving from here. To hear. That will be your point A to point B. But if you're not given that, if you're just asked with the difference in the potential between two points, it's just going to be the magnitude. Alright, so so one thing that this all these equations mean. Is that a charge? So, for instance, if I put a little Q over here at this charge at this location point a and it moves to point B, it's moved through this potential difference. In other words, it's actually gained or lost some energy. And one way we can see that is through this formula right here. If you is equal to Q V, that means that Delta you The change in energy is equal to Q times the Delta V, which is the potential difference. So for charge moves from a potential to another one, it experiences a potential difference, and now it's gained or lost some energy. And really all that depends on is the magnitude of the charge. If it's positive and the potential difference is positive, then it's gained and vice versa. Right? Alright, that's basically it. So let's go ahead and take a look at some examples and see how the stuff that works out. So we've got this point charge right here, and it could produce a potential at 0.5 m away, so this is p one and this is equal to 0.5 m. So we're supposed to figure out what the potential is at this specific locate location, and we know what this Q is. So in other words, we've got for part A. We're just gonna figure out what V one is equal to. Now we know V one is just gonna be k Q divided by R one, which is just the initial distance, which is this guy right here. So all we have to do is just plug that in. We've got 8.99 times, 10 to the ninth, and now we've got the two, and this is micro cool. Um, so this is gonna be times 10 to the minus six and then divided by 0.5. If you go and work this out, you're gonna get 3.6 times 10 to the fourth. Now, what I want also want to also point out is that the signs here are actually very important because because we're talking about potential differences here, the signs are actually very, very important. So go ahead and plug in. So if this was a negative mic Micro Coleman charge we would have plugged in a negative sign. Okay, So part B is saying what is the potential 1 m away? So in other words, if this other distance here is just 1 m and by the way, it doesn't have to be necessarily in the same direction. It could be in any other direction because it's not a vector. Then what is the potential at this location? So it was V two, and this is gonna be V one. So now the two is just gonna be cake you over our two. In other words, we've got 8.99 times 10 of the ninth. Now you've got to micro cool looms divided by 1 m away. And so one way to think about this is this was double the distance, which means that this should be half the number. So in other words, 1.8 times 10 to the fourth. And that's volts. Alright, so that is volts. So I wanna point out these units right here, our volts and, uh, this see part right here. What is the potential difference from 0.12 point two? So, in other words, what I like to do is just draw a little arrow right here. So I know which one is the final and which one is the initial. So for part c, the potential difference. Delta V. That's the voltage is going to be V two minus V one. And that's just gonna be equal to 1.8 times 10 to the fourth, minus 3.6 times 10 to the fourth. So that means that the potential difference from 100.12 point two is just equal to negative 1.8 times 10 to the fourth. The negative sign is very important and this is the voltage. So I want to write out that as well. So that is the voltage. So remember, voltage is Delta V, not V. That's very important. And the other thing is that the final minus initial is also important. If I were asked what the potential differences from point to 2.1, then I would get the same number. But the sign would just be opposite. And that's important. We going to see why that is later. Alright, guys, let me know if you have any questions and I'll see you guys the next one
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