1

concept

## Electric Potential

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Alright, guys. So in this video, we're gonna be talking about the electric potential. We talked about the electric potential energy between two charges. And even though those two things sound similar, we're going to see how in this video other different. Let's check it out. So electric potential is sometimes just simply called the potential and the electric potential energy is sometimes just simply called the potential energy. It's kind of assume that we're talking about electricity. So a lot of people just don't even say the electric potential energy. We just see the potential and the potential energy. But one important distinction to make is that even though these two things are related and they sound the same, they're actually represent different things. So we have to be very careful about our word choices between how we use these things. Now, the best way to understand what the difference is between a potential and a potential energy is to go back and talk about the way we explored what fields where electric fields. So he said that basically a single charge, whether it was a positive or negative charge, so I'm just gonna assume like it's a positive charge right here admitted these field lines, these electric field lines and basically these field lines were just information, and this information or field told charges that were in the vicinity. How much force to feel And basically what happens is that a single charge alongside with producing an electric field also produces something called an electric potential and sort of very similar as to how it works. So if you have a positive charge at the same time that it's producing this electric field outwards, that's telling other charges. How much force to feel? Well, a positive charge is also emitting some information a field called a potential, which, by the way, has the symbol V. And this symbol basically tells charges how much energy toe have or how much energy to feel. And the thing was, is that we were talking about single charges in which this was like a big queue. We said that that was the producing charge and then admitted this field lines and basically nothing happened unless you actually dropped a second charge inside of here. Q. And once you had a second charge. All of a sudden, now there is a force on this thing because if you have some electric field lines that point in this direction, and if you drop a charge here, then for instance, if it's a positive charge, then this is gonna feel a repulsive force like this. And we have the relationship between the force and the electric field that was just given as F equals q E. So once there is a second charge, there was a force well similar to potential right here. This single charge sets up a field called an electric potential, and once you drop a second charge inside of this potential, now there is energy. So these two things are different, but the mechanisms in which they sort of set up these force fields and energy fields is very similar now. We said that the force that we could calculate on a charge from an electric field is just given by this equation. F equals Q E. Well, it's very similar for energy. What happens is once there's a second charge that you put in between these two things. Now it basically creates some electric potential energy, which we know the equation for, and this electric potential energy is given as Q times V in which, in the case of cool OEMs law in the case of electric fields, this e represented the strength of the electric field that this feeling charge was put inside of. Well, this V is the strength of the energy field that is put inside off. So a lot. Another way you might might see that is actually the potential, sometimes the potential field. So basically, we know that the queue that this little Q here always corresponded to the queue that was feeling the field that it was put inside off. So, in other words, this Q is always the feeling charge. Well, it's the same way with the potential in this formula right here. U equals Q V. This cue always represents the thing that is feeling the potential at that specific spot. All right, so I just wanna go ahead and wrap up everything really quickly, once more, so you have a single charge. It produces something called an electric field, and that field tells charges that air inside of it, how much force to experience, and once that second charges put there, there's force called Columns Law, and it's given by this equation or cake over R squared, where is the strength of the electric field? And that Q. Is the feeling charged? Well with the potential. It basically does the same exact thing because if for energy and the equation slightly different, a single charge produces an electric potential out here. And once you in that potential tells charges inside of it how much energy toe have, And once there is a second charge, all of a sudden now there's energy. There's potential energy between these two charges that potential energy is given as U equals Q V or U equals K Q Q over our where that V is the strength of the energy field or the potential field. And this little Q is also the feeling charge. Okay, so the unit of this electric potential is called the Vault, and it's given by the letter V. And this V is actually defined as one Jewell per one. Cool. Um, now we have to be very careful here because this V is the symbol for both the electric potential. So it's actually like the symbol that we use, but it's also the same symbol for the unit. So, for example, it would be perfectly sensible. Toe have an equation like this. V equals three volts. This would be perfectly sensible. It was just some guy who decided hundreds of years ago that the symbol for the letter and the unit we're gonna be the same. So this right here is the symbol, which for electric potential. Whereas this right here is the unit. So just so you know, don't get confused between those two. And that's basically all we need to know about the electric potential. Let's go ahead and check out an example. We have a five and a three Coolum charge That air separated by some distance right here. So if the five Coolum charge feels 200 volts from the three column charge, what's the potential? Great. So we have these two charges right here. This is gonna be a five. Cool. Um, actually, let's do it the other way around. Let's do this. Is the three cool? Um, this is the five Coolum charge, and now we're supposed to figure out what is the potential energy on the five Coolum charge. So in other words, we're trying to figure out what you is. We know that you is just going to be K Q. One Q two over are Now, here's the problem here. We could use this. We could try to use this potential energy right here to figure out what the potential energy of the five. Oops. I didn't mean to do that. I didn't mean to write volts. I meant to write cool homes. We could use this formula to figure out what the potential energy of this five Coolum charges. The problem is, we actually don't know what this our distances so we can't use this potential energy formula. Instead, we're gonna have to use the different potential energy formula, which is that U is equal to Q times V. So we have with the charges. This charge corresponds to the feeling charge, and we know that we're the five column charge is feeling 200 volts from this charge over here. So, in other words, this is actually the producing charge Q. And this is actually the feeling charge little Q. So this is actually going to be the charge that we use in this formula and what we're doing is we're basically saying this producing charge here is producing some potential field, some some potential out in this field here. And this little cute is feeling it. Okay, So that means that this potential energy is just going to be the five cool OEMs times the potential, which is 200 volts at the specific point. So at right here, the Volta. Sorry that the votes, the potential is 200 volts. So that means that the potential energy is gonna be five times 200 which is equal to 1000, and that's it. So basically, just let me know if you guys have any questions, let's go ahead and do some examples.

2

example

## Movement of Charges in Potential Fields

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Hey, guys. So now that we've talked about electric potentials, it's time to talk about very quickly. How charges move inside of potential feels there's not a whole lot of calculations that you'll need, but it's definitely some conceptual points. Need to know. So let's check it out. So basically, the whole deal is that positive charges will always move towards lower potentials and negative charges. According being the opposite of those will always move towards higher potentials. The way that I like to think about it is think back when we're talking about energy. If you have, like a roller coaster like this, then Mass will always try to move towards the lower potential. It's kind of like that, but that's basically the whole entire game, and it's because potential is when we're talking about electric charges is a field that sort of provides the motivation for charges to move, and it gives them potential energy, so positive charges always want to reduce that potential and the negative charges always gonna do the opposite of that. All right, so before we talk about how electric fields are gonna be sort of incorporated into potentials, let's go ahead and just do this quick example. So we have an electron that's at rest. So we have an electron that's at rest, and we have two points. So we've got this point right here. A and we're told that that is at 10 volts, and then we have another point B, that zero volts. So somehow we actually know what the potentials are. Both of these points. And then we're gonna have to stick an electron inside of here. And we have to figure out which direction that that electrons gonna move to while that electron is a negative e, which means it's a negative charge. And negative charges always move to where they always move towards higher potentials. So that means that this electron is always just gonna go to the left, and that's the answer. So it's gonna go towards a and that's the answer. All right, so let's move on to this next question here because now we're actually gonna be relating the way that charges move and potentials with electric fields. So you have a metal rod, and that's actually important because that metal rod means that is a conductor. It's placed in a uniformed electric field and I'm just gonna have that electric field has a strength of e. And we're supposed to figure out which end of this rod here is at a higher potential. Okay, so basically, we know how charges in electric fields move. So if we have a positive charge, that's inside of this. We know that the force on those charges always wants to go with the flow, right, because of f equals Q E. So we know that the force, if we have a charge in electric field if that charges positive, always wants to move in the same exact direction or as it's the opposite for negative charges, any negative charge basically wants to go against the flow. So we can say if this is if this charge right here, which is negative, wants to go against the flow and we know that negative charges always move towards higher potentials, then that means that the left side of this electric field has to be one with higher potential, whereas the right side is gonna be the one with lower potential. So basically kind of follows their discussion of charges inside of electric fields, and those were basically the answers. This is high potential, and this is low potential. Alright, guys, let me know if you have any questions

3

concept

## Potential Due To Point Charges

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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

4

Problem

How far from a 5μC charge will the potential be 100 V?

A

4.5×10

^{−3}mB

450 m

C

45,000 m

D

450,000 m

5

Problem

A −1μC and a 5μC charge lie on a line, separated by 5cm. What is the electric potential halfway between the two charges?

A

1.44×10

^{4}VB

7.19×10

^{5}VC

1.44×10

^{6}VD

2.16×10

^{6}V6

example

## Potential Difference Between Two Charges

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Alright, guys. So you've got these two charges they're lying on this line and we're supposed to figure out what the potential difference is between point A and point B. So, in other words, what is the potential between these two? Sorry, the potential difference between these two points. Another thing that could have asked us is instead of this, they could have asked us for the voltage because those things meet in the same exact thing. In other words, or in any case, we know that the potential difference between or from point A to point B is just gonna be VB minus V a. So, basically, we know that at these at these points right here, we're gonna have to contributions at the from the potential we're gonna have the negative three Q charge and acute charge producing potentials at both of these locations. Basically, which need to do is we need to figure out what these things are Now. I just want to warn you, the math here in the algebra is gonna get really messy. But the procedure is fairly straightforward. We know that at point B, we're gonna have to contributions the potential from Q at this point, plus the potential from the negative three Q at this point, So basically, we just need to figure out what those things are. We know our equation. We know that V is just equal to K. Big Q over a little are. In fact, I'm just gonna I'm just gonna scoop this up over here, So that means the potential from Q at point B is just going to be. Let's see, we've got K. Then we've got to queue. Now we've got divided by the distance involved here. Now, where this gets a little tricky is that we have this s distance, that the complete distance between these two charges and then we have these X is right here. So that means that the distance between Q and B is actually s minus X. Is this whole entire distance minus this little piece right here? So that means it's just gonna be s minus X now from the negative 33 charge. We just have this distance Little X over here, So this is gonna be K times negative three Q divided by X Now, one of the things that we can actually do in this case is we have these denominators that aren't the same. So one of the things we could do with fractions that don't have the same denominators is essentially, like cross multiply. So they do have the same denominator. So basically, what we have to do is just move these things over and multiply. So what? This ends up being and this is where the algebra gets a little messy is this is gonna be cake you times x from this guy over here divided by and then the denominators become the same s x s minus x. And then this guy over here this You have to remember that this is a negative three. Q charge is gonna be minus three K. Uh, this is gonna be cake. You This is gonna be s minus X divided by X s minus X. All right. So you can already see how the math is gonna start to get a little tricky over here. Um, so let's see, I've got how can I simplify this? Okay, well, I've got this is gonna basically gonna expand out to K Q X over S X s minus X and then I have minus three k Q s over, X s minus X. And then we've got this minus and the minus over here are actually gonna sort of turn into a plus. And this is gonna be another three K Q X over X s minus X. So one of things that happens is that this guy over here well, actually group up with this term in the front, and all you're gonna get is you're just gonna get, uh, four k Q x over X s minus X minus three K Q s over. X s minus X. All right, so this is what the potential looks like at point B. Now all we have to do is basically the same exact thing. So I'm just gonna separate this the same exact thing for the potential at point A. So we've got at a This is gonna be Let's see, we've got a k q X over our Sorry Que que? Let's see cake divided by X. That's right. Yeah. So we've got this distance right here, and then we've got plus K negative three Q divided by And now we have this, uh, this piece right here, which is s minus X again. So this is just gonna be s minus X. And now we basically have to do the exact same procedure. Eso We're basically just gonna take these terms up here and then on, then cross multiply them. So I know this is gonna get a little tricky, Guys. Eso we have cake you and then we have s minus X over X s minus X and then we're gonna have, uh, Plus, Or I guess, actually, this is gonna turn into a minus sign because of this negative right here. This is gonna turn into three K Q x over X s minus X. Okay, so one of the things that we can do is we can sort of distribute this this cake, you It's kind of like the same way how we pulled out this k this three k Q x term over here, we just have to distribute this cake you into this minus X, and then this cake you X that you get from this term and this minus three cake X are actually going to be the same thing. So, in other words, we're just gonna get cake us over X s minus X minus four k Q x over X s minus X So I just wanna point out. So just give myself some room. Just wanna point out that when you distribute this cake, this cake s term comes from the first and this cake you into the negative X term actually goes inside of this and groups up, and that's why it becomes a negative for So I just want to point out, just in case you got lost a little bit. So basically, let's see what is the sense of being is Yeah, this is the actual final results. So that means that we can get back to the voltage calculation, which is basically going to be the subtraction of these two things. So we have this term, which is VB, and then this term, which is va and we all you have to do is just subtract them. Eso we have this. Let's see, we have, um, Delta V is gonna be Let's see, I've got this four k Q x term over here, and then I'm gonna subtract this entire term over here. When I do that, the subtraction of this term is actually going to turn into a positive. So this and this actually group up to form eight K Q x over X s minus X. And then what happens is this term over here, this negative three cake us when I subtract v A, which is cake us. It's just gonna be minus four cake us over X s minus X, and that is the answer. So that is the potential. And then all you need to do to actually solve numbers for this is you just need to know exactly what the distances involved are. So I know again, the algebra is kind of messy. But if you guys could do this, then you should have no problem with working with these potential differences between point charges. All right, let me know in the comments that any one of these steps sort of like tripped you up or got you confused. I'd be happy to explain it. Just let me know, guys. All right,

Additional resources for Electric Potential

PRACTICE PROBLEMS AND ACTIVITIES (17)

- A thin spherical shell with radius R_1 = 3.00 cm is concentric with a larger thin spherical shell with radius ...
- Two stationary point charges +3.00 nC and +2.00 nC are separated by a distance of 50.0 cm. An electron is rele...
- (a) How much excess charge must be placed on a copper sphere 25.0 cm in diameter so that the potential of its ...
- Two large, parallel conducting plates carrying opposite charges of equal magnitude are separated by 2.20 cm. ...
- Two large, parallel conducting plates carrying opposite charges of equal magnitude are separated by 2.20 cm. ...
- An infinitely long line of charge has linear charge density 5.00x10^-12 C/m. A proton (mass 1.67x10^-27 kg, c...
- At a certain distance from a point charge, the poten-tial and electric-field magnitude due to that charge are ...
- At a certain distance from a point charge, the poten-tial and electric-field magnitude due to that charge are ...
- An electron is to be accelerated from 3.00x10^6 m/s to 8.00x10^6 m/s. (a) Through what potential difference mu...
- At a certain distance from a point charge, the poten-tial and electric-field magnitude due to that charge are ...
- A positive charge q is fixed at the point x = 0, y = 0, and a negative charge -2q is fixed at the point x = a,...
- Two point charges q_1 = +2.40 nC and q_2 = -6.50 nC are 0.100 m apart. Point A is midway between them; point B...
- Two point charges q_1 = +2.40 nC and q_2 = -6.50 nC are 0.100 m apart. Point A is midway between them; point B...
- Two point charges of equal magnitude Q are held a distance d apart. Consider only points on the line passing t...
- Two point charges of equal magnitude Q are held a distance d apart. Consider only points on the line passing t...
- Point charges q_1 = +2.00 μC and q_2 = -2.00 μC are placed at adjacent corners of a square for which the lengt...
- A small particle has charge -5.00 μC and mass 2.00x10^-4 kg. It moves from point A, where the electric po-tent...