Learn about Electric Potential Energy Video

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Learn about Electric Potential Energy

Let's review a little bit of what we have learned many, many videos ago about gravitational potential energy. And then see if we can draw the analogy which is very strong to electrical potential energy. So what do we know about gravitational potential energy, we said this was the surface of the earth and we don’t have to be on earth but it makes visualization easy. We could be anywhere that has gravity and the potential energy would be due to the gravitational field of that particular mass. But let's say this is the surface of the earth. We learned that if we have some mass, M, up here, some mass M and that the gravitational field at this area or at least the gravitational acceleration is G or 9.8 meters per second squared. And it is h, we could say meters but we can use any units. Let's say it is h meters above the ground. But the gravitational energy of this object at that point is equal to the mass times the acceleration of gravity times the height. Or you could view it as the force of gravity, the magnitude of the force of gravity, the vector but we could say the magnitude of the vector times height. And so what is potential energy? What we know that has something has potential energy and if nothing stopping it, we just let go, that energy with gravitational potential energy, the object will start accelerating downwards. And a lot of that potential energy and eventually all of it will be converted to kinetic energy. So potential energy is energy that is being stored by an object situation or a kind of this notional energy that an object has by virtue of what it is. So in order for something to have this notional energy, some energy must have been put into it. And as we learned with gravitational potential energy, you could use gravitational potential energy as the work necessary to move an object to that position. Now if we’re talking about work to move something to that position or whatever, we always think about, well move it from where? Well when we talked about gravitational potential energy, we were talking about moving it from the surface of the earth. And so how much work is required to move that same mass, let's say it was here at first, to move it from a height of zero to a height of h. well the whole time the earth or the force of gravity I going to be F sub g, so essentially, if I'm pulling it or pushing it upwards, I'm going to have, and let's say the cons of velocity, I'm going to have to have the equal opposite force to its weight to pull it up, otherwise it would accelerate downwards. I’d have to do a little bit more just to get it moving to accelerate it however much. But once again, just accelerating, essentially I’d have to have applied it upward force which is equivalent to the downward force of gravity and I would do it for a distance of h. What is work? Work is just force times distance. And it has to be force in the direction of the distance. So what's the work necessary to get this mass up here? Well the work is equal to the force of gravity times height. So it’s equal to the gravitational potential energy. Now this is an interesting thing, notice we picked the reference point as the surface of the earth but we could have picked any arbitrary reference point. We could have say, well from, I don’t know, 10 meters below the surface of the earth which could have been down here. Or we could have actually said from a plat form that’s 5 meters above the earth. So it actually turns out, when you think of it that way, that potential energy of any form but especially gravitational potential energy and we’ll see electrical potential energy, it’s always in reference to some other point. So it’s really a change in potential energy that matters. And we know when we studied potential energy, it seem like there was kind of absolute potential energy but that because we always assume that the potential energy is something is zero at the surface of the earth and we want that potential energy relative to the surface of the earth so it be kind of how much work does it take to take something from the surface of the earth to that height. But really, we should be saying, well the potential energy of gravity like this statement should read, this is just the absolute potential energy of gravity, we should say that this is the potential energy of gravity relative to the surface of the earth is equal to the work necessary to move something, to move that same mass from the surface of the earth to its current position. We could have said, we could have defined some other term that is not really used but we could have said potential energy of gravity relative to -5 meters below the surface of the earth. And that would be the work necessary to move something from -5 meters to its current height. And of course, that might matter. What if we cut up a hole and we wanted to see what was the kinetic energy here, well then that potential energy would matter. Anyway, so I just wanted to do this review of potential energy because now it will make the jump to electrical potential energy all that easier because electricity, it’s pretty much the same thing, it’s just the source of the field and the source of the potential is something different. So electrical potential energy, we know that gravitational fields are not constant. We can assume they're constant maybe near the surface of the earth and all that. But we also know that electrical fields aren't constant. Actually they have very similar formulas. But just for simplicity of explaining it, les assume a constant electric field. And if you don’t believe me, that one can constructed, you should watch my videos that involve at least a bit of calculus that show that a uniform electric field can be generated by infinite uniformly charged plain. And let's say this is the side view of the infinite uniformly charged plain. And let's say that this is positively charged. Of course, you can ever get a proper side view of an infinite plain because you can never cut it because it’s infinite in every direction. But let's say, this one is the side view. And so first of all, let's think about its electric field. Its electric field is going to point upward and how do we know it points upward? Because the electric field is essentially what is, and this is just a convention, what would a positive charge do in the field? Well, if this plain is positive, a positive charge is going to get away from it. So your electric field point upward and we know that it is constant. that if this were a field vectors that they're going to be the same size no matter how far away we get from the field as from the source of the field. I'm just going to pick a number for the strength of the field. We actually proved in those fancy videos that I made on the uniform electric field of an infinite uniformly charged plain, that we actually proved how you could calculate it but let's just say that this electric field is equal to 5 newtons per coulomb. That’s actually quite strong but it makes the math easy. So my question to you is how much work does it take to take a positive point charge, let me pick a different color, let's say I have, so let's say this is the starting position, it’s a positive 2 coulombs. Once again that’s a massive point charge but we want easy numbers. How much work does it take it to move that 2-coulomb charge 3 meters within this field? How much work? So, we’re going to start here and we’re going to move it down towards the plain 3 meters and that’s ending position is going to be right here. That’s where it’s when it’s done. How much work does that take? Well what is the force of the field right here? What is the force exerted in this 2-coulomb charge? Well electric field is just force per charge, right. so if you want to know the force of the field at that point, let me draw that in a different color, the force of the field acting on it, so let's see, the field force, the force of the field actually, is going to be equal to 5 newtons per coulomb times 2 coulombs which is equal to the newtons. And we know it’s going to be upward because this is a positive charge and this is a positively charged infinite plate. So we know this upward force of 10 newtons. So in order to get this charge to push it down here, we essentially have to exert a force of 10 newtons downwards, right. Exert a force of 10 newtons in the direction of the movement. And of course, just like we did with gravity, we have to do maybe a little bit more than that just to accelerate a little bit just so you have some net downward force. But once you do, you just have to completely balance the upward force. So just for our purposes, you have a 10-newton force downward and you apply that force for a distance of 3 meters. The work that you put to take this 2-coulomb charge from here to here is going to be equal to, the work is going to be equal to 10 newtons, that’s the force, times 3 meters. So the work is going to equal 30 newton meters which is equal to 30 joules. A joule is just a newton meter. And so, we can now say since it took us 30 joules of energy to move this charge from here to here, but within this uniform electric field, the potential energy of the charge here relative to charge be here. You always have to pick a point relative to where the potential is. So the electrical potential energy here relative to here, potential energy and this is electrical potential energy, and you could say P2 relative to P1. I’m using my made up notation but that gives you a sense of what it is, is equal to 30 joules. And how could that help us? Well if we also knew the mass, let's say that this charge had some mass, we would know that if we let go of this object, by the time it got here, that 30 joules would be essentially, assuming that you know none of it got transmitted to heat or resistance or whatever, we know that all of it will be kinetic energy at this point. So actually we could work it out. Let's say that this does have a mass of 1 kilogram and we were to just let go of it, we use some force to bring it down here and we let go. So we know that the electric field is going to accelerate it upwards, it’s going to exert a force, upward force of 5 newtons per coulomb, and the thing that it’s going to keep it accelerating it until it gets to this point. What's its velocity going to be at that point? Well all of this electrical potential energy is going to be converted to kinetic energy. So essentially, we have 30 joules is going to be equal to 1/2mv2, right, we know the mass is 1. So we get 60 is equal to v2. So the velocity is the square root of 60, so 7 point something, something, something meters per second. So if I just pull that charge down, it has a mass of 1 kilogram and I let go, it’s just going to accelerate and be going pretty fast once it gets to this point. Anyway, I'm 12 minutes into this video so I will continue the next. But hopefully that gives you sense of what electrical potential energy is and really it’s no different than gravitational potential energy. It’s just the source of the field is different. See you soon.

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Let's review a little bit of what we have learned many, many videos ago about gravitational potential energy. And then see if we can draw the analogy which is very strong to electrical potential energy. So what do we know about gravitational potential energy, we said this was the surface of the earth and we don’t have to be on earth but it makes visualization easy. We could be anywhere that has gravity and the potential energy would be due to the gravitational field of that particular mass. But let's say this is the surface of the earth. We learned that if we have some mass, M, up here, some mass M and that the gravitational field at this area or at least the gravitational acceleration is G or 9.8 meters per second squared. And it is h, we could say meters but we can use any units. Let's say it is h meters above the ground. But the gravitational energy of this object at that point is equal to the mass times the acceleration of gravity times the height. Or you could view it as the force of gravity, the magnitude of the force of gravity, the vector but we could say the magnitude of the vector times height.
And so what is potential energy? What we know that has something has potential energy and if nothing stopping it, we just let go, that energy with gravitational potential energy, the object will start accelerating downwards. And a lot of that potential energy and eventually all of it will be converted to kinetic energy. So potential energy is energy that is being stored by an object situation or a kind of this notional energy that an object has by virtue of what it is. So in order for something to have this notional energy, some energy must have been put into it. And as we learned with gravitational potential energy, you could use gravitational potential energy as the work necessary to move an object to that position.
Now if we’re talking about work to move something to that position or whatever, we always think about, well move it from where? Well when we talked about gravitational potential energy, we were talking about moving it from the surface of the earth. And so how much work is required to move that same mass, let's say it was here at first, to move it from a height of zero to a height of h. well the whole time the earth or the force of gravity I going to be F sub g, so essentially, if I'm pulling it or pushing it upwards, I'm going to have, and let's say the cons of velocity, I'm going to have to have the equal opposite force to its weight to pull it up, otherwise it would accelerate downwards. I’d have to do a little bit more just to get it moving to accelerate it however much. But once again, just accelerating, essentially I’d have to have applied it upward force which is equivalent to the downward force of gravity and I would do it for a distance of h.
What is work? Work is just force times distance. And it has to be force in the direction of the distance. So what's the work necessary to get this mass up here? Well the work is equal to the force of gravity times height. So it’s equal to the gravitational potential energy. Now this is an interesting thing, notice we picked the reference point as the surface of the earth but we could have picked any arbitrary reference point. We could have say, well from, I don’t know, 10 meters below the surface of the earth which could have been down here. Or we could have actually said from a plat form that’s 5 meters above the earth. So it actually turns out, when you think of it that way, that potential energy of any form but especially gravitational potential energy and we’ll see electrical potential energy, it’s always in reference to some other point. So it’s really a change in potential energy that matters.
And we know when we studied potential energy, it seem like there was kind of absolute potential energy but that because we always assume that the potential energy is something is zero at the surface of the earth and we want that potential energy relative to the surface of the earth so it be kind of how much work does it take to take something from the surface of the earth to that height. But really, we should be saying, well the potential energy of gravity like this statement should read, this is just the absolute potential energy of gravity, we should say that this is the potential energy of gravity relative to the surface of the earth is equal to the work necessary to move something, to move that same mass from the surface of the earth to its current position. We could have said, we could have defined some other term that is not really used but we could have said potential energy of gravity relative to -5 meters below the surface of the earth. And that would be the work necessary to move something from -5 meters to its current height.
And of course, that might matter. What if we cut up a hole and we wanted to see what was the kinetic energy here, well then that potential energy would matter. Anyway, so I just wanted to do this review of potential energy because now it will make the jump to electrical potential energy all that easier because electricity, it’s pretty much the same thing, it’s just the source of the field and the source of the potential is something different.
So electrical potential energy, we know that gravitational fields are not constant. We can assume they're constant maybe near the surface of the earth and all that. But we also know that electrical fields aren't constant. Actually they have very similar formulas. But just for simplicity of explaining it, les assume a constant electric field. And if you don’t believe me, that one can constructed, you should watch my videos that involve at least a bit of calculus that show that a uniform electric field can be generated by infinite uniformly charged plain. And let's say this is the side view of the infinite uniformly charged plain. And let's say that this is positively charged. Of course, you can ever get a proper side view of an infinite plain because you can never cut it because it’s infinite in every direction. But let's say, this one is the side view. And so first of all, let's think about its electric field. Its electric field is going to point upward and how do we know it points upward? Because the electric field is essentially what is, and this is just a convention, what would a positive charge do in the field? Well, if this plain is positive, a positive charge is going to get away from it. So your electric field point upward and we know that it is constant. that if this were a field vectors that they're going to be the same size no matter how far away we get from the field as from the source of the field.
I'm just going to pick a number for the strength of the field. We actually proved in those fancy videos that I made on the uniform electric field of an infinite uniformly charged plain, that we actually proved how you could calculate it but let's just say that this electric field is equal to 5 newtons per coulomb. That’s actually quite strong but it makes the math easy. So my question to you is how much work does it take to take a positive point charge, let me pick a different color, let's say I have, so let's say this is the starting position, it’s a positive 2 coulombs. Once again that’s a massive point charge but we want easy numbers. How much work does it take it to move that 2-coulomb charge 3 meters within this field? How much work?
So, we’re going to start here and we’re going to move it down towards the plain 3 meters and that’s ending position is going to be right here. That’s where it’s when it’s done. How much work does that take? Well what is the force of the field right here? What is the force exerted in this 2-coulomb charge? Well electric field is just force per charge, right. so if you want to know the force of the field at that point, let me draw that in a different color, the force of the field acting on it, so let's see, the field force, the force of the field actually, is going to be equal to 5 newtons per coulomb times 2 coulombs which is equal to the newtons. And we know it’s going to be upward because this is a positive charge and this is a positively charged infinite plate. So we know this upward force of 10 newtons.
So in order to get this charge to push it down here, we essentially have to exert a force of 10 newtons downwards, right. Exert a force of 10 newtons in the direction of the movement. And of course, just like we did with gravity, we have to do maybe a little bit more than that just to accelerate a little bit just so you have some net downward force. But once you do, you just have to completely balance the upward force. So just for our purposes, you have a 10-newton force downward and you apply that force for a distance of 3 meters. The work that you put to take this 2-coulomb charge from here to here is going to be equal to, the work is going to be equal to 10 newtons, that’s the force, times 3 meters. So the work is going to equal 30 newton meters which is equal to 30 joules. A joule is just a newton meter.
And so, we can now say since it took us 30 joules of energy to move this charge from here to here, but within this uniform electric field, the potential energy of the charge here relative to charge be here. You always have to pick a point relative to where the potential is. So the electrical potential energy here relative to here, potential energy and this is electrical potential energy, and you could say P2 relative to P1. I’m using my made up notation but that gives you a sense of what it is, is equal to 30 joules. And how could that help us? Well if we also knew the mass, let's say that this charge had some mass, we would know that if we let go of this object, by the time it got here, that 30 joules would be essentially, assuming that you know none of it got transmitted to heat or resistance or whatever, we know that all of it will be kinetic energy at this point.
So actually we could work it out. Let's say that this does have a mass of 1 kilogram and we were to just let go of it, we use some force to bring it down here and we let go. So we know that the electric field is going to accelerate it upwards, it’s going to exert a force, upward force of 5 newtons per coulomb, and the thing that it’s going to keep it accelerating it until it gets to this point. What's its velocity going to be at that point? Well all of this electrical potential energy is going to be converted to kinetic energy. So essentially, we have 30 joules is going to be equal to 1/2mv2, right, we know the mass is 1. So we get 60 is equal to v2. So the velocity is the square root of 60, so 7 point something, something, something meters per second.
So if I just pull that charge down, it has a mass of 1 kilogram and I let go, it’s just going to accelerate and be going pretty fast once it gets to this point. Anyway, I'm 12 minutes into this video so I will continue the next. But hopefully that gives you sense of what electrical potential energy is and really it’s no different than gravitational potential energy. It’s just the source of the field is different. See you soon.

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