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Sal explains the difference between electrical potential (voltage) and electrical potential energy. Created by Sal Khan.
Video transcript
Before we move on, I want to clarify something that I've inadvertently done. I think I was not exact with some of the terminology I used. So I want to highlight the difference between two things that I've used almost interchangeably up to this point, but now that we are about to embark on learning what voltage is, I think it's important that I highlight the difference, because initially, this can be very confusing. I remember when I first learned this, I found I often mixed up these words and didn't quite understand why there was a difference. So the two words are electrical-- or sometimes you'll see electric instead of electrical. So "electric potential energy" and "electric potential." I think even in the last video, I used these almost interchangeably, and I shouldn't have. I really should have always used electrical or electric potential energy. And what's the difference? Electrical potential energy is associated with a charge. It's associated with a particle that has some charge. Only that particle can have energy. Electrical potential, or electric potential, this is associated with a position. So, for example, if I have a charge and I know that it's at some point with a given electric potential, I can figure out the electric potential energy at that point by just multiplying actually this value by the charge. Let me give you some examples. Let's say that I have an infinite uniformly charged plate. So that we don't have to do calculus, we can have a uniform electric field. Let's say that this is the plate. I'll make it vertical just so we get a little bit of change of pace, and let's say it's positively charged plate. And let's say that the electric field is constant, right? It's constant. No matter what point we pick, these field vectors should all be the same length because the electric field does not change in magnitude it's pushing out, because we assume when we draw field lines that we're using a test charge with a positive charge so it's pushing outward. Let's say I have a 1-coulomb charge. Actually, let me make it 2 coulombs just to hit a point home. Say I have a 2-coulomb charge right here, and it's positive. A positive 2-coulomb charge, and it starts off at 3 meters away, and I want to bring it in 2 meters. I want to bring it in 2 meters, so it's 1 meter away. So what is the electric-- or electrical-- potential energy difference between the particle at this point and at this point? Well, the electrical potential energy difference is the amount of work, as we've learned in the previous two videos, we need to apply to this particle to take it from here to here. So how much work do we have to apply? We have to apply a force that directly-- that exactly-- we assume that maybe this is already moving with a constant velocity, or maybe we have to start with a slightly higher force just to get it moving, but we have to apply a force that's exactly opposite the force provided by Coulomb's Law, the electrostatic force. And so what is that force we're going to have to apply? Well, we actually have to know what the electric field is, which I have not told you yet. I just realized that, as you can tell. So let's say all of these electric field lines are 3 newtons per coulomb. So at any point, what is the force being exerted from this field onto this particle? Well, the electrostatic force on this particle is equal to the electric field times the charge, which is equal to-- I just defined the electric field as being 3 newtons per coulomb times 2 coulombs. It equals 6 newtons. So at any point, the electric field is pushing this way 6 newtons, so in order to push the particle this way, I have to completely offset that, and actually, I have to get it moving initially, and I'll keep saying that. I just want to hit that point home. So I have to apply a force of 6 newtons in the leftward direction and I have to apply it for 2 meters to get the point here. So the total work is equal to 6 newtons times 2 meters, which is equal to 12 newton-meters or 12 joules. So we could say that the electrical potential energy-- and energy is always joules. The electrical potential energy difference between this point and this point is 12 joules. Or another way to say it is-- and which one has a higher potential? Well, this one does, right? Because at this point, we're closer to the thing that's trying to repel it, so if we were to just let go, it would start accelerating in this direction, and a lot of that energy would be converted to kinetic energy by the time we get to this point, right? So we could also say that the electric potential energy at this point right here is 12 joules higher than the electric potential energy at this point. Now that's potential energy. What is electric potential? Well, electric potential tells us essentially how much work is necessary per unit of charge, right? Electric potential energy was just how much total work is needed to move it from here to here. Electric potential says, per unit charge, how much work does it take to move any charge per unit charge from here to here? Well, in our example we just did, the total work to move it from here to here was 12 joules. But how much work did it take to move it from there to there per charge? Well, work per charge is equal to 12 joules for what? What was the charge that we moved? Well, it was 2 coulombs. It equals 6 joules per coulomb. That is the electric potential difference between this point and this point. So what is the distinction? Electric potential energy was associated with a particle. How much more energy did the particle have here than here? When we say electric potential, because we essentially divide by the size of the particle, it essentially is independent of the size of the particle. It actually just depends on our position. So electric potential, we're just saying how much more potential, irrespective of the charge we're using, does this position have relative to this position? And this electric potential, that's just another way of saying voltage, and the unit for voltage is volts. So 6 joules per coulomb, that's the same thing as 6 volts. And so if we think of the analogy to gravitation, we said gravitational potential energy was mgh, right? This was force. This was distance, right? Electric potential is essentially the amount of gravitational-- if we extend the analogy, the amount of gravitational potential energy per mass, right? So if we wanted a quick way of knowing what the gravitational potential is at any point without having to care about the mass, we divide by the mass, and it would be the acceleration of gravity times height. Ignore that if it confused you. So what is useful about voltage? It tells us regardless of how small or big or actually positive or negative a charge is, what the difference in potential energy would be if we're at two different points. So electric potential, we're comparing points in space. Electric potential energy, we're comparing charges at points in space. Hopefully, I didn't confuse you. In the next video, we'll actually do a couple of problems where we figure out the electric potential difference or the voltage difference between two points in space as opposed to a charge at two different points in space. I will see you in the next video.