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Potential energy and position

The potential energy between two objects due to long-distance forces can be thought of as being stored in a field. When the objects move due to the field forces, the energy stored in the field decreases.  Created by Sal Khan.

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Video transcript

- [Presenter] In this video, we're gonna talk about how energy is stored in field and in particular, how if we change the position of things within that field, how it might change the energy. So, just as a bit of a refresher, let's remind ourselves what energy is. It is the capacity to do work. And we've also seen that work, we can view it as equal to the magnitude of force times the displacement in the direction of that force. And then we can also remind ourselves what a field is. And I'm not just talking about a big lawn or something like that, a football field. I'm talking about a general idea in physics that's used. It's really just a concept that allows us to predict and explain how to things that are not touching each other are still interacting, are still able to exert forces on each other. And in other videos, I've also talked about that. Really nothing in this universe is touching. We just conceptualize that sometimes they are. But just as an example of a field, we have an electric field here. I could have done another type of field, we could have done a magnetic field, we could have done a gravitational field. Although when you study general relativity which Einstein gave us, we realize that it might not exactly be optimal to think about it as a field. But in an electric field, right over here, we have a positive charge, we have a negative charge. We know from experience that these two things attract each other and the convention is to draw these field lines that go from the positive towards the negative. Now, if we were to just let go of these two point charges over here, what would happen? Well, we know that due to the electric field constructed or created or that we imagined was created by this negative point charge, this positive charge would have a force acting on it towards the negative charge and vice versa due to the electric field that is created by the positive charge. The negative charge is going to also be attracted to the positive charge. They're both going to move towards each other. And so, when we talk about energy in fields or energy stored in fields, in our initial configuration, how is there energy in this field? How is their capacity to do work? Pause this video and think about that. Well, think about it this way. Imagine if each of these charges were attached to some type of a mass, let me do this in a color you can actually see. So, let's say that this is towing some type of a mass and this is towing some type of a mass right over here. Well, when you let go and the forces are exerted on each of these point charges, assuming that the forces are large enough, they're going to be able to pull these masses towards each other. So, there's a potential amount of work that could be done and it would essentially keep happening until these point charges touch. And I used air quotes with my hand even though you can't see it, or until they can't get any closer to each other or some other is keeping them from getting any closer to each other. So now, let me think about how could I increase the energy that is stored in this field. Pause the video and think about that. Well, what if I were to keep the positive charge where it is, but if I were to take the negative charge and if I were to move it in a direction opposite from the force direction that the field is trying to exert. So, instead of the negative charge there, what if I moved it all the way out there? Once again, let me do that in a color you can actually see. Well, if I moved it out here and we're still towing some type of a mass, you can see that when I moved it against the direction that the force of the field is trying to exert, that I've increased the energy in the field because now I can do more work. I can drag this potential mass over a larger distance. So, we have a general principle here. If we let these charges go in the direction of the forces that are being exerted on them due to the field, we're going to reduce the energy in the field. But then if we are able to move them against the forces of the field, and as you can imagine, we're going to have to put energy into the system to do that. But if we do that, then we're storing more energy in this field because in that case, they're going to be further away from each other and so they could drag their little masses that they're towing even further.