 Potentials and potential energies can be so confusing. So let's try to solidify our understanding by solving a couple of conceptual problems. So here's problem number one. We are given, or we are asked, find which point P or Q has higher electric potential. So we have two cases. In both cases, we have P and Q and we have charges. We need to figure out which point has a higher electric potential. How do I do that? So the first thing I do is I ask myself, hey, what's the meaning of potential? Well, you can think of electric potential as basically how much potential energy a coulomb would have at any point. So all I have to think about is when I take a coulomb of charge and I move it from one point to another, what happens to its potential energy? If it increases, then the potential increases. If it decreases, then the potential decreases. So that's all I have to do. But before I do that, I always like to go back and think from gravity perspective because gravity helps me logically because I have more experience with gravity than charges in my life. So just to remind ourselves so that we make sense of this, in gravity also we define potential in a very similar way. If I take, imagine this is my test mass, all right? If I drop it, then I know as it goes down its potential energy drops. And the reason we say that is because it's kinetic energy picks up. So we say that potential is getting converted to kinetic. So the potential energy drops and therefore I know as I go down, the potential also drops. So now all I have to do to figure out what happens over here is imagine a positive test charge. So here it is. And just keep it at one point and see if I let go of it in which direction it moves. So along that direction, the potential must drop. So can you now use this and pause this video and see if you can figure this out yourself? So pause and try. All right. So let me keep it over here at point P. Let me start over there and see what happens. Well, if I let go of this charge, this repels this. And I know as it, because of repulsion and let's assume this is fixed. This is a very tiny charge, let's assume, okay? So due to repulsion, this starts moving away. Ooh, so that means if I were to keep it at point Q, it will automatically starts moving towards P or accelerate towards P. So that means, and let me write that over here, that means if I keep this positive charge over here, it will accelerate this way. It will accelerate in that direction, meaning it will pick up kinetic energy in that direction, meaning it should lose potential energy in that direction. And therefore I know that this must be high potential. So let me just write that over, okay? This is high potential and this side should be low potential. So over here, Q, the potential of Q should be higher than potential of P. All right, now before we go to the next one, and I know I'm pretty sure you are motivated and excited to do the next one, I wanna tell you that there are more than one ways to solve these things. And so I'm gonna show you another way to think about it. If I go back to gravity, from this I can just see that along the direction of gravity, potential reduces. And that makes sense because along the direction of gravity, body accelerates and loses potential. So if I just know what direction the field lines are, in that direction the potential reduces. And so that's another way I can look at it. I can just say, let me draw field lines due to this positive charge and along the field line, the potential would reduce. And we know that due to a positive charge, the field lines will always be away from it. So I can draw field lines like this. And notice, even I could have said this way, along the field line potential reduces and we get the same answer, high, low. Okay, how about you give it a shot for the second one? So pause the video, use the same logic and see if you can figure out which has higher potential. All right, let's see. Let's do both methods. Let's first use the positive charge. Let's say I keep it at point P and see what happens. I let go of it and I see it gets attracted by this negative charge. And again, we'll assume that the negative charge is fixed. This is a very tiny charge. So it gets attracted, it gets attracted, meaning it accelerates at this way. So let me write that down. So I know this my charge is accelerating, accelerate this way. So it's kind of like falling towards Q, losing potential energy. So I know that this should have higher potential and this should have low potential. And remember, whenever you're doing this, you should always use a positive charge because our potentials are always defined by positive charges, not negative. Okay, so this means VP over here is higher than VQ. And we can use the field lines as well. If I draw field lines for this charge, negative charges have field lines towards it. So field lines would be like this. And we just said, looking at gravity along the field, potential reduces. Again, again, don't mug this up. Don't ever try to memorize anything. Always go back to gravity or help. So along the field, potential reduces, high to low, makes sense. All right, let's try another problem. A similar setup, but this time we're given, if a small negative charge is moved from P to Q, what happens to its potential energy? So this time you have to move a negative charge from P to Q and see what happens to its potential energy. So again, why don't you pause the video and first give it a shot yourself? All right, hopefully you've tried. Let me start with problem A. I'm gonna, this time, bring in a negative charge and put it over here. So we have to move the negative charge from P to Q and see what's gonna happen. And we're gonna use a similar, very, very similar approach. If you want to know what happens to its potential energy, just let go of it and see which direction it accelerates. In that direction, it should be losing potential energy. Okay, so I'm gonna keep my negative charge over here at P and I'm gonna move it from P to Q now. Okay, that's how I'm gonna do it. I'm gonna move it from P to Q and ask myself, as I move it from P to Q, what happens to its speed? Think of it that way. So let's see, if I keep it at point P, I know it's being attracted by this positive charge. And as a result, automatically it'll start moving, moving, moving and it'll start accelerating. Its speed starts increasing. So let me just write that down. Let me write that down. All right, so I know that as it goes from here to here, it accelerates, accelerates. And as a result, its speed must be increasing. Kinetic energy must be increasing. Therefore, its potential energy must be decreasing. And so at this point, it must have high potential energy. So let me just write that over here. It should have high potential energy. And at this point, you should have, let me move this to the side. Okay, at this point, it should have low potential energy. So what happens as it goes from P to Q, its potential energy drops. But before we move on, there could be some confusion based on what we did earlier. So if you looked at what we did earlier, what we found out earlier, we said as you go from here to here, potential drops, right? Like we said, there's a field line over here like this. And then we said along the field line, the potential drops. So if I use a positive charge, then it's the exact opposite. We said this is high potential and this is low potential, right? And this can be very confusing, what's going on. So think about it. When we talk about potential, electric potential, we are always thinking in terms of a positive charge. All right? So if you think in terms of a positive charge, it will accelerate this way. And as a result, you have high potential here and a low potential here. But a negative charge just does the opposite thing. It'll accelerate in the opposite direction. And so negative charges potential energy will be in the opposite direction. But if somebody asks you, which point has a higher electric potential, you always think in terms of positive charge. And that's why the answer would be, in the previous case, what we got is this point is high and this point is low. And I know at first this could be very confusing. But remember, positive is your standard. So when people say, what's electric potential, think from positive charges point of view, positive test charges point of view. And a negative test charge, if you are asked to do that, it'll have the opposite effect. The concept remains the same. And you may ask, okay, do I have examples like that in gravity? Unfortunately, no, because in gravity only have positive masses. But you can think about a helium balloon. You can imagine a helium balloon, although it's not negative mass, you can kind of sort of think of it that way. And you can see a helium balloon naturally tends to accelerate upwards. And so it naturally accelerates from low potential to high potential. Naturally, the opposite of what normal masses do, just like what we got over here. All right. So why don't you try using this for the second one and solving the second one? All right. Let's see. So I'm gonna bring my negative test charge. I have to move it from P to Q and see what happens. So let's think about it. If I take this charge and move it from P to Q, what happens to its speed? Now notice it's being repelled by this charge. And so it automatically wants to go away. See, this charge wants to go away. But if I want to bring it from here to here, I have to like throw it. Sort of like when you take a ball, you have to throw it up if you want to go it up upwards, right? So imagine I throw this charge from here to here. What happens to the speed of that charge? Ooh, it slows down, slows down, slows down, slows down. Which means that kinetic energy is getting converted into potential, potential, potential. Ooh, let's write that down, let's write that down. It's interesting. So if my negative charge went where to go from P to Q, it will decelerate, not acceleration, it will decelerate. It'll slow down, meaning its potential energy should increase. All that kinetic gets converted to potential. And so I can now say, ah, this should be low potential energy. It'll have low potential energy here. And as it goes over here, its potential energy picks up, picks up, picks up. And so it should have high potential energy here. And so what's the answer? What happens to its potential energy as it goes from here to here? It increases this time. It increases. And again, just like before, if I ask you what happens to the potential, electric potential as you go from here to here, then you have to think from a positive charges perspective because positive is our standard. Then it will be the other way around.