 When charges are moving in electric fields, it can be quite confusing to figure out the signs of the work done. So let's solve a couple of conceptual problems to solidify their understanding. All right, so we are given a positive charge is moved slowly from P to Q, find the sign of the work done by the electric field and by the external force in both the cases. So in both cases, we have one fixed charge. And then we are said imagine a positive charge, another charge is moved from P to Q is moved from P to Q in both these cases. And we need to find in doing so, what is the sign of the work done? So we don't have to calculate anything, we just have to figure out what's the sign, whether it's positive or negative, the work done by the electric field or the electric force and the external force. So how do we do this? So let me let me start with the first one. The first thing I'm looking at is it's moved slowly. And that's, that's important. Why is that important? Well, I go back to gravity because I can always imagine things in terms of gravity. So think of it this way, if I had to say take this ball and move it slowly down, then what would I do? Well, I already know that gravity is going to push a pull on it downwards and it's going to try and speed it up to ensure that it doesn't quickly go down to move it slowly, I will have to use my hand and say push it upwards. So what's important to see is that when you're moving things very slowly in a field, your force will always be in the opposite direction of the force due to that field. Does that make sense? Only then you can move it very slowly. If you put the force in the same direction, well, it's going to accelerate fast, very fast. And so what that means, because what that tells me is because because our forces are in the opposite direction, that means when gravity does positive work, I do negative work. So for example, when the ball goes down, notice gravity is doing positive work force and displacement in the same direction. And I would be doing negative work because my force is upwards and the displacement is in the downward direction. And similarly, say if I have to move this ball even further up, in that case, I would be doing positive work, the external force would be doing positive work and gravity would be doing negative work. So what this means is that if I just know the sign of one of them, I would get the sign of the other. Okay, so all you have to do is imagine there's a positive charge at P and you imagine moving it to Q and just asking yourself whether the you can either think in terms of the external force and electric force, whichever you want, and figuring out which one is doing a positive work and the other one would be doing the negative work. So if you know one, you can get the other. Okay, so why don't you pause the video and see if you can use this logic to figure this out. Don't use any formula. Just try to do it logically. So start with this one, pause and try. All right, let's do this. So I'm going to bring in a positive charge and I'm going to keep it at point P or I've already placed at point P. Nice. So this is what we're going to do. We're going to move it from P to Q. And we have to think about whether I'm doing whether the external force is doing positive work. Okay, basically signs, right? So here's I'm doing here's I'm thinking just like I put forces over here, I'm going to put force signs over here as well. So I know that electric field, the electric force is going to be in the opposite, it's going to be to the right, it's going to get repelled by this charge, like charges repel each other. And so electric field is going to push, put a force on it towards the right. Let me write that down. So electric field is going to put a force this way. And so to move it slowly from here to here, I, my external force, I, why should I external force has to go this way, I have to push it this way. And I also know that it's going from P to Q. So I have everything I need now. So it's going this way. Therefore, what is the sign of the work done by the external force by me? Well, my force and the direction is in the same direction. And therefore I am doing positive work. So external force, oops, external force, work done by the external force is positive. But what about the work done by the electric force? Notice it's in the opposite direction. Notice electric force really wants it to go away, but it's coming in the other direction. So the external force, sorry, the electric force, electric force is doing negative work. Alright, so does that make sense? Okay, why don't you try doing the same thing for the second problem? Pause the video and think about that. All right, let's do this. I'm going to make a copy of my test charge and I'm going to bring it over here. The question is the same, move it from P to Q. So I'm going to keep it at P. And I'm going to ask myself first in which direction electric field is putting a force on this. So notice the negative charge pulls on a positive charge. Okay. So electric force this time is towards towards this charge. And therefore my force has to be in the opposite direction. Notice I will always put my force in the opposite direction. Otherwise, I will never be able to move it slowly. This is my force. Hope the color helps you recognize. Okay. And I'm moving it from P to Q just like before. So this charge is going from P to Q, like this. And yeah, and now, well, what about the work done? What is the sign? Again, notice my force and the direction in which the charge would be traveling is the same. Therefore, again, I end up doing positive work. So external work is positive. And in fact, if you think about it, it makes sense. I can feel it, right? I can actually feel the charge separating the charge requires efforts. It's like separating magnets, stuck magnets, it requires efforts. So clearly I'm doing positive work. I can feel that. And so electric, electric force is doing negative work. Let's try one more similar setup. But we're given this time a negative charge is moved slowly from P to Q. And we have to find the sign of the work done by the electric field and the external force. So again, why don't you give this one a shot yourself first? Alright, hopefully you've tried. So for the first one, again, I'm going to do exact same thing. But this time it's a negative charge, but the concept stays the same. It won't matter. So here's my negative charge. Where is that? Okay, here it is. And we're moving it from P to Q. So I'm going to keep it at P. And we're moving it from P to Q. So the first thing I do is ask myself, Hey, what direction are the forces? Because to find the sign of the work done, I need to know which direction the forces are, which direction the displacement is. So when I keep it over here, positive will attract. So the electric force is downwards. So I know that downwards. And therefore to move it slowly, my force should always be in the opposite direction. And I know it's being moved from P to Q. So I know it's going this way. So what direction, what's the sign of the external work? My force and the displacement in the same direction. So my work done is positive. So I do positive work. External is positive. What about the electric field? It ends up doing negative work. Electric does negative work. What about this one? Well, let's do the same thing. Let's copy it and keep it at P. That's where we're going to keep it. Okay. And again, ask myself, what direction does the electric force act? Well, these are repelling each other. And so it'll move, try to make it move away. And therefore the electric force is this way. And therefore my force has to be in the opposite direction. And therefore, which direction is going? It's going from P to Q. It's P to Q. And one of the common confusions or common mistakes people usually make over here is, you know, you think like this or I used to always think like this is, hey, I'm moving from P to Q. So my force must be downwards. It's not like that. Go back to gravity. Remember, even if I have to move this ball down, if I have to move it slowly, I have to keep pushing it up. Even though I want that ball to go down. So yeah, it takes a little while to get used to it because we usually tend to think that whichever direction you push that object goes in that direction, but when a multiple force is acting on it, you have to be a little bit careful. A little bit of practice you'll get it. Don't worry. Okay. So this time notice electric force is doing positive work. So electric force is doing positive work. And I, I am doing negative work. And there we have, we have it, we have solved, we now know how to figure out positive works and negative works and all of that thing.