Electric pot. : Find sign of work done

when charges are moving in electric fields it can be quite confusing to figure out the science 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 it's 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 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 um whether the you you can either think on in terms of the external force and or 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 oh i've already placed that point be 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 what i'm doing here's how 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 uh 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 my eye 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 all right 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 time 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 are 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 all right 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 gonna keep it at p i'm gonna move 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 uh what's the sign of the external work so 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 i ask myself what direction does the electric force act well these are 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 is 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 multiple forces 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