Electric pot.: Where is potential (energy) more?

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 you know i have more experience with gravity than charges in my life so just to remind ourselves so that you know we make sense of this in in gravity also we define potentially 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 its 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 oh so that means if i were to keep it at point q it would automatically starts moving towards speed will 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 down 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 now before we go to the next one and i know i'm i'm pretty sure you're like motivated to go and excited to do the next one i want to tell you that there are more than one ways to solve these things and so i'm going to show you another way to think about it if i go back to gravity i can 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 can 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 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 do the same uh 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 muck this up don't ever try to memorize anything always go back to gravity will help so along the field potential reduces high to low make 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 over here so we have to move the negative charge from p to q and see what's going to happen and we're going to use the 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 going to keep my negative charge over here at p and i'm going to move it from p to q now okay that's how i'm going to do i'm going to 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 it's it's increase it 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 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 should have high potential energy and at this point you should have let me 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 was 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 you have high potential here and a low potential here but a negative charge is this 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 the 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 you'll have the opposite effect the concept remains the same and you may ask okay can i do i have examples like that in gravity unfortunately no because in gravity you 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 hearing 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 going to 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 uh upwards right so imagine i throw this charge from here to here what happens to the speed of that charge oh it slows down slows down slows down slows down which means that kinetic energy is getting converted into potential potential potential 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'll 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 will 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 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 theo perspective because positive is our standard that will be the other way around