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Current time:0:00Total duration:11:15

Electric potential at a point in space

Video transcript

let's talk about electric potential V this is confusing this is one of if not the most confusing ideas in all of physics for one it sounds just like electric potential energy but it's not this is different it's related to electric potential energy but the electric potential V is different from electric potential energy so that was a poor choice of naming and the other reason it's confusing is that the electric potential V is a number just a number that's it associated with points in space so it's abstract this is an abstract idea you get you can't go hold electric potential in your hand it's a number an abstract number at every point in space here's points in space I just put circles around empty spots on the screen there's like nothing here I just put circles here these are circles around empty points in space just so we can talk about them explicitly and well if there was no charge around if you literally had an empty universe the V value at every point in this universe would be zero it'd be zero there and be zero over here the number associated with every point in space would be zero that'd be boring and useless how do we make it so that the V value the electric potential value is not zero we just stick a charge in here so let's take a big old positive Q at some point in space over here take a big old charge and we'll stick it right there now points in space around this charge will have a V value that's nonzero and they'll be big if you're near this Q so the V values around here are going to be really big and then the V values way out here will be smaller the farther away you go the smaller it gets and why do we care who cares the reason we care is this the units of electric potential are joules per Coulomb so electric potential has units of joules per Coulomb that's give you a hint of why you should care we care about joules joules or energy so if something can have energy that's useful you can get work out of that or it can turn into kinetic energy and joules per Coulomb that lets you know our well if this point over here happen to have say 100 joules per Coulomb let's say the V value at this point in space happen to be a hundred joules per Coulomb what that means is remember there's nothing there but if there was something there if we happen to take say we had a positive two coulombs arge and we took that charge and we put it there at that empty point in space before we put it there the V value was a hundred when we stick it here who cares why do we care about this hundred value cuz look at it's a hundred joules per Coulomb that's what V the electric potential is telling us so if it's a hundred joules per Coulomb and I stick two coulombs there how many joules of energy do you think it's going to have it will have two hundred and that's the key that's why we care about electric potential because it lets us find electric potential energy either PE sometimes people write electric potential energy as u so the formula is just Q you take the Q that you stick at that point in space in this case it was two coulombs take whatever Q there is multiply it by the value of the electric potential and that tells you how many joules there will be for the charges in that region so this electric potential energy is between these two charges here the charge that created the V and the charge that you stick at that point and the V is a quick way to figure out how much potential energy electrical potential energy there would be so in other words in this case since I had two coulombs there I'd take my two coulombs and I multiply by 100 joules per Coulomb because that's V value and I'd get that there are two hundred joules of potential energy now stored between these charges so that's why we care about electric potential V it's a way to figure out the electric potential energy for a charge that's placed at that point in space that has that V value but how do you get this V value if I hadn't given you the hundred joules per Coulomb we wouldn't have been able to figure this out we need a way to figure out the V value at points in space based on the charges creating them because charges create the V value there's a formula for it and the formula says that the V the electric potential created by point charge is equal to K K is the electric constant nine times 10 to the ninth and it has units of Newton meter squared per coulombs squared so that's always K you take that K and you multiply by the charge that's creating the V value so in this case it's this Q this positive Q here whatever Q it is creating the V value that you want to find and that's key if you plug in five coulombs here you're finding the V created by that five coulombs if you plug in negative three coulombs you're finding the V created by the negative three coulombs sometimes there's problems with multiple charges in it like this one and this Q has got to be the charge creating this V not the charge you placed at that point in space I don't put the two coulombs up here I put the charge creating the V value that I want to find and then you divide by the distance so I divide by the distance between this charge and the point in space that I want to figure out the V value at some people call this the radius I don't like calling it the radius makes it sound like there has to be a circle there doesn't really have to be a circle this R would be the distance from this point of charge creating this V value to the point in space where I want to determine the V value that's R so this is R so how would we determine this well let me just give you some numbers let's say the charge we've stuck here was one nano Coulomb nano is 10 to the negative ninth so let's say that was one nano Coulomb and let's say the distance from this charge to this point in space was let's say it was nine centimeters and I want to know what's the V value well I can solve for and now we've got our formula the V would equal alright my K is nine always times 10 to the ninth and it's Newtons meters squared per Coulomb squared and then I multiplied by my charge and I told you that the charge here was ten to the negative ninth coulombs is nine and my distance I divided by the R value when the R value is nine centimeters but be careful everything's got to be in terms of meters kilograms and seconds when you're doing physics with constants look at this is in terms of meters so I've got to use meters here so nine centimeters is point zero nine meters and if I multiply all this out what you'll get this 10 to the negative ninth cancels this 10 to the ninth by powers of 10 these just go away and then I have 9 divided by 0.09 that's going to equal 100 so I chose this so that we got the same answer down there get 100 joules per Coulomb you might be like where the joules come from and houses joules per Coulomb well let's look at it if we took look at one of these meters cancels one of these meters one of these coulombs cancels one of those coulombs what are we left with we're left with Newton times meter over Coulomb but Newton times meter that's Force Times distance that's the joules that's where we get joules per Coulomb so this really does give us the number of joules there will be at a point in space per Coulomb of charge that you put there and it works for any point you pick any point if I picked a point twice as close that's half as far away say some point over here let's say this R value here was only four point five centimeters well I'm dividing this by R so if the R is half is big this point over here would have a V value of 200 joules per Coulomb and the closer I get if I went even closer if I went to a point that was three centimeters away well this is a third as much as this other distance so if I'm only dividing by a third as much distance I should get three times the result this R is not squared it's just R so this point what have a V value of 300 joules per Coulomb this tells me if I wanted to get a charge to have a whole bunch of potential energy I should put that thing nearby I should stick it over here this would give me a lot of potential energy not quite as much even less the farther I put my charge the less potential energy would have there'll be no potential energy until there is a charge that will just be electric potential but once you place another charge in that region to go with the first one then you'll have electric potential energy and this would be a way to find it Q times the V that you get out of this calculation you've got to be careful though sometimes people get sloppy and V looks you know we use V for electric potential and we use V for voltage what's the difference are they the same not quite you sometimes you can treat them is the same and you don't get in the trouble but sometimes you do it messes you up voltage is a technically a change in electric potential between two points this is the difference in electric potential between two points in space so it's got the same units because the change in electric potential still going to have units of Joule per Coulomb it's just when it's a change in we give this a new title we call the Joule per Coulomb unit a volt so joules per Coulomb or volts but the word voltage specifically refers to a difference in electric potential what am I talking about well look at this points 300 joules per Coulomb this point over here 100 Joule per Coulomb so the Delta V if I were to take Delta V between these two points right here and asked what's the difference in V the difference in V is 200 200 joules per Coulomb that means the voltage between those two points in space is 200 volts that's what we mean so when you're talking about a difference in electric potential between two points in space we call it a voltage when you're talking about just the electric potential value at one point in space we call it the electric potential and that's how they're related