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# Electric field

## Video transcript

let's imagine that instead of having two charges we just have one charge by itself sitting in a vacuum sitting in space this charge here and let's say it's charged as I don't know it's Q that's some number you know but whatever it is that's his charge and I want to know if I were to place another charge close to this Q somehow you know somehow within its you could call it sphere of influence what's going to happen to that other charge what's going to be the net impact on it and we know if this has some charge you know if we put another charge here you know this is I don't know one Coulomb and we put another charge here that's one Coulomb that they're going to you know if they're both positive they were going to repel each other so there will be some force that pushes the next charge away if it's a if it's a negative charge and I put it here it'll be even a stronger force it pulls it in because it'll be closer so in general there's this notion of what we can call an electric field around discharge and what's an electric field it's it's I mean you can we can debate whether it really exists but what it allows us to do is imagine that somehow this this charge is affecting the space around it in some way that when I whenever I put it's creating a field that whenever I put another charge in that field I can predict how the field will affect that charge so let's put it in a little more quantitative terms so I stop confusing you so Coulomb's law told us that the force between two charges the force between two charges is going to equal two Coulomb's constant times and in this case the first charge is is big Q and let's say that the second whatever notional charge that I eventually put in this field is small Q and then you divide by the distance between them sometimes it's it's called R because you can kind of view the distance as the radial distance between the two charges so sometimes it says R squared but it's the distance between them so what what we want to do if we want to calculate the field we want to figure out how much force is there placed per charge at any point around this Q so it say you know the given distance out here you know this distance we want to know for given Q what is the force going to be so we can do is we could take this equation up here and divide both sides by this q and say okay the force and I will arbitrarily switch colors the force per charge at this point you know whatever let's call that D 1 is equal to Coulomb's constant times the charge of the particle that's creating the field divided by well in this case at D 1 and D 1 squared right or we could say in general and this is going to be this is this is the definition of the electric field right and actually the well this is this is the electric field at the point D 1 and if we wanted a more general definition of the electric field it'll be you know we'll just make this a general variable so instead of having a particular distance we'll define the field for all distances away from the point Q so the electric field could be defined as Coulomb's constant times the charge creating the field divided by the distance squared the distance we we are away from the charge so essentially we've defined if you give me a force and a point around this around this charge anywhere I can now tell you the exact force for example if I told you that I have a I don't know a 1 Coulomb let's go say a what a minus 1 Coulomb charge that's and and the distance is equal to oh I don't know the distance is equal to let's say let's make it easy let's say 2 meters so first of all we can say in general that what is the electric field 2 meters away from so what is the electric field out here if this is 2 right and it's going to be 2 meters away its radial so it's actually along this whole circle what is the electric field there well the electric field at that point is going to be equal to what and it's also a vector quantity right because we're dividing a vector quantity by a scalar a scalar quantity charge so the electric field at that point is going to be K times whatever charge it is divided by 2 meters so divided by 2 squared so that's for right distance squared and so if I know the electric field at any given point and then I say well what happens if I put a negative 1 Coulomb charge there all I have to do is say well the force is going to be equal to the charge that I place there times the electric field at that point right so in this case we said the electric field at this point is equal to and then and the units for electric field are our Newton's per Coulomb and that makes sense right because it's force divided by charge so Newton's per Coulomb so if we know that the electric charge but let me put some real numbers here let's say that this is I don't know it's going to be a really large number but let's say this let me let me pick out a smaller number let's say this is 1 times 10 to the minus 6 coulombs right if that's 1 times 10 in the set net minus 6 coulombs what is the electric field at that point and let me switch colors again what's the electric field at that point well the electric field at that point is going to be equal to Coulomb's constant which is 9 times 10 to the 9th times the charge generating the field times 1 times 10 to the minus 6 it's coulombs and then we are 2 meters away so 2 squared so that equals to C 9 times 10 to the 3rd divided by 4 so I don't know what is that 2.5 times 10 to the 3rd or 2500 2500 Newton's per Coulomb so we know that this is generating a field that when were 2 meters away at this you know at a radius of 2 meters so roughly that whole area you know that circle around it this is generating a field that if I were to put let's say I were to place a 1 Coulomb charge here let's say I place a 1 Coulomb charge the force exerted on that 1 Coulomb charge is going to be equal to 1 Coulomb times the electric field times 2500 Newton's per Coulomb so the coulombs can't slide and we'll have 2500 Newton's which is a lot and that's because 1 1 Coulomb is a very very large charge and then a question you should ask yourself if this is 1 times 10 to the negative 6 Coulomb this is one Coulomb in which direction will the force be well they're both positive so the force is going to be outwards all right so let's take this notion and see if we can somehow draw an electric field around a particle just to get an intuition of what happens when we later put a charge anywhere near the particle so there's a couple of ways to visualize an electric field one way to visualize it is if I have a let's say I have a point charge here Q what would happen if I what would be the path of a positive charge if I placed it someplace near this Q well if I put a positive charge here then and this Q is positive that positive charge is just going to accelerate outward right it's just gonna go straight out and it's gonna it's gonna go but it's going to accelerate an ever slowing rate right because here when you're really close the outward force is very strong and then as you get further and further away the the elect the electrostatic force from this charge becomes weaker and weaker right or you could say the field becomes weaker weaker but that's the path of a of a it will just be radially outward of a of a positive test charge and then if I put it here well it would be radially out radially outward that way and it wouldn't curve the way I drew it it would be a straight line I check she's a line tool if I did it here it'd be like that but then I can't draw the arrows if I was here it would go out like that and you I think you get the picture at any point a positive test charge would just go straight out away from our charge Q and to some degree one measure of actually and these are called electric field lines and one measure of how strong the field is is you could actually if you actually took a unit area so if you actually took a unit area and you saw how dense the field lines are so here they're relatively sparse well if I if I did that same area I don't know up here I don'ts not that obvious I'm getting more field lines in but actually that's not a good way to view it because I'm I'm covering so much area let me undo both of them you can ratify had a lot more lines if I did this area for example in that area I'm capturing two of these field lines well if I did that exact same area out here I'm only capturing one of the field lines although you could imagine there you could have a bunch more in between here and that makes sense right because as you get closer and closer to the to the source of the electric field the charge gets stronger another way that you could have done this and this would have actually shown probably more clearly shown the magnitude of the field at any point is you could have you say okay if that's my charge Q you could say well really close the field is strong so at this point you know the vector is the Newton's per Coulomb is that strong you know that's strong that's strong that's strong and you have to we're just taking sample points you can't possibly draw them at every single point you know so at that point though that's the vector that's the electric field vector but then if we go a little bit further out the vector is going to be you know it falls off it gets this one should be shorter than this one should be even shorter right you could pick any point and you could actually calculate the electric field vector and it the further you go out the shorter and shorter the electric field vectors get and so in general you know you we could there's all sorts of things you can draw the electric fields for you if we had a let's say that this is a positive charge and that this is a negative charge let me switch colors so I don't have to erase things if I had to draw the path of a positive test charge it would go out radially from this charge right but then as it goes out it'll start being attracted to this one the closer it gets to the negative and then it'll curve in to the negative charge alright and these arrows go like this and if I went from here the positive one will be repelled really strong really strong it'll go really it'll accelerate fast and it'll its rate of acceleration will slow down but then as it gets closer to the negative one it'll speed up again and then that would be its path and similarly if there was a positive test charge here its path would be like that right if there was here its path would be like that if it was here its path would be like that if it was there maybe its path is like that and at some point its path might just you know never get to that pot you know this out here might just go straight out that way I mean at some point right I mean that one would just go straight out and here the field lines would just come in right a positive test charge would just be naturally attracted to that negative charge so that's in general what electric field lines show and we could use our little area method and see that over here if we picked a given area the electric field is much weaker than if we picked that same area right here we're getting more field lines in than we do right there so that hopefully gives you a little sense for what an electric field is it's really just a way of visualizing what the impact would be on a test charge if you bring it close to another charge and hopefully you know a little bit about Coulomb's constant and you know let's let's just do a very simple I'm getting this out of the AP physics book but they say let's do a little simple problem calculate the static electric force between a 6 times 10 to the negative 6 Coulomb charge so 6 times I don't know that's not an electric field over here it says what is the force acting on an electron placed in an electric in an external electric field where the electric field is they're saying it is 100 Newton's per Coulomb at that point wherever the electron is so the force on that the force is in general is just going to be the charge times the electric field and they said it's an electron so what's the charge of an electron well we know it's negative and then in the first video we learned that its charges 1.6 times 10 to the negative 19 coulombs 10 to the negative 19 coulombs times 100 Newton's per Coulomb the coulombs cancel out and this is 10 squared right this is 10 to the positive 2 so it'll be so 10 to the minus 19 times 10 to the positive 2 the force will be minus 1 point 6 times 10 to the minus 17 Newtons so the problems are pretty simple I think the more important thing with electric fields is to really understand intuitively what's going on and and kind of where the strength you know how its stronger near the point charges and how it gets weaker as goes away and what the field lines depict and how they can be used to at least approximate the strength of the field I will see you in the next video