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# Electric field definition

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## Video transcript

so here's a question if you've got two positive charges we know they're gonna repel so if I put these next to each other this blue charge would repel the green charge and vice versa but how is that working exactly I mean there's nothing in between these charges so how is the blue charge pushing on the green charge when it's not even touching it this is kind of a weird thing right if I want to push on something in my room I need to walk up to that thing and actually physically touch it and then give it a shove yet this blue charge seemingly exerts a force on the green charge with just empty space in between right there's no strings here what is the mechanism so physicists were kind of embarrassed and concerned about this it was like all right we can calculate exactly how much force there would be on each charge but we don't really know how that is actually working it doesn't seem to make any sense that a charge can push on another charge across potentially vast stretches of the universe here this could be a huge distance and yet somehow this charge over here knows ah there's a charge over here pushing on me how is that possible and this isn't new to electrical forces this was a problem when Newton came up with the force of gravity when Newton figured out how to calculate the force of gravity he showed okay we can calculate how much the earth is going to pull on the moon and people were like this is great because now we can calculate and predict the orbits of the planets and comets but when people were like hey Newton that's really cool but how is the earth pulling on the moon when there's nothing in between Newton was basically like I don't know exactly why that works but I know the math lets me predict it exactly and so ever since the time of Newton this has been kind of in the back of physicists minds for hundreds of years now as we led up to the electric force people were kind of like all right how is this force at a distance actually being transmitted is there something in between here that's actually letting the earth pull on the moon and so finally when people were dealing with this electrical phenomenon they decided alright it's time it's time to answer how do two objects exert forces on each other across to what are potentially vast distances of space and the person who came up with an explanation was named michael faraday so the is Michael Faraday right here he did his science in the 1800's generally regarded as one of the most important physicists / chemists of all time really and what Faraday said is this he said guys here's how it's working so this positive charge over here so forget about the other positive forget about this green positive for a minute let's just focus on this blue one he said here's what the blue charge is really doing he said this blue charge is creating an electric field all around it and we'll abbreviate this electric field with a capital e and since it's a vector we'll put a little vector arrow over the top so Faraday said this positive charge creates an electric field everywhere around it at all times whether there's other charges in your buyer or not and the electric field gets weaker and weaker the further out you go so near the charge you've got a big electric field and then the further away you go the weaker the electric field is so this is kind of like a spiderweb surrounding a spider except the spider is like the charge and the web is like the electric field now you got to be careful people see this and they think oh this is just like electric force right but this is not a force these vectors here are not forces this is where people get really mixed up they look like forces because people are like we used arrows to draw forces before aren't these just forces they're not it's a vector so we represent them with arrows but the electric field is not the exact same thing as electric force so you've got to keep that straight they are not the same thing they're very related but they are not the same thing electric forces F we represent it with F and maybe a little e for electric force and since it's a vector we could draw it with a vector sign but the electric force is not the same thing as the electric field E how were they related here's how it works so even though the electric field is not a force it can cause an electric force on other charges so as it stands right now if all we had was a positive charge creating its electric field in the region surrounding it there would be no electric force you need two charges to have an electrical force this charge is not going to exert a force on itself so this blue charge and to keep these all straight let's just give this a name we'll call this Q 1 this charge Q 1 creates an electric field but that electric field the e1 because it's created by q1 this e 1 does not exert a force on Q 1 it will exert a force on any other charges that wander into this region to this electric field that gets created by q1 just sits and waits patiently just like a spiderweb waits around the spider for another charge to wander in and then it will exert a force on it so let's put another charge in here but say this positive charge wandered into this zone for some reason who knows why if it wanders into this region there will be an electric force on this charge and here's the story that Michael Faraday told us that made us feel better about how this force at a distance works Michael Faraday said here's what's really happening this positive charge q1 is creating an electric field all around it including this point over here where q2 is so we'll call this charge q2 so there was already an electric field at that point that was being created by q1 and now when this q2 wanders into this region the q2 just has to look at its immediate surroundings this point right here it sees this electric field it senses it and it knows ok an electric field pointing to the right that's going to cause a force on me to the right so it causes an electric force the electric field is not an electric force but it will cause an electric force on a charge that wanders around into it and you might wonder how is this any better well it keeps things local so physicists like it when things stay what we call local and by local we mean ok this charge q2 in order to figure out what it should do all it has to know about is the things in the space immediately surrounding it so it just samples the electric field at this point right here it says oh there's an electric field pointing this way I'm going to feel an electric force in that direction in other words it doesn't have to know it doesn't have to say oh there's this positive charge on this other side of the galaxy and that's the thing exerting a force on me nope it just knows oh there's an electric field right here that's all I need to know to figure out the electric force on me so that's sort of how Faraday got around this question of how does one object exert a force on another object when there's nothing in between he said there's a mediator basically that this first charge creates a field everywhere including at this point and then that field is creating a force on this charge that wanders into that zone so I guess conceptually the way you could think about it is this this charge q1 is creating the electric field e1 in this electric field in this region is causing a force on this charge q2 and that's how q2 knows to feel the force it's supposed to feel which keeps things local this q2 just has to know about the field right in its vicinity in order to figure out what to do it doesn't have to know about things on the other side of the universe but you could complain at this point you might be like wait a minute doesn't q2 also create its own electric field wouldn't q2 also create an electric field everywhere around it we could call that e - since it's created by charge - doesn't it create its own electric field just like all charges do yeah it does in fact it'll create an electric field over here next to q1 and that's how q1 knows that it's supposed to feel the force it feels in the direction that it feels it so that's how these charges talk to each other you can think about it that way the way charges talk to each other is with the electric field one charge creates an electric field over by the other charge that charge feels a force the other charge creates a field by the first charge that first charge feels a force so conceptually that's how this electric field works and that's what it does so this point you might not be impressed you might be like are we just making up a story to make ourselves feel better here is it's just some elaborate fairy tale that makes it so that we don't feel so awkward talking about things exerting forces on each other at a distance is there any benefit for doing this and there is there's a big benefit mathematically in terms of physics talking about the electric field makes describing the physics way easier and in fact it makes it so that you don't even have to know about the charge creating that field at all if you have a way of knowing the field even if you don't know what charge is creating that field you can figure out what the force is going to be on any charge in that field without even knowing the charge that created that field and that turns out to happen a lot so knowing the electric field is extremely useful it lets you determine the electric force on a charge even if you don't know what charge is exerting that force so up to this point I've been trying to motivate why we would want this idea of the electric field why physicists would come up with this idea but I wouldn't blame you if at this point you weren't thinking hice know what electric field is I know what it isn't electric field is not electric force but what exactly is the electric field so let me give the electric field a proper definition here the electric field E at a point in space is defined to be the amount of electric force per charge exerted at that point in space so this is what the electric field is it's the force per charge and the way physicists usually think about this is imagine throwing a test charge in here we call this a test charge we like to imagine that this charge is really little so that it doesn't completely like swamp and overwhelm the other charges creating this field otherwise if you threw some huge charge in here all the other charges would scatter and it would change the whole situation so let's say we put a really small test charge in here if I want to know what the electric field is at a point in space I could just bring my test charge over here measure the amount of electric force on that test charge and then I just divide by how much charge was there on that test charge so what was the charge of that test charge I'll call this charge - if I take the force on charge 2 divided by charge 2 that would be the value of the electric field at that point in space so this is how we define the electric field the definition of electric field is the amount of force per charge in other words let's put some numbers in here let's say Q 2 was 2 coulombs this is actually an enormous amount of charge this is kind of an unrealistic example but it'll make the numbers come out nice and conceptually it's the same thing so it's a positive two coulombs which was placed here that's the value of Q - and let's say when we measure the force on Q - we're getting 10 Newton's of force well in that case we could just say alright then the electric field in that region at that vicinity is going to be 10 Newton's of force / 2 coulombs of charge and we get an electric field of five and then the units are Newton's per Coulomb and that makes sense because what the electric field is really telling you is how many Newton's of force you would get per Coulomb if you put more coulombs at that point in space there'd be a greater force and this numbers telling you the number of Newtons you would get per Coulomb so since we had two coulombs at this point in space and there was five Newton's per Coulomb the force was 10 Newtons number five Newton's per Coulomb is important because it's the same for any charge you put there and this is why the electric fields useful at this point in space right here if the electric field is 5 it's 5 Newton's per Coulomb no matter what charge you put there so if I put a 4 Coulomb charge at that point since there's 5 Newtons for every Coulomb there'd be a 20 Newton force there because there's 5 Newton's for every Coulomb if there's 4 coulombs there'd be 5 times 4 Newton's which is 20 Newtons so you can imagine rearranging this formula another way you could just multiply both sides by Q and you get that the electric force on a charge is equal to the value of that charge at that point in space multiplied by the value of the electric field at that point in space but it's important to note this electric field is not created by this charge Q - this was created by some other charge or collection of charges remember this charge Q 1 is creating this electric field E 1 and that electric field is causing this electric force on Q 2 Q 2 did not create the electric field E 1 that it interacted with Q 1 created that electric field E 1 so people get mixed up they see this formula they start to think maybe this Q 2 is creating this electric field it's not this electric field is causing the electric force on that charge not the other way around this Q 2 is not creating this field this field is causing the Force on that charge so this formula is extremely useful if you know the electric field at a point in space you can figure out the electric force on any charge at that point by just multiplying the two values together to get the electric force so you can see now that the electric field is not the electric force it's the amount of electric force per charge at a point in space very related but different different enough that you have to keep these ideas separate electric field is not electric force and vice versa electric force is not electric field the electric field is the amount of electric force per charge and the electric force on a charge at some point in space is the amount of charge times the electric field at that point in space so recapping electric charges create electric field these electric fields in turn caused forces on charges that exist in that region the value of the electric field is representing the number of Newton's of force per Coulomb at that point in space and in terms of a formula the electric field is the amount of force per charge or in other words the amount of electric force is the charge times the electric field at that point in space