Dielectrics in Capacitors and Otherwise | Doc Physics

did I ever tell you what happens if you have a metal sphere and you put that metal sphere inside of an electric field let's say there was an electric field facing that direction now the thing about this metal sphere is it will become ionized if the electric fields facing that direction let me just draw you one electric field line up here and another electric field line down there if the electric field is facing at that direction that means there must be some source of it over here some positive charges and some sink for it over here some negative charges so you can bet that this sucker will become polarized and in fact you'll get some positive charges stacking up over here and some negative charges stacking up over on that side yeah that's polarization and the reason polarization happens is these field lines that would have been coming in here can now terminate on the negative charges that they see right here and those field like yeah if this had been a uniform field it would have been all parallel lines but you see they come in there and they stop and inside the conductor well inside the conductor our electric field is exactly zero because that's one of the definitions of an ideal conductor then these guys right here these positive charges well they get to start electric field lines and those electric field lines would then go on forever this direction and we back to the situation of our uniform electric field if you get some distance away from this polarized conductor so polarization is a really wonderful thing and I guess what I mean by a conductor is that a conductor can perfectly polarize this sucker has all negatives over here point to completely prevent the entry of any electric field lines and over here there are enough positives to completely prevent the entry of any electric field line so the electric field just stops here and then begins again there the reason that nature prefers to do this is electric field lines cost energy in order to maintain an electric field in space that requires energy so notice and here's another example of that nature really prefers if you've got a plus charge and a minus charge it's got all these electric field lines that exist here you've got electric field lines here and here and here and here and the electric field lines would rather not exist because it costs energy for them to exist so what is that force then the force that's we think of as Coulomb's law is truly nature trying to minimize the potential energy of the system and in order to minimize it it has to get rid of this electric field that's pervading all this space in here and the way to get rid of it is to put these two charges on top of each other because you know what the electric field learn the electric field looks like if you've got a plus charge on top of an equal negative charge well it is not an electric field so that's really lovely if things are neutral there's no electric field hanging around them and that's why there's a force that brings those two suckers together that's not what I wanted to talk about today oh look here's Greg hurt but he's upside down come on Greg turn around here's my point my point is if you get yourself hang on this is probably a big mess all right if you get yourself a capacitor here's a parallel plate capacitor nearly parallel plate capacitor if you get your capacitor and inside of that capacitor you stick a piece of can I do yellow I don't even know if yellow work you stick some insulator in here now it's very important that it be an insulator you don't want it too perfectly polarize but you want it to polarize pretty well I've stuck a piece of I don't know what do you want to call this glass or plastic or pure water or something like that I guess it could be even B paper but let's say that all of these things could be summarized by one word it could be called a dielectric so I'm going to put a dielectric inside of my capacitor remember capacitors have these wires one on this side and one on that side and it's a parallel plate capacitor and well let's say we charge the capacitor right let me back up just a second we get ourselves an equation you know that the charge on the positive plate of the capacitor Q is C V is the way that I prefer to remember it so the way of thinking about this could I mean you might be a C is Q over V kind of guy and then that would that to hold a given charge on the capacitor Oh No let's solve it for V hack let's say that that's Q over C to keep a given amount of charge on the capacitor you need to put a voltage on it and I guess if the capacitance is really big then the voltage you need to keep a given charge on the capacitor is small and if the capacitance is really small then the voltage you need to keep a given charge on the capacitor is really big so voltage can be thought of as an electric pressure we're gonna have to put this sucker in quotes it's kind of an electric pressure and so it can kind of be thought of as how hard you're pushing if you're trying to keep a large charge on a small capacitor you have to push really hard and if you're trying to keep a large charge on a big capacitor you don't have to push very hard because the capacitor can efficiently store that charge so let's take this understanding of capacitance and charge and voltage and such and go over here to this capacitor which we are presently charging up let's put the positive side over here so we got one two and three and four and five and a six and probably at the same time because there's probably some circuit over here did I want to tell you about that and then I guess I've got myself a battery facing this direction and somebody hooked up this battery to here and to here and if this is 1.5 volts you bet your pants so you get more pants that the potential difference between those two plates when everything is said and done will be 1.5 volts that's cool now I'm going to put some negative charges over here because you know charge is conserved especially with a simple circuit like that we've charged our capacitor now I really don't want this battery in here anymore because it's going to confuse this entire thing and we'll work with batteries and dynamic interactions like that later primarily in class sorry internet-only people you're not going to get this kind of cool stuff so the neat thing is that this glass or plastic or paper is polarizable and the dielectric constant which we're going to use as but Kappa is a measure of how polarizable the thing is so Kappa ranges between 1 and infinity so a large Kappa means that it's extremely polarizable substance and a Kappa that small I mean that's that it's not very polarizable or that it's not very dense or something like that I don't know air has a very very similar Kappa to 1 it's like 1.00 2 or something and water has a very large polarizability so it's well it's a very polar molecule right so it's Kappa is really big like 80 or 90 or something but whatever I put in here will become polarized not perfectly polarized but polarized nonetheless so let's mmm how do we do this let's put ourselves an electric field first of all before I put the dielectric in there the electric field will be like this it'd be a joke to do it and I'm just going to give you six electric field lines going straight across showing us a uniform field but after the dielectric is in the dielectric that comes polarized which means that this side becomes negative not really negative but a little negative maybe four one two three four negative charges over here and I guess I'll have to go red to stay honest with you one two three four positive charges over here now how do these positive charges get to this side it's a leaning the electrons in every single molecule inside the dielectric are leaning away from these negative charges and they're leaning towards these positive charges it's not a migration because these suckers must be insulators but it's a leaning so inside of the dielectric we have another electric field and you know that electric field obeys the principle of superposition but the electric field caused by the dielectrics surface charge points the opposite direction and you notice that as a result you will have a do ooh you've got a small electric field inside the dielectric now that means that nature is happy I don't want to argue that it's a zero electric field like it's some kind of conductor forget about that but we've got a smaller electric field in there so something is more efficient we can actually store charge more efficiently when we've got a dielectric filling the inside of a capacitor and again I should say that this dielectric really should fill the capacitor but I'm drawing it a little bit smaller so that you can see these charges slightly decreased but if I were to honestly draw myself a capacitor with a dielectric inside of it let's see I'll get you some some plates what we're doing doing purple and then I'm going to put a dielectric completely inside of it as a consequence what we've really done is we've decreased look at this we've net decreased the charge on this plate the total charge here is plus two charge that's on that plate right there and the total charge over here total charge over here is minus two charges and so although there's still six charges that the battery pumped into the capacitor it only looks like there's two because there are these surface charges that are oppositely charged cancelling out that effective charge so the wonderful thing is this greatly reduces the voltage needed to keep that charge right there wait a second if to keep a certain charge on our capacitor we don't need nearly as much voltage well that means that our capacitor capacitance of the capacitor has gone up in fact sometimes quite dramatically so now I'll enter the typical derivation let's look at how big the electric field inside this dielectric is going to be and that it turns out that that electric flow that electric field inside of the capacitor is the electric field if there's no dielectric divided by Kappa Kappa is that well it's sort of like the polarizability I'll put that in quotes it's called would you call that I guess you'd call it the dielectric constant but it should sort of be thought of as polarizability of the dielectric that we've decided to put in there I guess I should label it as strictly as the dielectric constant if you're hanging around fancy people then they will want you to call it that the dielectric constant is a constant for every particular material you'd want to stick in there and it represents how much the material is able to decrease the field within it okay so the dielectric constant of a metal is infinity because the electric field inside of a metal is zero compared to the electric field outside the metal which might be whatever you want but pure I mean ideal metals are infinitely polarizable but hmm all gasp all dielectrics have some polarizability but if you're making mmm well let's just go on and see what sorts of results this gives us you know that V is IDI right yeah I'm a big fan of that too and we know that the electric field inside the capacitor if I've got myself a dielectric is the electric field outside of the dielectric divided by Kappa and then I'm supposed to multiply that by Dean fair enough so this is the outside electric field times D divided by Kappa but guess what this thing here this electric field times D that would be the voltage before adding the dielectric and I'm supposed to divide that then by Kappa OH so voltage decreases we go doing great making a video for the internet yeah so the voltage decreases because remember Kappa is greater than one and so if the voltage decreases then let's find out what's happening to the capacitance can we go green for that yeah you should always go green the capacitance is the charge on the capacitor divided by the voltage but remember the voltage has decreased and now I'm dividing by something that's small well you could see what's going to happen here it's going to be Q because the Q is going to be the same and I'm supposed to divide that by V naught Oh over Kappa and I've got a denominator of a denominator well that's just Kappa times Q over V naught and Q over V naught you can check what Q over V naught is Q over V naught is the original capacitance so we've got Kappa times the capacitance that we had before we added a dielectric and you win if you have a dielectric of a hundred if your dielectric constant is a hundred then you've now multiplied the capacitance of your capacitor by a factor of 100 that's actually incredibly awesome the capacitance increases linearly with the with the dielectric that we've put in there and then we can argue that instead of this old equation that we had for capacitance where it had to do with epsilon naught an area and the separation of the plates we can then multiply it by Kappa and our book just stops there but I want to point out to you that Kappa times epsilon naught is usually written in most books this is truly typically written as instead of Kappa times epsilon naught it's usually written as regular epsilon times area over D so this is called the permittivity of free space and this is just called the permittivity and so we define then Kappa times epsilon naught is epsilon which it whoa automatically put those knots in there sorry this is the permittivity of the substance so you could call the dielectric permittivity and this is the dielectric constant which is a little bit old school I don't know why our book does that by hi T's gia dielectric breakdown voltage of air is three million volts per meter so if you have a capacitor this is crazy if you have a capacitor and the separation between the plates is one meter if you charge that capacitor up so that a volt meter would read three million whoa three million volts then the air within that capacitor will break down that means it will ionize and when ionizing it gets ions and ions guess what ions conduct electricity so there will be up its a spark that means that it's lightning inside of here and I guess if you had a capacitor and the separation was just one millimeter what's the maximum voltage for that simple capacitor you figure it out based on the dielectric breakdown voltage of air let's see this is the way that's volts per meter right that's an electric field well so that's the same thing as three times ten to the sixth Newton's per Coulomb if the electric field is big enough it will separate an electron from nitrogen ding that's polarization the nitrogen itself becomes permanently polarized where the positive ion that's left is ripped away from the independent electron that's manages to escape and that happens in really really big the electric fields let's see if I can find a picture of that polarization in the trash here nope it's gone I'm finished

Channel: Doc Schuster

Views: 55,227

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Keywords: Physics, Dielectric, help, solve, Capacitance, problem, Capacitor, tutor, understand, Design, AP, Permittivity

Id: P8A1U-RZDao

Length: 16min 37sec (997 seconds)

Published: Fri Jan 11 2013