 Hi, I'm Zor. Welcome to Unisor Education. Today we will talk about how to store electric charge. And the device which we are considering is called capacitors. So I will talk about how to store electric charge in the capacitors. Now, this lecture is part of the course Physics 14 presented on Unisor.com. I suggest you to watch this lecture and all other lectures because it's a course actually from the website. They are presented in a logical order. There are some problems solved and there are exams. And the site is completely free. So go to Unisor.com. Now, so our purpose is to store electric charge. Well, first of all, let's just think about it. Let's assume that we are somehow capable of making electric charge. What does it mean? It means that we have an object where we have an axis or deficiency of electrons, right? Well, let's say axis. I mean, axis means we have to take it from somewhere. Now, the world is relatively neutral, right? So we can't really take anything from some storage of electrons which is somewhere created by God or something. Now, we have to take any kind of a neutral object, electrically neutral object and just borrow some electrons from them, from the atoms of this neutral object and put them into another object which let's call it x minus. Now, whatever is left will have deficiency of electrons, right? And that would be x plus. But that's how we create both positive and negative charges from the neutral. How is a different question? We're not talking about this right now, but there are some devices which do this type of thing. But for now, let's just assume we are managing somehow to create from one object, create another one and separate these electrons into another one and whatever is left will be with a positive charge. By the way, equal in magnitude. This is negative, this is positive. Now we have to store it somehow. Well, for practical reason, obviously, we cannot store it very far away because that means we have to transport these electrons somehow. It's kind of difficult. So let's consider we have two close to each other objects which we have managed to create by separating electrons. Now we have to prevent, if we want to store it somehow, for future reasons. For future reasons means we have to really put some kind of a lamp, let's say, in between and then the flow of electricity will light it up, etc. It doesn't matter. To have it, to store it, we have to prevent discharge between them because if we will just put two different objects together relatively close to each other, one is negative, another is positive, maybe the spark will be between them and the spark is actually discharge. Electrons will go back to wherever they came from and our work becomes basically useless. So we have to prevent them from discharge. So that's our purpose to store as much electric charge as possible separately but relatively close to each other. Now let's talk about, let's say, two spheres. I have negative here and positive there. Now, obviously, since positive and negative attract each other, I will have more concentration of electrons here and more concentration of absence of electrons here and less on the opposite side. Now, the intensity of the field between these two will be greater than if these electrons are evenly distributed in the object. If they are evenly distributed and those absences of the electrons, that would be less because now this is more concentrated so this is intensity more and this is evenly distributed intensity less. But how can I prevent this type of organization of electrons and their absences? Well, there is only one way to make the whole object very even in terms of distribution of electricity and one of the best ways at least is to have it as two flat planes. One plane would be negative, another would be positive and since they are flat and relatively large, we can definitely say that there is no abnormalities in the distribution of electrons or in distribution of absence of electrons. They will be evenly distributed along the whole surface. So these are two planes and this is ideal kind of configuration when there is no peaks, let's say, where electrons would concentrate and cause spark faster than at that particular point. Well, by the way, that's how the lightning strikes. Lightning strikes to something which is like a stick of metal whatever on the roof we are using specifically for the purpose so the lightning will go into this metal rod and somewhere to the earth rather than to a tree or a house or something like that. So we are trying to make this even. That's one thing. Now, next thing that we will consider is something which we did before as a problem number four. Problem number four was about intensity. If this is a disc and you have a perpendicular to a disc line where you have a point the disc has certain radius r, the A is the height h above the center of the disc. Now there is a sigma density of electricity charge and I would like to know what's the intensity of the field at point A. Well, this is E. It depends of h and it's equal to... Okay, where is it? Sigma divided by 2 epsilon r epsilon 0 1 minus 1 over square root 1 plus r squared divided by h squared. That's the formula which we have derived. In the previous lecture is a problem four. So I refer you to this lecture to basically see exactly how it's derived. But I'm just using it as given. All right, fine. So we have this formula. That's good. Now what we are going to do is we are going to the capacitor's configuration like this. Let's assume these are two discs parallel to each other on the same central line which is perpendicular to the discs. And I would like to know what's the value of intensity of electric field in between these two. So this will be my x minus and this will be my x plus. So all my electrons go to the left disc and the absence of electrons will be in the right disc. Now my question is how to increase the capacity of this capacitor. This is called capacitor. Which means I would like to put as much as possible electricity, Q, Coulomb's electricity and not to have a spark. Now not to have a spark actually means that my voltage between these two should be as small as possible. So that's my purpose. My purpose is to decrease the voltage between these two. Now voltage as you remember is amount of work which is needed to transfer one Coulomb's electricity from one point to another in the electric field. So if my voltage is less, so electrons are not really pushed very hard towards from one plate to another. So that's what basically allows me to store more electricity. So my purpose is increase Q and decrease voltage. Well Q is given so I can't really increase it. I mean whatever it is it is. I have to store certain amount of electricity. But now how I store it, that's what voltage depends on. So let's just calculate what is the voltage between these two. First I have to know the intensity of the electric field. Now what is intensity here? Well let's just think about it. This is E of H. Now let's consider this distance is D and this is H. Now what I can say is that 0 is less than H less than G. So H is between 0 and G obviously. It's in between these two. Now obviously intensity is a vector. And if I am talking right now about a point which is on the center line of these two disks. I can use this particular problem and this formula to find out what's the intensity at this point from one disk. And then what's the intensity of another disk. And obviously we know that from the different considerations the intensity which is a force. It's a vector which is directed along this line perpendicular to a center. So it will be the common line because we are talking about being on the line which is connecting to centers perpendicular to the disks. So I can use this formula for one and then for another disk. And I will add these two vectors together. Now if my probe object is plus one cologne. Now the negative plate would attract it. The positive plate would repel it which means in exactly the same direction. So I basically add these two forces together. So one force from this would be E of H where E is the formula. Another would be E of D minus H because this distance is D minus H right. And I'm adding them. I'm not using the sign at all. I'm just adding the absolute value of these two things. Considering sigma is the same here and here although one is negative and other is positive. Now and here I will do something which mathematician would definitely don't like. But the physicists are doing it all the time. Which is the approximate. The formula is kind of cumbersome if I will just put it all together. However, if my radius of the disk is relatively large and my distance between them D and H therefore as well are very small. Then the whole R squared divided by H squared is very very large. Which means the denominator is large which means that the whole fraction is very small. And apparently it's so small that again physicists have decided that for practical cases which we are talking about it's really completely irrelevant and they dropped it. So they basically have only sigma divided by two epsilon R epsilon zero and then another one so it would be together epsilon sigma divided by epsilon R epsilon zero. Where epsilon R is a relative permittivity of the media in between these two plates. Epsilon zero is a permittivity of the vacuum. So and as you know the relative permittivity is also called dielectric constant. It's very important this dielectric it prevents the electricity right. So the greater A epsilon R the smaller the intensity of the field in between these two plates. Obviously with increasing density of electricity we are increasing the field and with increasing dielectric constant which means using some other substance in between these two which prevents electric field to propagate as much as in the space. So the greater epsilon R the less intensity we will have. Now if I will multiply intensity by the distance between these two plates I will have the voltage difference and that's what I have to minimize. So let's just think about it. So again my voltage is something which we should minimize which is equal to sigma D divided by epsilon R epsilon zero. Now sigma is basically a total amount of electricity divided by area right. So by diminishing distance between these two plates we are decreasing the voltage. By increasing the area of the plates we are decreasing the voltage and by increasing the dielectric constant I mean using a substance with a greater dielectric constant we are decreasing the voltage. So the voltage will be increased the greater our surface is which means that the discs are of a greater radius right. The closer they are to each other and the greater dielectric constant is of the media between these two things. Okay let me just continue a little bit further towards physicist's approach. Now let's consider that these discs are really very very big and the distance is very very small and we have a point in between somewhere. Now does it make much of a difference whether it's closer to the middle of the discs to the center line or it's off the center. Well the bigger the discs the less difference it makes. I mean it's generally understood. I mean obviously we can make exact calculations and have a huge formulas etc. But this is an obvious result. The greater the surface of the disc is the less the point which is somewhere on this disc knows about what exactly is on the edges. Well if it's at the edge then yes it's important but anywhere within the middle of the disc it's really the same thing whether it's in the center line or it's a little bit off center line and the bigger the disc the less difference it makes. So another again physical consideration is it important that this is really a disc what if it's a rectangular. Again if it's a big rectangular there is no difference. So what people have basically decided that we can use the formula which looks like this for basically any large size capacitors which has large area and very small distance between the plates. Now what's important is a characteristic of these capacitors which is I'll call it f equals q divided by b. So this is amount of electricity and this is the voltage which can be observed between the plates. And it's equal to q divided by v which is q d A epsilon r epsilon 0 which is A epsilon r epsilon 0 divided by d. So you see there are three major characteristics. Epsilon 0 is a constant obviously it's a permittivity of the vacuum. The area of the capacitor the distance between the plates and the dielectric characteristic of media between the plates. So this is basically something which is called capacitance k, p, c, n's of a capacitor. The ability to store certain amount of electricity at certain voltage. That's what it is. So the greater capacity means, now obviously voltage is something which allows electrons to travel from one to another and the greater voltage the greater possibility for electrons to jump between the plates. So we are interested in the smaller voltage. So we're interested in increasing the capacity in terms of amount of electricity, coulons and we have to decrease the voltage between the plates. So the capacitors with greater capacitance are of value. So we need capacitors of big capacitance. So what else is important here? Important is to measure the capacitance. So if we are putting one coulon of electricity on a minus and on a plus. Minus one coulon plus one coulon. And we observe one volt of voltage between these two plates. This particular capacitance is one farad. Again physicists immortalize themselves by calling the units by their names. So Michael Faraday, a famous English physicist and his owner, this unit is called farad. But basically it's a coulon volt. And what is volt? Volt is joule by coulon. So you can convert it into, so it will be coulon squared divided by joules, etc. So these are all conversions. But let's just concentrate on one particular unit called farad. Capacitance of one farad means that electricity, electric charge of one coulon, has the voltage of one volt between the plates. Alright, now how can we increase the capacitance of the capacitor? Well, look at this formula by increasing the area, by increasing the dielectric constant, and by decreasing the distance between them. Well, distance, let's not talk about distance right now, but we can very easily increase the area. Here is how. Now let's consider we have two plates. Let's consider we have two other plates. Minus plus, minus plus. So what if we will distribute our charge q, not among these two, plus and minus, but among these four? So we will connect them, and we will connect them. So this will be minus, and this will be plus. Well, actually it's the same thing as if I will just increase the area of the left plate by two and right plate by two, right? So basically if this capacitance of this is c1, capacitance of this is c2, capacitance of the whole thing is c1 plus c2. It's called parallel connection of capacitors. Now, why is it important? Well, here is why. We don't have to reorganize it in this way. We can organize it in this way. So let's say we'll take this, this and this, connect this to minus, and this, this and this, connect it to plus. So what I have here, I have stacked. You see, this is capacitor by itself, and this is capacitor by itself, and this is, and this is, and this is. Because each one of them is, this is minus, this is plus, this is minus, this is plus, this is minus, this is plus, right? That's how they're connected. So I'm stacking in the third dimension. So I don't need really two dimensions, two flat things, increase it in two dimensions. I can use the third dimension and stack them one above another. And if the distance between them is very small, filled with a media or some kind of a substance of a very high dielectric constant, then my capacity will be increased. What else they do? Not only they can do it vertically, they can do it in a roll actually. Let's consider you have two very, very long metal plate, minus and plus. They will put one on the top of another, put in between obviously some kind of dielectric, and then roll them together. So they will be rolled like this. One of them and another would be in between. It's exactly the same thing. So we are using the third dimension to either stack or roll to increase the capacity of the capacitor in a relatively small volume. That's all we need. We need to use relatively small volume to store relatively large amount of electricity. So this is how we increase the area. We increase the area and how to increase the capacitance by using better dielectrics. Well, we do have certain dielectrics with very high dielectric constant. And if we will use them in between the plates in this way or in this way, this would suffice to diminish the voltage between them. Diminishing the voltage is the most important because that diminishes the probability or possibility of the discharge. And basically that's all I wanted to talk about today. So these are capacitors they are serving for storing electricity. In all electrical devices, whatever we are using, we definitely have these capacitors in every computer, on every electric power station, whatever. We are always using the capacitors. Sometimes they are very large capacity, with very large capacitance, but they are always used to store electricity, which we have managed somehow to generate by separating electrons from the other places where now are in lack of electrons. Okay, that's it for today. Thank you very much and good luck.