 Let's talk about charge distributions. Charge distribution basically means collection of charges. So it is collection of charges. And you've actually dealt with them. For example, you may have dealt with situations where you're given there is a, I don't know, maybe a plus one nano-coulomb chart somewhere. And there's a minus five nano-coulomb chart somewhere. And then you are asked to do maybe calculate the force between them or ask to calculate the electric field somewhere. So this is a collection of charge. And so this is a charge distribution. But you know, this particular kind of charge distribution is called discrete charge distribution. What do I mean by that? What I mean is here you can count and you can say, ah, there is one charge over here and there is another charge over here and there are no charges in between. When you can count and you have such point charges, we call that collection a discrete charge distribution. But the focus of this video is the other kind, which I find more interesting. This is called continuous charge distribution, continuous. And let me immediately give you an example of that. So let's say we have a wire and let's imagine I charge up this wire and let's say it gets a positive charge. So now the positive charge will be continuously spread along this wire. Now I don't mean that there is a charge here and then there are no charges in between and there is a charge here. That's not what I'm saying. What I'm saying now is the charges are spread out. There's charge everywhere. This is what we call a continuous charge distribution. And do you know what's interesting about this? I can have that same wire and I can have that same amount of charge. Let's say this total charge is, I don't know, maybe 100 coulomb and I can distribute it continuously in a different way. For example, you know what I can do? I can distribute it maybe somewhat like this. Now again, I don't mean that there are no charges in between. It's a continuous distribution. There are charges everywhere. And so the total charge here is the same as the total charge over here. But what's the difference? Well, the difference is the charges are more crowded over here and they are less crowded over here. That's what I'm representing. But over here, the charges are equally crowded everywhere. And that's why when we're talking about continuous charge distributions, this is an important quantity. How crowded the charges are? Are they uniformly crowded everywhere? Or are they more crowded at one place and less crowded at some other place? And that's why when it comes to continuous charge distribution, we introduce a new quantity called charge density. And you may have heard of the word density. The word density, sorry, the word density basically means how crowded something is. So when we say charge density, we're talking about how crowded the charges are. And then we're dealing with charge distribution over a line and we'll talk more about different kinds of distribution in a minute. Whenever we're dealing with that, the symbol that we use to represent charge density is the Greek symbol lambda. And this number basically tells you how crowded the charges are over a given length. And so the way we represent lambda or with the way we calculate lambda is we say how much charge is present over unit length. And I'll give you an example. But before that, let's talk about the units. What would be the units of charge density? Well, the unit of charge density would be coulomb per meter. So for example, I could say, hey, the charge density over here for this wire is 20 coulomb per meter. What does that mean? That means if I were to take one meter of this wire, and I don't know how long this wire is, but let's say it's a very long wire and I took one meter of this, in that one meter I would find 20 coulombs of charge. That's what this means. And I can take that one meter anywhere and I'll find 20 coulombs. The charge density over here is a constant because it's equally crowded everywhere. So what if I take two meters of length? How much charge would I find over there? Well, per meter is 20, so in two meters I'll find 40 coulombs of charge. If I take half a meter, how much charge would I find over there? Well, I would find 10 coulombs of charge. Does this make sense? Do you understand what charge density is? Okay, what about charge density over here? Can I give one number for charge density over here? No, because the charge density varies. You have a, you can kind of say there's a very high charge density over here and there's very low charge density over here. And how do I represent that? How do I figure, how do I give a number to it? The way to give a number over here is you could say, you could take a very tiny, very tiny length and let's say that length is, I don't know, maybe a nanometer, okay? Take a very, very tiny length and in that length find out how many charges are present. Maybe in that one nanometer I find, I don't know, maybe 50 nanocoulombs of charge. Now I will say at that point, lambda, which is our charge density, is 50 nanocoulombs divided by one nanometer. So that would be 50 coulomb per meter. And now what's interesting is this does not mean I take one meter and I'll find 50 coulombs. No, this basically says at that point, you will find if you take the charge and divide by length, that ratio turns out to be 50. So this is the value at that point. Similarly, if I were to take maybe at this point, I take one nanometer over here and I'm just using nano as an example. You imagine it's a very incredibly tiny, tiny point, tiny distance you're taking. In that one nanometer, maybe I'll just find only two nanocoulombs at this point. So we will say the lambda at this point would be two nanocoulombs divided by nanometer. It would be two coulomb per meter. So over here, how do you calculate charge density? Well, we calculate charge density lambda by taking very tiny lengths, dL. That's how you write it mathematically, even though I've shown using real numbers over here, but mathematically it's an infinitesimal length and over that, you find how much charge is present and that ratio tells you the charge density at individual points. So if the charge is uniformly distributed, then whether you take it at a point or you take it over a large length, that value stays the same and that's pretty much about charge distribution. But now you could ask, wait a second. Here, charges were distributed over a line and so we like to call this a continuous line charge distribution and therefore this density, we like to give it a name, we call this linear charge density because it's telling you how much charge is distributed over a line, over a meter, right? So this is one kind of charge distribution. Are there other kinds of charge distributions? The answer is yes. And if you got this, then the rest of it's very similar. So let me show you another kind. In fact, there are three kinds. So the second one, let me just write over here or let me do that over here. In fact, let me do that over here. Second one would be surface charge distribution. Surface charge distribution. And you can kind of imagine just by looking at the word. Now, instead of charges being distributed over a line, we have charges distributing over a surface. So you can imagine, let's say this is some kind of, I don't know, maybe a metallic plate or you can imagine this is a surface of a balloon. What do you want? And let's imagine now there is, there are charges everywhere on the surface. And again, it's continuous, the charge is everywhere. This is what we call a surface charge distribution. And we have the same nuances like we saw over here. You could either have distributions which is uniform. So the density would be the same everywhere or you could have non-uniform. But my question is, how would you define charge density here? Here it was charged per length, coulomb per meter. What would we be over here? What would be the units? Can you pause and think about it? Well, over here, since we had charges are distributing over an area, here we introduce surface charge density and the symbol we use is sigma. And surface charge density is just charge divided by area. So the unit over here would be coulomb per meter square. So for example, if I said this was a uniform charge distribution and let's say sigma is, I don't know, maybe 10 coulomb per meter square. What am I saying? What is the meaning of that? It means if I go anywhere on this surface and if I take, let's say, one meter square area, I'll find 10 coulombs of charge on it. But if I take two meter square area, then I'll find 20 coulombs of charge on it and so on and so forth. And lastly, the third and the final kind of charge distribution, I'm just like, I've not arranged this very nicely. But the third kind would be volume charge distribution. And again, I'm pretty sure you can kind of guess what this is. Now charges are distributed in space, in 3D space. So you can kind of imagine, let's say there's a box and let me draw a cube type, a cube over here, a cuboid over here. Maybe this is my room. Yeah, my room is cuboid, I think. Anyways, now I imagine there are charges everywhere inside in 3D space. This is volume charge distribution. And exactly the same thing holds here. You can either have uniform charge, charges uniformly distributed over a volume, or you can have them non-uniformly distributed over a volume. And again, the question is, how do you define a charge density over here? Can you think? Well, since it's spread over a space, here we define charge density as, and the symbol we use is rho. I think these symbols is something you need to remember. But with the way we define it over here would be charge per volume. And the units would be coulomb per meter cubed. And just like before, if you are dealing with non-uniform charge distribution, then you have to do DQ over DV. At every point you would have different volume charge distributions. So let's put it all together. Let's put this all in one screen. Let me, all right. So if you put it all together, continuous charge distribution is basically when charges are spread out continuously, you can have them spread out over a line, or a surface, or over a volume. And one of the most important quantities is charge density. It tells you how crowded charges are distributed over a line, over a surface, or over volume. If the value is a constant, which is my favorite, then that means it's a uniform distribution. If the value is not constant, it changes at different, different points, then you'll have to use differentiations. Then it means that charge density, charge distribution, it's not uniform. It's varying. At some points you have more crowdedness compared to some other points.