 Imagine we have an infinitely long line containing uniformly charged distributed over it. The question we want to try and answer in this video is what's the electric field everywhere? So if you take any random point p at some distance r, what would be the electric field at this point? That's what we want to figure out. Now very quickly you might say, hey, we don't know how many charges are present. How many charges are there on this line? Because the electric field depends on the charges. Well, because this is an infinitely long line and charges are uniformly distributed, that means the total charge is infinity. So how do we represent the amount of charges over here? Here we're going to represent something called the charge density. It's a number that tells you how crowded the charges are. So if the charge density lambda is more, it basically means there are more crowded, charges are more crowded. On the other hand, if lambda is less, it means charges are less crowded. And if you look at the number, it tells you how many coulombs of charges are present per meter. So if lambda is say 10 coulombs per meter, it basically means every meter has 10 coulombs of charge. So let's say we know the charge density. Every meter has lambda coulombs of charge. That's given to us. Now how do we figure out the electric field at point p? Before we begin, another question you might be having which usually doesn't get asked in exams is why are we doing this? I mean, infinitely long things, like do they exist in our... I mean, do they have any application in our real life? Yes, they do. Imagine you want to calculate the electric field close to a lightning strike. Now a lightning strike, this is very long. It's not infinitely long, but it's pretty long, kilometers long. And I imagine you want to calculate electric field some few feet away from it. Now, when you consider the distance of few feet and you compare it with the few kilometers, you can pretty much assume that this lightning strike, this length is pretty much infinity. And so you see, whatever answer we're going to get over here can be applied to a lightning strike and people do that. So in short, in real life, this is applicable when you're dealing with very long things compared to the distance at which you're calculating the electric field. So it can be applied. All right, with that said, now comes the question, how do we do that? Now, of course, the title gives it away. You might already guess we have to use Gauss's Law. But I want to really ask the question, why do we want to use Gauss's Law? I really want to first come towards that question. And so to do that, we will first forget about Gauss's Law and think about what do we already know? Well, we know Coulomb's Law. That's all we know so far. If we have any point charge Q, then we know electric field due to that point charge Q is going to be equals Q divided by 4 pi epsilon naught r squared. So the first question that I have is, can I calculate electric field over here using just Coulomb's Law? The answer is, yeah. In fact, you can use Coulomb's Law anywhere. The problem is I can't do it directly because this is not a point charge. It is, you know, a distribution of charges. And so really, the first question I have before even we think about Gauss's Law is, how would you use Coulomb's Law over here? And that's the question that I really want you to think about because that'll help you understand why we're going to apply Gauss's Law later on. And because I would really want you to think about this and also make the rest of the derivation an interactive experience for you where you and I can work on this together. I'm going to pause over here. In fact, I'm going to stop the video over here and we'll move on to our Khan Academy website. In these new articles, you get to interact and try working things out yourself first. Turns out this is a much better way to learn than just me telling you what to do. And so let's continue by moving to the next article. And of course, if you're watching this on YouTube, you can click on the link over here to take you to our Khan Academy article. All right. Happy studying. See you over there.