 Now we're going to do something called electric flux. So your first question is going to be, what is flux? One way to think about it is a measure of flow through a surface. So if I've got something flowing through a surface, how much do I have flowing through that surface? Well, then the next question is the flow of what? I've just said flow. Well, in this case, we're looking at electric field lines. So this electric flux is going to depend on three factors. First, it's going to depend on the field strength. Remember that in electric fields, the stronger the magnetic field, the more dense the lines were. So a stronger field is going to have more lines, and therefore you're going to have more lines going through a particular surface. It also has to do with the area. The more area you have, the more lines are going to go through that area. A smaller area, you'll have less lines going through that area. Then you've got the angle of the surface. You can imagine this surface as being a disc that's standing up. Well, depending on how that disc is slanted, you might have more or less lines going through that. Well, I can take these three factors and put them into an equation that looks like this. So let's take a closer look at this equation. So over here on the left-hand side, I've got the flux. And this is actually the Greek letter phi. Over on the right-hand side, my E stands for the electric field. The A stands for the area. And my theta is the angle. And I'm going to take the cosine of that angle. Now if I want to take a look at the units for these quantities, let's start with the ones we already know. Electric field has units of newtons per coulomb. Area has units of meters squared. Your angle is going to be degrees or radians, but once you take the cosine of the angle, it doesn't contribute any units anymore. So that means if I take and put these units together, what I've got is a newton meter squared per coulomb. And this doesn't actually have another name. You have to use the full newton meter squared per coulomb in order to be able to work out exactly what my units are. Let's come back to this concept of the angle. If I've got a surface, how do I define the direction of that surface? Well, mathematically, I use something which is called the normal. And that's a vector which points perpendicular straight out from the surface. And it doesn't matter if my surface is flat or curved, at that particular point on the surface, which direction is perpendicular to it. So even if I'm off at an angle here or I've got a tilted surface, I'm going to define the direction of that surface by the normal vector. Now, another way to represent the same equation here and to include both the electric field area and the angle, I could use the vector form called the dot product. And in this case, the way I would read this equation is e dot a. So it's the dot product between the electric field and the area. Now, this isn't just a normal multiplication here. It's a vector quantity telling you exactly how to deal with the vector directions. So if I were to multiply this out to think in terms of components, what I do is I take the x component of both the electric field and area and multiply those two quantities. I do the same thing with the y components and the z components. And then I add these three numbers together so they don't stay as separate x, y, and z components. Instead, I get a single number representing the electric flux. Now, that number could be positive or negative, but it doesn't have a direction in space. So far, I've been talking about a single value for the electric field. But what if I've got some sort of non-uniform field or surface such that as I look over the surface, my electric field might either vary in direction or it might vary in strength and my surface might be changing as I'm whirling around. On that case, I can't do a simple dot product. My dot product's got to be inside an integral and I have to integrate over the surface by breaking it down into little small segments of DA. So that introduces our electric flux equation.