 Now let's look at magnetic flux. So flux in general. Well, we've already seen the concept of electric flux. And magnetic flux is really the same sort of concept. And again, that was a measure of the flow through the surface. In this case, it's the flow of magnetic field lines through a surface. And so you can think of it kind of like in this picture. If I've got a particular surface, I've got some field lines going through it. And I want to measure that. Now that magnetic flux is going to depend on three factors. It's going to depend on the field strength. Remember that the field strength is represented by the density of the arrows. So the stronger your field is, the more arrows you've got more closely packed together representing those field lines. Then we've got the area. Well, if your surface has a larger area, you're going to have more flux going through it than if you've got a smaller area. Then we talk about the angle of the surface. So depending on how that surface is tilted, you could have more or less field lines going through that surface. Well, we can wrap all of these concepts up into a single equation that says the flux is equal to Ba cosine theta. So let's take a closer look at that equation. Well, flux is over here on the left-hand side. That's our Greek letter phi. B, that's a B field, your magnetic field strength. A represents your area. And theta is the angle between those two things. Now if I look at the units real quick, B field is measured in Tesla. Area is measured in meters squared. An angle, well it could be measured in degrees or radians, but once I take the cosine of the angle, it's not going to contribute any units. So that means if I take everything together, what I've got is that flux has units of Tesla meter squared. And we sometimes give that a new symbol, WB, which stands for a Weber. So you can represent magnetic flux either as Tesla meter squared or as Weber's. Let's come back to that angle here a little bit closer. If I have a surface out in space, I have to define the direction somehow. And the choice that's used in geometry is to use what we call a normal. And that normal is a vector that points straight out perpendicular to that surface. And it doesn't matter if the surface is flat or if the surface is rounded. At that particular point on the surface, I can define its direction with the normal vector. Even if my surface is tilted off to the side, well then my normal is also going to tilt off over to the side but still perpendicular to the surface at that particular location. So that brings us to our dot product form. If I've got this BA cosine theta, I've just talked about the angle being measured for the angle of that area. I could also represent this as the dot product between the vector magnetic field and the vector area. We've already seen that magnetic field can be a vector. Now we can see that the area is also a vector where the direction is defined by the normal. Now if I break down the dot product, what I do is I multiply the x components of both magnetic field and area, multiply the y components, and then multiply the z components. And then I add those three numbers together. So in the end I'm left not with separate x, y, and z parts but just a single number to represent the flux. Now so far we've talked about a uniform field and mostly we've been talking about a uniform flat surface. If I have a non-uniform field or surface where my surface might change directions over the course of it, or where my magnetic field might even change directions or strengths at different places on the surface, I can't do just a simple dot product. Instead I'm gonna have to integrate over the surface using the dot product of the magnetic field with each little sub-segment of area over the whole thing. So that takes a little bit more work. So that introduces magnetic flux for you.