 Now we can develop the concept of emotional EMF. So I start with the concept of a conductor moving in a magnetic field. And from our previous review we know that there's a force on the charges inside that conductor, the electrons and protons, as it moves through the magnetic field. Now I want to note right away that if I happen to move with my velocity in the same direction as the magnetic field, then when I do that cross product, I'm going to end up with a force of zero. Instead, if I move across the magnetic field perpendicular to it, it might be upwards, it could be downwards. In that case, the amount of force I have can be simplified to being QVB. And I don't have the cross product in here anymore because it's already perpendicular. Now to help us see the directions a little better, I'm going to go ahead and use a magnetic field that's pointed into the page, represented by our little X's here. So I put my conductor in this field and I move it perpendicular to the field. In this case, I'm going to move it upwards. Well that's going to create a force and we can figure out the direction of the force by the right hand rule. Your fingers are going to point in to the screen because that's the magnetic field. Your thumb is going to point upwards and that means the palm of your hand is going to face left. You want to actually put your hand up here to make sure you understand this. That means the positive charges would be forced to the left. Of course, in a conductor, we know that it's really the electrons moving to the other side, leaving some positive voids. So now I've got this conductor moving through a magnetic field and that's caused charges to separate. Well, it's a force of QVB causing the charges to separate. But as soon as the charges start to separate, it creates an electric field. And so there's a force trying to pull them back together, which is equal to Q times E. The charges are going to keep separating until those forces balance out. In other words, till QE equals QVB. So let's focus in on that equation here. So we've got our balanced forces QE equals QVB. We notice right away that it doesn't matter what the Q's are, but we will develop an electric field which is equal to the velocity times the strength of the magnetic field. Temporarily, I'm going to take away the symbols for the magnetic field so that I can focus on what's happening with my electric field. So I've got this electric field established because I've got positive charges on one side, negative charges on the other side. That creates a potential difference across that material where I've got a higher potential where my positive charges are and a lower potential where my negative charges are. As a matter of fact, the amount of potential difference across this conductor depends on the electric field and the distance across that conductor. Now if I define that distance across the conductor as the length L, that means that the amount of potential difference I establish across this conductor is equal to VB, which was the electric field, and the length of the conductor, which was the distance across which that electric field is acting. Taking that equation, we can represent it in a more standard form to describe our emotional EMF. In this case, we specifically say that that potential difference, that's the EMF we're talking about. And then they just sort of rearrange it a little bit because the common way is to represent BLV. I have a magnetic field of strength B, a length of L, and I'm moving at a velocity of V. You'll also sometimes see this equation written out with a minus sign. That minus sign helps to indicate which direction the potential difference is set up. And we'll talk about that more in other lectures when we get to Lenz's law. I do want to caution you very much here when we start talking about the length. We need to make sure we're using the perpendicular length. So for example, on the conductor we've already been looking at, if my velocity is moving upwards, my perpendicular length is this horizontal length across the conductor. If instead I were moving the conductor to the right, the length I would have to use is the perpendicular length. And so it's going to be this shorter distance, which you might call the height, but it's the length perpendicular to the velocity. Now most of the time we're not applying this to a big rectangular conductor. We're often working with wires. So if you want to use emotional EMF to create sort of the maximum EMF across that wire, if you've got a wire which has a length horizontally, you want to move it vertically, up or down. If you have a wire that's shown vertically so that it's longer side is up and down, you want to move that wire horizontally to the left or right. Now you could still have emotional EMF if you move these in other directions. But for example, if you move this one upwards, you'd have to use the length horizontally across it, which is a very small length so you won't develop a large EMF that way. So remember that when you're working with these equations, you want to use the length which is perpendicular to the velocity and that velocity and length should both be perpendicular to the direction of the magnetic field. That wraps up our introduction to the concept of emotional EMF.