 Let's do a really quick review on what we've learned so far about magnetic forces. In our first lecture, we introduced our equation for the magnetic force caused by a charged particle moving through a magnetic field. And that's the magnetic force is equal to q times v cross b. If I was going to write this out in words as a quick reminder, that's the vector magnetic force is equal to the charge multiplied by the cross product between the vector velocity and the magnetic field. And again, remember that this cross product is not just a regular multiplication. As a quick review for the cross multiplication, we can write that out in several ways. One of those is if I'm given the angle rather than doing the full vector multiplication as a cross product, it's the magnitude of the charge, the speed, the magnetic field strength and the angle in between them. If I have the components, I can use this form all written out, but I also remind you that if you know how to do the determinant of a matrix, you can work it out by doing your crosses as you're going through. If I took a look at the units and break this down, force has to have a unit of Newton, charge has a unit of coulombs, velocity is going to be meters per second, and the magnetic field is measured with a standard unit of Tesla. And it was knowing that these two sides of the equation had to be equal is how we came up with our definition that a Tesla is a Newton times a second divided by a coulomb times a meter. We're going to see this come back into play when we start looking at the units for the equation we're going to introduce today. If I've figured out my force by using the QVB sine theta, I still need to figure out the direction and we use the right hand rule to do that. We're going to see this again a little bit later, but just as a reminder, your thumb represented the direction of the velocity. Your fingers represented the direction of the magnetic field. And in that case, your palm, flat pushing outwards, keeping your hand nice and flat, shows you the direction of the force on a positive charge. There's just another way of drawing that. If you've got your velocity, you've got your magnetic field, the force is coming out. It's really hard to draw these things, but we'll get a chance to practice this. Again, if you've got a negative charge, however, we learned in class that it's actually the backwards direction for the force because we've got that negative Q in there. And so it's going to be the direction that the backside of your hand is pushing. We then had a lecture where we looked at the motion on free charges, where free charges were the charges that were not constrained by any other forces. Could be an electron, could be a proton, could be a charged ionic particle. And as long as I've got the velocity moving across the magnetic field, there's going to be a force perpendicular to the motion, which causes a centripetal acceleration. Most of the cases we looked at, we were talking about the circular path that would cause, but we recognize it could also be a helical path where it moves along the magnetic field. Electrons are going to move in the opposite direction of protons. So while a proton might go counterclockwise in this situation, an electron would go clockwise, yeah, clockwise. Proton counterclockwise, electron clockwise. And again, we're going to see a little bit about this, but the main focus of our lecture today is on charges which are not free. This is the end of the quick review. If you have concepts that you still need to work on, you can go back and watch this video. But mostly I recommend you go back and look at your old lecture notes.