 Now we're going to look at magnetic forces. As we've been discussing fields and forces, we started off with electric fields. And one of the things that we found was that electric fields can exert a force on charged particles. Had to be charged, but if there was a charge, as soon as I put that charge in the electric field, it experiences a force. So now that we've come up with a magnetic field, the question becomes, do magnetic fields exert a magnetic force? And again, E stood for electric, B stood for magnetic. Well, the answer to this question is yes, but with different conditions. When it comes to magnetic forces, we have to actually have four things to get a force. First thing is you have to have a magnetic field. You're not going to have a magnetic force without some sort of magnetic field. And you have to have a charge in that magnetic field. These are the same things that we have with electric fields. But we additionally have that there's got to be movement. The charge can't be sitting still. It's got to be moving. And direction matters. Specifically, what we're going to see is that we want a perpendicular component to the motion. So let's look at this in a little bit more detail. So when it comes to the perpendicular direction, I can think about this as there's got to be a component of my velocity, which is perpendicular to my magnetic field. So if I've got a magnetic field and I've got a velocity off at some angle, well, that velocity has two components. One component along the magnetic field and one component perpendicular to it. And it's this perpendicular component of the velocity that matters. And if I were to move that component sort of over to complete the triangle, then from trigonometry I see the perpendicular side is opposite of my angle. And therefore, my perpendicular component is v sine theta. Now I can also think of this as the component of b, which is perpendicular to v, or my magnetic field perpendicular to my velocity. So now if I've got a velocity in some direction and my magnetic field is off at some angle, again, that magnetic field has components. One component is the perpendicular one. And if I look at that perpendicular component, again, I can represent it as b sine theta. So if I have velocity and magnetic field in any arbitrary direction, the theta I care about is the angle between those two vectors. And to multiply the perpendicular part, it's v, b sine theta, either thinking of the b sine theta as the perpendicular part of the magnetic field or the v sine theta as the perpendicular part of the velocity. So in terms of my overall equation then, I end up with my charge matters, my velocity matters, my magnetic field matters, and the angle matters in the sense that I'm going to have the sine. So my force is equal to the charge times the velocity times the magnetic b field times the sine of the angle. So that's my equation I'm going to be using for the magnetic force.