 Now we're going to look at the equation for the magnetic force on a current-carrying wire. We've already looked at the concept, so we know there should be a force. In order to understand this, we're going to step back for a minute and go back to that force on just a moving particle in a magnetic field. F equals QVB sine theta. And I'm just reminding you here with these bars that what I really had here was just the magnitudes of each of these quantities without regard to direction. So right now I want to look more at this quantity V and remind myself that this V or the speed that the particle is moving because I don't care about the direction at this point, well I could represent that in terms of the distance per time. If I substitute that equation in, I end up with this F equals Q D over T B sine theta. So now I'm going to take this equation and I'm going to focus on these first couple of quantities over here. And remember that if I've got charge times distance over time, that because these are multiplied and divided, that's communicative, I can rearrange this slightly. So I'm going to take this, I'm going to pull the Q inside the parentheses and then just express the divided by time associated with the Q rather than the D. So algebraically these two forms are exactly equal to each other. So now I've got this new rearranged quantity. Let's think about what this Q over T is. That's a charge per time. Well we defined that, that was the current I. And if I'm thinking about this in terms of a current moving down the wire, the distance it's going to travel, that's going to be the length of the wire. So I can actually substitute these quantities in so that Q over T becomes I and D becomes L and I'm left with F equals I L B sine theta. So this is my final equation for the force due to a magnetic field on a current carrying wire. And right now this F equals I L B sine theta, that only gives me the amount of force. Direction would have to come from the right hand rule. Now when I have this for a charge particle, in addition to having the how much force I have with the Q V B sine theta, I could also express it in terms of a cross product form. So our current carrying wire has a cross product form as well, where the vector force is equal to the current times the vector length crossed with the vector B field. And here I associate the direction for the length and in terms of the direction the current is flowing along that wire. So that's your equation for the magnetic force on a current carrying wire. . . . . .