 So now we're going to look at the magnetic force on parallel wires. To do that we're going to review a few equations we've already taken a look at. One is the B field, short for magnetic field, along a straight wire. And that's this equation here. And just as a quick reminder, the I in this equation stands for current, and the A in this equation stands for distance from the wire. Now we're going to look at the force on a wire, just given by this equation. Now I have to have a current here too, but the B field is an external B field. So it's not the magnetic field created by the current in this wire. It has to be created by some other current. So that brings us into our parallel wires case. So here I've got two parallel wires. In this case they're both pointing in the same direction. But you could also have one of these two wires flipped around to the left. That would be just fine. For convenience, I'm going to label them I1 and I2 to represent the two different currents. And these two wires are separated by a distance A. Now if I wanted to find the force on wire two, then I would need to know the current in wire two, the length, and the magnetic field. But since it has to be an external magnetic field, this is actually the magnetic field created not by wire two, but the magnetic field created by wire one. So what is that equation? Well, current one is going to create a magnetic field. And again, since it's separated a distance A, I've got current one and A as my two values that go into this equation. Plugging that in for my B1 into my original equation. And noting that I've got a nice 90 degree angle, so the sine of theta part can simply be reduced to one. I've got I2L mu naught I1 over two pi A. Now to figure out the direction of that force, I have to come back up to thinking about the magnetic field around wire one. Using a right hand rule, you should be able to figure out that it should circle around wire one in this kind of a direction where it's coming out of the page above the wire and going back into the page below the wire. So that means down here at the location of wire two, it's going into the page. So I use my little green X's here to show the magnetic field from current one on the location of where current two is, is going into the page. Now I can look at my right hand rule. Well, my magnetic field, my fingers of my right hand have to point into the screen. My thumb has to point towards the right, the direction of current two. And that's gonna cause me to have a force that's going upwards. Now I can do the same sort of thing, but look at the force on wire one. And again, that's gonna depend on current one, but the magnetic field created by wire two, which is a very similar equation. And plugging that in, again, I get something that looks like this. I can do the same sort of thing with directions for the magnetic field created by current two. Where I see that I'm out of the page above the wire two and into the page below it. So that means I'm actually coming out of the page at the location of wire one. And if you use your right hand rule, you would see that the force then is downwards. Now I'm gonna take these two things and sort of put them together. I had the force on wire two upwards and the force on wire one downwards. Now here I've just taken my equation and sort of rearranged the factors. But you can flip back to the previous slides earlier and see that these are indeed what I had for my previous two equations. You'll also notice that these two forces are exactly equal to each other, but opposite in direction. They form a Newton's Third Law pair. So in general, the force on either one of the wires in a parallel wire pair depends on the current in each one of the wires. It depends on the separation between the wires and the length of the wire. We'll often see this equation rearranged slightly, where they actually talk about the force per unit length. And in that case, it just depends on the currents in the wire and the separations between the two wires.