So, magnetism is something that you're all familiar with, you've played with magnets in your life, right? You're a little kid, and you grab the magnet, you go down to the sandbox and you start digging around in the sandbox, and you surprise yourself by finding a whole number of sharp objects in the sandbox. Everybody notice that? It's like nails and staples and stuff coming out of the sandbox? It's kind of scary so don't ever do that. Okay, what does a magnet look like? A bar magnet looks like the following. Bar magnet, let's see if we can spell correctly. It looks like this. It's a bar. And as Professor Torikachvili told us, a magnet has a north pole and a south pole. Okay. you're all familiar with this. So, let's say we take that bar magnet and we cut it in half. Okay, so I'm gonna cut the thing in half right there and if I do that, that south pole was down there, the north pole is up there. Is that it? Is that all that happens? The answer is no. You, in fact, develop two new magnets. Both of those have a north pole and a south pole. And now if you do it again, and I cut this little piece and that little piece, I cut them in half again, each one has a north pole and a south pole. Okay, north and south, north and south and so on. And you can keep doing that all the way down until you get to essentially nothing, and at no point do you get just a north pole or just a south pole. And this is the statement: There are no magnetic monopoles. You can't have just a north pole, you can't have just a south pole, anytime you have a north pole, you automatically have a south pole. Okay, north and south always come together. And this is very different than charge. When we talked about charge, you can have a positive charge sitting all by itself, a proton. You can have an electron sitting all by itself. But you can't have a North Pole just sitting all by itself or a South Pole sitting all by itself. Now there is a little bit of a caveat which professor Torikachvili alluded to. There are theories that magnetic monopoles should exist. That there should be a north pole all by itself, and there should be a south pole all by itself. But currently, there has been no experimental proof that those exist. Okay, so this is the current understanding of the universe, but ten years from now, fifty years from now, this may no longer be true. Remember, physics, like any science, is an evolving field Okay, we are continually evolving our models of the universe, and this is the current understanding. But ten years from now, fifty years from now, maybe in your lifetime Maybe they'll say aha there are magnetic monopoles, we found them definitively and here they are. Okay? Alright. What do these magnets do? Well, I have a magnet here, let's put another magnet right next to it. So if I put another magnet right there, something's gonna happen. What is going to happen? You've probably done this experiment. If I take two magnets and I try to push the north poles together, and I try to push the south poles together, they push apart. there is a repulsive force F, which is pushing them apart. But if I flip one of them over, now they are attracted together. So in the first case, they pushed apart, in this case they attract, they're gonna pull together. And so this is a statement that we talked about yesterday, with magnetism, likes repel, opposites attract. Which is very consistent with what we have already been talking about with electrostatics. Positives repel each other, those would be likes, negatives repel each other. But opposites attract. If I had a positive and a negative, they would attract, if I had a negative and a positive they would attract. So likes repel and opposites attract. Okay, let's see what the B field looks like for a bar magnet Okay, so here's our bar magnet, and before we do that, let's redraw the dipole. We remember what the dipole field looks like, it looks like this. Okay, and you can draw as many as you like, and now if I draw the bar magnet, it looks extremely similar. Comes out of the north, it goes into the south It's a dipole field. Just like the electric dipole, this is a magnetic dipole. So one question that you may have is the following, if north and south always come together, then I must always have a dipole field for magnetism. And that is true. There is no monopole field. There's no just north charge. So lines of B, in fact are continuous. And this is an important statement They always connect back on themselves, whereas lines of E do not. They start on positive charge, they end on negative charge. And so now here's a question. What is the direction of the magnetic field inside this thing, inside the bar magnet? And let's go back to the dipole for a second. The field in between these, E, is going down from the positive to the negative. But over here, the fields of B, in fact, are going up through the center of the magnet. And that continuous line is the B field. The B field is a continuous loop, when it comes down here it doesn't just stop at the south pole, it continues back up to where it started and goes back around again. So B fields are a little bit different than E fields, because B fields are continuous.