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Anderson Video - Cyclotron Motion

Professor Anderson
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Okay, so let's say we have a region of space here, and in this region of space we have a B field that is everywhere going into the screen. And B field is everywhere pointing into the screen. And now you want to put a charge in this thing and send it flying through. So I'm going to take a q and let's see, which way do I want to send it? I want to start right here, we'll make it a positive q, and let's send it this way. Alright, this thing is gonna feel a force, and it certainly has to feel a force either up or down. Okay, remember B is going into the screen. So, which way is that force going to be? Is it up or is it down? Look at the computer monitor over there, pick up your right hand, put your finger straight in the direction of V, curl them into the screen for the direction of B. Which way is the force? It's got to be up or down. What do you guys think? Anybody get an answer on that one? Let's try it. V is going to the right. B is into the screen so I'm going to curl my fingers into the screen right? That's to you what looks like into the screen? Okay, and so I'm going to end up with a force that is up and that means that this thing is going to move in a circle. That particle that came flying in is, in fact, going to move around in a circle Is that right? Did everybody see that? Okay? V is to the right, B is in to the screen, thumb as the direction of force, so it's towards the center of a circle at this point. Later on, V is going up, B is into the screen, and so I again get a force towards the center of the circle. And everywhere around it's always a force towards the center of the circle. Okay, but we know what that force is, it's qVB sine of theta. let's just worry about the magnitude of it, we already figured out the direction qVB, what's the angle between those two? Well V was to the right, B was into the screen, and so we get 90 degrees, but 90 degrees is just one. So what's the force? qVB. Alright. But this thing is moving in a circle now, of radius r. And what we know from last semester is if things are moving in a circle, we can consider the forces adding up to something very specific, namely mv squared over r. Right, this is uniform circular motion, the centripetal force is mv squared over r. But the only force is this magnetic force. Okay, and so that becomes the left side of this equation. So we get qVB equals mv squared over R. And now we can quickly solve this thing for the radius. Alright, I multiply by R I'm gonna divide by qVB, one of the V's is going to cancel out and I get mV over qB. What's the radius of that circle? It's that. It's the momentum of the particle divided by the charge times the magnetic field. So when you are doing a high energy physics experiment and you create all these charged particles that are moving very quickly, how can you determine something about them? W ell you put them in a big magnetic field and you watch them spin around in a circle and when you do that you can determine this quantity right here. All you have to do is determine the radius of the circle. And so when you see those pictures from CERN and places like that where they have particles coming in and then doing this sort of stuff and this sort of stuff and all these circles and beautiful pictures like that, what those are are charged particles moving through magnetic fields. And from those pictures, all they have to do is measure the radius and if they know the magnetic field that was in there they can figure out something about how fast it's moving. What's the mass? What's the charge on it? Positives are gonna go this way. Negatives are gonna go the other way Ones that are very lightly charged, have a small q, have a bigger radius. If they have a bigger mass they have a bigger radius And so you can determine a lot just from taking these sorts of pictures. And it's really not that complicated, right? We just did it with the force law, magnetic force law, and the centripetal force law