Hey guys. So some questions will ask you to find the mass to charge ratio of particles going through a mass spectrometer. And that's what we're going to do here. So let me show you. So here it says a mass spectrometer has a velocity selector, electric field of magnitude 20. So remember you get accelerated and then you go through a velocity selector, that's going to have an electric field and we're telling you here that it has a magnitude of 20. It says when a certain charge is accelerated to a constant 30, so it gets accelerated over here, it goes through the little hole and then it's now going to move here with a constant 30. It collides 40 meters away from the velocity selector. What does that look like? Well, it means it's going to curve this way and it's going to hit this wall here at a distance d equals 40 meters. Remember also that distance is twice the radius because you have a radius and radius, which means if the distance is 40, this means that the radius is 20. And the reason we want to change it to radius is that our other equations, or the one other equation we're going to need here, is in terms of radius and not in terms of distance. I drew it down even though it could have gone up, we don't actually know. We are not being given enough information to figure out which way this is going but it doesn't matter. I just picked one for the sake of illustration. Okay? In this question we're going to find the mass to charge ratio. Okay? Mass to charge ratio which is m/q. By the way, if I hadn't told you that we were looking for m/q, you can just interpret that from the question. The mass to charge ratio, you would do this and say, hey, I'm looking for this. Which means you're not looking for m or q. You want to leave this as a fixed unit and then solve it. So how the heck are we going to do that? Well, we got these 3 equations and one of them hopefully
q ∆ V = 1 2 m v 2 .By the way, this is a potential difference or voltage, and this is a velocity, 2 different things. The other equation is that
v = E B .And the other equation is that
r = m v qB .And we're looking for the ratio m/q. Luckily, this is actually really straightforward. Because if you look here, you'll find one of these equations has an m and a q and it's right here. And not only do they have it, but they're already sitting next to each other which is awesome. So all you got to do is move stuff around in such a way that the m and the q stay exactly where they are. So we're going to move the B to the other side. So I'm going to get BR/v. Do I have b? Yep. Do I have b? No, I don't have b. Got excited there. For a second, do I have r? Yep. R is 20. Do I have the velocity? The velocity is 30. So we don't have b. We got to get it. Can we get b? This equation here seems to be going to work. So
v = E B .Therefore, b is E/v. The e is 20, electric field strength and the velocity is 30. So b is 0.67. Okay. 0.67 Tesla. So that's what's going to go over here. 0.67 Tesla. And if you do all of this, you're going to get that ratio is 0.44. The units are kilograms per coulomb. Okay. So that's how you could do this. The second you got stuck here because you didn't have v, you just go to a different equation and you get it. Alright? That's a bonus one. Let's get going.