Hey guys, so in this video, we're going to talk about how charges moving through a magnetic field actually experience circular motion. Let's check it out. Right, so first of all, remember that the magnetic force on a moving charge is always perpendicular to its velocity. So you can remember this from the right-hand rule. The force is always perpendicular to the velocity. This is the velocity, the force is always the palm of your hand so it's going out this way and even if it's this way, right? This is always going to be a 90-degree angle, okay? So because of this, you're going to have circular motion. Let me show you. So let's imagine that there's a magnetic field inside of this square and you have a charge q, let's say a positive charge q right here that's moving this way. So it moves with a constant speed, but as soon as it gets right here, it's going to now experience a force because it's moving inside of magnetic fields and we're going to use the right-hand rule to figure out that direction. Okay? So right hand, we're going to go into the plane. I want you to do this with me, right? So I want you to point away from your face and into the page because that's what the little x's mean. Now notice my hands like this and I want my thumb to actually go in the other direction, so I'm going to do this. Okay? So please follow me and do this yourself and when you do this, you're pointing away from yourself with your thumb to your right, your palm should be pointing up And your palm pointing up means that the direction of the force is upward. Okay? So there will be a force here. The magnetic force will be up. What that means is that this thing will start to curve because it was moving this way, but now it got tugged up a little bit, so it's going to do something like this, okay? And actually let me do a little bit differently. It's going to do something like this, and then once it's over here, it's going to, again, what it's going to start doing now, your hands like this, it's moving like this. So now the force is going to go in this direction, okay? So now you have a magnetic force that points this way. Now it's going to curve a little bit more. The magnetic force is always going to point, it's always going to be perpendicular to the velocity, right? And the velocity vector is going to be like this, like this, tangentially and the force is going to keep you in a loop. Okay? And you end up doing something like this. You end up doing something like this. Okay? So whenever you have a charge inside of a magnetic field, it's going to move in circular motion.
Cool, so that's that And you're going to be able to write an equation for that. So we have circular motion so we can write that F=ma. And we can say that this is a centripetal force. So it's going to be ma⁀centripetal. Remember the centripetal acceleration is v2/r, where r is the radius of the circle. So r is radius of the circular motion. And the force here that's responsible for the centripetal acceleration is our magnetic force. I'm going to replace this with Fb and it's going towards the center equals m I'm going to replace a with v2/r and you'll see what we're going to get. This is a magnetic force on a charge so this is going to be qvbsinθbut the angle is 90 degrees and the sine of 90 is simply 1. So that goes away and then you end up with this. And notice that the this V here, one of the V's is going to cancel with this one and you're able to by moving some stuff around calculate or write an expression for R. And R is going to be, if you move some stuff around, you move R to the other side and you move the QB to the other side and you get this r=mv/QB which is a huge equation in this chapter. It's going to come back over and over again, okay? So, you may need to know how to derive this depends on how picky your professor is about this kind of stuff. But even if you remember how to derive the whole thing, you also should memorize this equation so you can work with it faster. Okay, super important equation. I have a silly trick to remember this equation. Sometimes people get the letters confused. There's a lot of letters. MV, if you remember is momentum, momentum P equals MV. So I think of this, the way I remember this is I think of momentum, which is top and then QB is short for quarterback. So momentum quarterback. It's a phrase that makes no sense, but it just sticks. Right? Momentum quarterback or at least for me it sticks and it's a way for me to quickly remember this. And if I forget, you can just, I can always just go to F=ma and sort of re derive it. Okay? So that's it for that. Let's try a quick example here.
In an experiment, an electron, electron, so that means that q is going to be negative 1.6 times 10 to the negative 19 coulombs, enters a uniform field b equals 0.2 Tesla, directed perpendicular to its motion, perpendicular to its motion. Meaning the angle is going to be 90 degrees. Therefore, the sine of 90 will be 1 which means you don't have to worry about plugging a sine, okay? So you measure the electron's deflection to have a circular arc of radius 0.3 centimeters. This is just the radius, right? Don't get thrown off by the word circular arc. What matters that the radius is this. Circular arc means that it's something like this. That it's going like this and then it sort of bends a little bit, right? And then it keeps going and then this little arc, if you make it into a big circle, will have that radius, okay? But long story short, it just means that that's what you use as the radius. Notice that this is 0.3 centimeters so it's 0.003 meters or 3 times 10 to the negative 3 meters.
