Hey, guys. So in this video, we're going to talk about forces, magnetic forces on moving charges, and I'm going to introduce the right hand rule. Let's check it out. Alright. So if you have a charge that is moving through an existing magnetic field and it's going to look like this, you have a magnetic field. Remember, fields are usually represented with multiple lines. Magnetic field is B and you have a charge, let's say q, that's moving, let's say this way with a speed v, that charge will experience a magnetic force due to the fact that it's moving in a magnetic field. Okay? The magnitude of that force will be given by this equation:

F B = q V B sin θwhere q is just the charge. V is the speed and it's a vector. Or I guess the velocity, the magnitude of the velocity vector. This is the magnitude of the magnetic field and times sine of theta where theta is the angle between the two vectors. Q is not a vector. V and B are vectors; they have directions. So the angle will be the angle between the two things with directions, between V and B. For example, here, v is going this way and B is going this way. So the angle here is this, which would have been, or which is 90 degrees. Okay? By the way, this is called Lorentz force, named after Mister Lorentz. And you should know that the units for a magnetic field are Tesla, named after Mister Tesla. Cool? And then 1 Tesla is 1 newton divided by 1 ampere times meter, if your professor likes you to memorize these things. Let's do a quick example and calculate some magnitude here.

So here we're saying a 2 coulomb charge, let's write that down. The charge is 2 coulombs, moves perpendicular to a magnetic field. Moves perpendicular to a magnetic field. Perpendicular means 90 degrees. It doesn't tell us, the problem doesn't tell us who's moving where, or which thing points in what direction. So we can just kinda make it up as long as they're 90 degrees apart. So we can say that the velocity is going this way and the magnetic field is this way because we're told that the angle between the two of them has to be 90 degrees. Cool. So let's say here that it's moving with 3 meters per second. So that's our V, 3 meters per second, and it feels a force, that's our magnetic force, of 4 newtons. These are unrealistic numbers but I just wanted to keep it really simple. What must be the magnitude of the magnetic fields? Magnetic field is big B and I want to know what is big B. So the question is, is there an equation that ties these four variables together? And obviously, there is. That's the one we just looked at.

F B = q V B sin θNow we have everything but we're looking for B, so all we have to do is solve for B.

B = F qV sin θ Sine of θ is easy. The angle between V and B is 90 and the sine of 90, you should know, is 1. So this whole thing just becomes a 1, so we don't have to worry about it. The force is 4. The charge is 2. The speed is 3. This is 4 over 6 or 2 over 3 or 0.67. We are talking about magnetic field strength. So this is 0.67 Tesla. Cool. That's it. That's all I got to do with that equation.

Now one thing we haven't talked about yet, so we talked about the magnitude but we haven't talked about the direction. And direction in magnetism problems are always going to come from the right hand rule, and there are going to be a few variations of the right hand rule. We'll tweak the rule, to make it work for different problems. Right hand rule abbreviated RHR in case you see it around. You know you're getting comfortable with things when you start using, abbreviations. So before we get into the ranking rule, which is massively important, a lot of people get confused here, so we got to go slowly through this, I want to warn you that there's a bunch of different rules. In fact, most books and most professors will use some version like this, which you might have seen in class. Okay. Where it's like you're shooting someone, but then like your middle finger sort of like sticks to the side. It's hard to do this on camera. But this is the most popular one and there's an engineering reason or sort of a more advanced physics reason why this is kind of a clever thing to do. I don't like that version. I use a different version. A long time ago I sort of thought about all the different ones and I've settled on the one I'm going to explain to you guys. It's got a bunch of advantages. You can't fully appreciate the advantages unless I explain the whole thing to you and that's too much. So you just have to kind of trust me or you can use whatever your professor uses or whatever else other valid method you find that you may like. So whatever you do, you have to pick 1 and stick with it. But if what you're doing is different from your professor, different from me, you just have to make sure that they match. What I mean by that is if I'm solving a problem and I got a direction to the left and you're using a different method, your method should still give the same answer. Same thing with your professor. So if you use my method and your professor is using a different method, you have to make sure that you're actually getting the answers that match his answers. Otherwise, something's wrong. Okay. So please be careful. Pick 1 and then go with it. So, when we so the reason we needed the, the right hand rule is because things are now going to be in 3 dimensions. And if you have 2 dimensions, you can be going up or down. That's 1 dimension. The second dimension