Hey guys. So in this example, we are looking for the force on a charge that's moving through a magnetic field in 3 different scenarios. Let's check it out. So we want the magnitude and the direction of the magnetic force. We want the magnetic force on a 3 coulomb charge. So q equals plus 3. It's positive. We're going to use a right-hand rule for direction. We would use the left hand if it was negative. And it's moving with this velocity here, v equals 4. And it has a 5 tesla magnetic field. That's the strength 5 tesla. And that field is directed in the positive x-axis. Okay. So that's the field right there. And we want to know what is this force if the charge is initially moving in these three directions here. So in all three cases, B is going to the right, but the direction of the velocity is different. Here the velocity is going up. Here the velocity because it says positive y-axis. Here the velocity is going to the left because it's negative x-axis. And here it makes 30 degrees with the y-axis. Now the positive y-axis over here, this is a little ambiguous because you can make 30 degrees with the positive y over here. Right? This guy is 30 degrees away from the positive y, but this guy is also 30 degrees away. We'll talk about that when we get there. So the equation we're going to use is the only equation that makes sense. The equation for force on a moving charge, which is qvBθ. I know q, v, B, we're just going to plug those in. So the challenge here is just making sure we find the right angle, the correct angle. So Q is 3, V is 4, B is 5. Those are given they're up here. And the angle we should use is the angle between the two vectors. Between V and B is the angle we should use. V is up, B is to the right. V is directly up. B is directly to the right. So they're exactly perpendicular to each other to make an angle of 90 degrees. So sine of 90 degrees. Sine of 90, by the way, is 1. So the answer is just 60 newtons. Okay. What about the direction? Well, we're going to use the right-hand rule. So remember, my fingers represent multiple lines. So it's my B field, it's going to point up like this and, it's actually going to go like this, right? And my velocity should go up. So it's already up, so this is the direction I should be looking for. Notice that my palm is out, my palm is away from me, and you've got to do this yourself looking at your page. Right, if you put your hand in front of you and you see that your palm is away from you, it's going into the plane or into the page. Okay. So the direction is into the page. Okay. What about here? F_b is going to be the same thing 3×4×5 times sine of theta. But here the angle between v and b is 180, right? They're anti-parallel to each other and the sine of 180 is 0. That means that there is no force at all. Okay. And if there's no force, then there is no direction for you to worry about, right. Now, how can you remember this? One way to remember this is if you look at your right-hand rule, this should serve as a reminder that B and V are supposed to be at 90 degrees. And what I mean by supposed to be is this is the scenario in which you get maximum force. Okay? If your V moves a little bit, now you have less force, you have less than maximum, but you still got some force. And then if you go all the way, right, as you do this you're decreasing the magnetic force all the way to here, and then you get here which is parallel, 0 degrees, right? Parallel, or now you have 0 force. Same thing if you go all the way over here and you are at 180, I can't really do that it hurts, then that's going to be 0 force as well. Cool? Maximum force, a little less force, 0 force. Cool. So let's jump into this one here. Here, we talked about how there are 2 directions, because it's not clear, it's ambiguous, but it actually doesn't matter because the magnitude will be the same. Okay. The magnitude will be the same. If you want, you could have calculated the two different angles. Right? The distance, the angular distance between this red arrow and this blue arrow here is 60. Remember, you don't necessarily use the angle that's given to you. You use the angle depending on the definition. The definition of the angles should be the angle between V and B. So you got to be very careful whenever you see an angle. Okay. So that's one angle you could have used. Let's call it theta 1 or you could have used the angle all the way to this blue arrow here and that theta 2 is 90 degrees right here plus the 30. So 90 plus 30 is 120. You could have used either one of these guys and you would have gotten the same answer because sine, I'm going to use 60. Right? Sine of 60, and you can plug this into double-check, equals sine of 120. Right? So it's the same thing. You get the same answer no matter what. And that answer is 52 newtons. Remember I told you that if you're slightly at an angle, you're going to get less than maximum. This is the maximum force you can get for this arrangement. This is a little less than maximum. Right? And this here is the minimum, which is just 0. Okay. Now what about the direction? Well, B is this way, and you can have your charge even move either moving that way or this way. Right? Either way, for both situations, my palm is away from me. So if you look at your page and your palm is away from you, which means you're looking at the back of your hand, that means that the force is going into the page as well. Okay. So the direction here is into the page for both of those situations. Cool. Let me get out of the way. It's into the page. Cool. That's it for this one guys. Let's keep going.