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Force on Charge Moving at an Angle

Patrick Ford
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Hey, guys. So in this example, we're looking for the force on a charge that's moving through a magnetic fields in three different scenarios. Let's check it out. So we want the magnitude and direction of the magnetic force. So we want the magnetic force on a three cool in charge, so Q equals plus three eso. It's positive. So we're gonna use the 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 four, and he has a five Tesla magnetic field. That's the strength five Tesler. And it is, uh, 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, be is going to the rights. But the direction of the velocity is difference. 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 axes over here. This is a little bit ambiguous because you could make 30 degrees with the positive. Why over here, right. This guy's 30 degrees away from the positive. Why? But this guy is also 30 degrees away. Eso we'll talk about that when we get there. So the equation we're gonna use is the only equation that makes sense of the equation for force on a moving charge, right, Which is Q v b sign of theta. I know Q V and Beaver's gonna plug those. So the challenge here is just making sure we find the right angle, the correct angle. So Cubans three V s four Bs five. Those who give it there 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 viens up bees to the rights these directly up these directly to the right, so they're exactly perpendicular to each other to make an angle of 90 degrees. So sign of 90 degrees sign of 90 by the way, is one. So the answer is just 60 Luton's. Okay, um, what about the direction? Well, we're gonna use the right hand rule. So remember, my fingers represents multiple lines. So it's my Byfield. It's gonna point out like this, and it's actually 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 poem is out. My palm is away from me. And you gotta 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, So we wanted the magnitude, we got it and we wanted the direction. And that's the direction. What about here? FB is gonna be the same thing. 345 times Sign of data. But here the angle between V and B is 1 80 right there, Anti parallel to each other. And the sign of 1 80 is zero. That means that there is no force at all. Okay? And if there is 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's B and V are supposed to be at 90 degrees. And what am I supposed to be is this is the scenario in which you get maximum force? Okay, if your moves a little bit, um, 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, your decreasing the magnetic force all the way to here. And when you get here, which is parallel zero degrees right parallel. Now you have 04 Same thing. If you go all the way over here and you are at 1 80 can't really do that, that hurts thing. That's gonna be zero force as well. Cool, maximum force. A little less Force zero Force. Cool. So let's jump into this one here. Here. I would talk about how there's two directions because it's not clear it's ambiguous, but actually doesn't matter, because the magnitude will be the same. Okay, the magnitude of the same. So if you want you could have calculated the two different angles, right? This the the distance, The angular distance between this red error in this blue arrow here is 60. Remember, You don't necessarily use the angle that's given to you. You used the angle, the depending on the definition definition of the angle that it should be the angle between V and B. So you gotta be very careful whenever you see an angle. Okay, so that's one angle you could have used. Let's call that data one. Or you could have used the angle all the way to this blue arrow here and that data to is it's 90 degrees right here, plus the 30 So 19 plus 30 is 1 20. You could have used either one of these guys and you would have gotten the same answer because sign, I'm gonna use 60 right sign of 60 and you can plug this in to double check equals sign of 1 20 right? So it's the same thing. You get the same answer no matter what. And that answer is 52 Newton's. Remember I told you that if you're slightly at an angle, you're gonna 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 zero. Okay, now, what about the direction? Well be 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 forces 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. That's it for this one. Guys, let's keep going.