28. Magnetic Fields and Forces
Force on Moving Charges & Right Hand Rule
Force on Moving Charges & Right Hand Rule
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Hey guys. So in this video we're gonna talk about forces, magnetic forces on moving charges. And I'm gonna introduce the right hand rule, let's check it out. Alright, so if you have a charge that is moving through an existing magnetic fields and it's gonna look like this. You have a magnetic fields. Remember fields are usually represented with multiple lines, magnetic fields is B. And you have a charge. Let's say Q. That's moving. Let's say this way with the 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 equals Q. V. B. Sine of theta where Q is just a charge. V is the speed and it's a vector or I guess the velocity magnitude of velocity vector. Um 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 degrees. Okay, by the way. This is called Lorenz Force named after Mr Lawrence and you should know that the units for a magnetic field is Tesla named after Mr Tesla. Cool. And then one Tesla is one Newton divided by one 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 too cool. Um, charge. Let's write that down the charges. Two columns 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 kind of make it up as long as they're 90 degrees apart. So we can say that the velocity is going to go 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. Um so it's saying here that it's moving with a three with three m per second. So that's our V three m per second and it feels a force that's a magnetic force of four 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 equals Q. V. B. Sine of theta. Now we have everything but we're looking for B. So all we have to do is solve for B. So moving over here, B is F. B divided by Q. V. Sine of theta. Sine of theta is easy. The angle between Q. The angle between V. And B is 90 and the sign of 98 you should know is one. So this whole thing just becomes A one so we don't have to worry about it. The forces four, the charges to the speed is three, this is 4/6 or 2/3 or 30.67. We are talking about magnetic field strength. So this is .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, we talked about the magnitude but we haven't talked about the direction and direction and magnetism problems are always going to come from the right hand rule and there's going to be a few variations of the right hand rule, will tweak the rule to make it work for different problems. Right hand rule, abbreviated R H. R 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 right hand rule, which is massively important, a lot of people get confused here. So we gotta go slowly through this. I want to warn you that there's a bunch of different rules. In fact, most books and most professors who 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 some camera. Um 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. Um 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 settled on the one I'm gonna explain to you guys. It's got a bunch of advantages. Um 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 one and stick with it. But if what you're doing is different from your professor different for 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. You're 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 one and then go with it. So when we so the reason we needed the right hand rules because things are now going to be in three dimensions and if you have two dimensions you can be going up or down, that's one dimension. The second dimension is left or right, but now we're going to have a third dimension. So one dimension is going to be let's say the X axis and you could be going right or left, that looks ugly but whatever and then here you can be going up or down but now we're going to have sort of a Z axis here that is going to be going either away from you or towards you. Okay, now doing this on camera is weird and I want to explain this so that you don't get confused when I point away from myself, I'm pointing towards you. Okay, so I don't want you to look at me, I want you to imitate me. Okay, so point away from yourself and towards yourself. Those are the two directions. Hopefully there's no one around, this is gonna get weird right. Um so the direction away from you again do this with me right away from you is the same thing as into the page? Into the page. So get your, get your clutch hand out right, look at the page away from you is into the page or into the computer screen. Okay, let's go into the page or into the plane and towards you towards you. So go ahead and point at yourself right, like an idiot towards you. Just like I'm doing um we're all we're all being idiots um is going to be out of the page out of the page. So here's the page. Right? And if I pointed myself you can think of it coming out of the page towards me. So go ahead and do that again. This is probably super simple but I want to make sure that we go slowly here. There are symbols for these things just like how up looks like this and down looks like this and right looks like this and left looks like this totally obvious. Um the symbols for these things for into and out of are not as easy. So the symbol for away from you is an X. And the symbol for towards you is a dots. And the classic way of remembering this is if you are looking this is my drawing of an eye. If you are looking at, I can't drop but if you're looking at an arrow, okay, so if you're looking at an arrow and the arrow is going away from you, what you see is sort of the little X in the back of the arrow. So as you see an arrow going away from you, you see the X. Right here. Okay. Um if the arrow is going towards you, you don't see the X. Instead you see this front of the arrow here, which looks like a big dot. Okay because you see this here, so that's how you're supposed to remember. If you have a better way. Cool. Just remember that away from you is into the page and that is an X. Because it's the back of an arrow. Cool. Alright so those are the things you need to know now there are three things that have direction and I already talked about two of them here. The velocity has a direction, the magnetic field has a direction but the force also has a direction. Okay, so we're gonna do is we're gonna use the right hand rule to figure out these directions. Remember I mentioned the magnetic field is typically drawn with lots of arrows. Therefore we're gonna use our four fingers Um hopefully got all four. So we're gonna use four fingers um to to indicate the direction of the magnetic fields. Okay, so this is going to be the direction of B. By the way, you're supposed to keep them together right? Like don't do weird stuff like this. So four fingers like this. Um and that's going to be be speed is usually represented with a single arrow, so that's gonna be our single thumb, right? Hopefully don't have two of these guys. So single thumb which is gonna go this way and what's left is the palm of your hand which is going to be the direction of the force. So fingers will be be the thumb will be v. Again fingers or B. Because there's multiple lines. So there's multiple fingers thumb single line. And then what's left is the palm which is going to be the magnetic force. And one of the ways to remember this is that you may want to hit someone right? Hit someone with the palm of your hand or hit something right with the palm of your hand. So B. V. Right here and then the force right slap something. Um So the palm of your hand. Now this works with your right hand and I have two versions of the right hand here. One this is with the palm looking towards you. Okay so I want you to do this right I want you to look at your palm. I'm gonna go real slow here because I wanna make sure you nail this, you're looking at your palm notice that your thumb is to the right right again. And you have to sort of do this with me. Look at your palm and pull it out and then notice that your thumb is to the right just like in this picture. So the direction of the force will be towards you in this case. Okay because your palm is pointing towards you. So would this be an X. Or a dot And I hope you're thinking that this would be a dot. Okay and then here this is the back of your hand, this is the back of your hand. Which again here's the back of my hand. I'm looking at it. Follow me. Don't look at me imitate me. Right? So do the same and then you're gonna see the back of your hand which means that the palm of your hand is actually going out that way. It's going away from you and away from you is X. Okay so this is out of the plane of the page or plane and this is into the page awesome. That's the right hand rule. The last thing I want to say is that all of this crap works for positive charges. So if you have negative charges, everything still behaves the same exact way. Except instead of using the right hand, you're gonna use the left hand. Okay? But everything stays the same. People have other people have different ways of doing this. I like just switching hands positive and negative hand. Okay. Cool. Same rule, let's do an example. And what I want to do is I'm gonna do two of these and I want you to do two of these and let's make sure that we can nail this. Okay so the first one we want to just find the direction of the magnetic force which remember is the direction of your palm um on a moving charge in each of the following situations. Remember charges have to be moving for you to have a force force equals Q. V. B. Sine of theta. If you don't have a V. You don't have an F. Okay, so in all these cases are moving. So here we have a proton. And then here we have an electron. What's the significance of this? While proton is positive, Which means we're going to use the right hands. Okay? An electron is obviously negative, which means we're gonna do the same thing, but with the left hand. Okay, so a proton is moving left. So let's just draw, moving left means the direction of the velocity. So moving left this way and the B field is pointing up. I'm going to draw a few lines here. B field is pointing up. What is the direction of the force. So what you do, you now have to get your hand in the same with the same setup that is described here. And to make this a little bit easier. I'm going to switch screens here and I'm gonna do this over here on paper. Okay. Because you need to be able to do this on paper for your test. So you're gonna draw that you have a V. This way and you have an F. Be this way and you want to find, I'm sorry, just a magnetic field. B and you want to find the direction of the force. Which way is the force. Okay, so remember multiple arrows means multiple fingers be right. So that's the direction of the right there and V. Is to the left. So this is really easy when you do this, you now have to look at the direction of the palm of your hand, the palm of my hand is going into the page into the page and away from me so the direction of FB is into serve page which into the page is remember the arrows going away. So it's an X. So FB is going in the X. Direction. So if you if you want to see what you can do is you can put a little X. Here and say that that's the direction of F. B. Okay. And then this is our V right here. Cool. So this is a thing, this is part A. I'm going to do part B. And I want you to try C. And D. On your own. So let's do part B part you have an electron which means we're gonna use the left hand rule, which is just the right hand rule with your left hand. So left hand ready pull yours out the electron is moving down. So moving down means that here's the election, it's moving down. Okay. And in a beet field that points out of the page out of the page out of the page. So if you look at the page and then you point out of the page you're pointing towards yourself right again. I want you to do this, make sure you point out of the page that means that you're pointing towards yourself. Okay, out of the page. Out of the page and this means that the arrows coming at you which means the symbol is a dots. So the way you would represent this, you put lots of little dots everywhere, okay, lots of little dots everywhere. And you'll see that this is the direction of my magnetic fields because the field exists sort of everywhere, right in lots of places. So how do we do this? Well let's get our left hand and position the left hand according to this. So V is a single arrow. So it's gonna be my thumb. So this is my V right there and if I do this, I end up with something like this. Okay, But my B. Is supposed to be into the page right now. My B. Is pointing to the right, that's not right. So I have to make sure I'm sorry out of the page. So I have to do something so that my fingers are gonna point towards me while keeping this guy pointing down being really slow here because I want you to totally get this. Okay, if you do this, I hope you see what happens right? I want you to be imitating me at this point. Um The bees are coming towards my face because it's out of the page and the V. Is going down when you do this, your palm is now pointing to the right, okay. Your poem is pointing to the right. The only way to get good at this is to do it a bunch of times. So this means that the magnetic force will be to the right. Okay, that's it. So I want you to pause the video if you have to and do C. And D. I'm gonna keep rolling here. But I hope you pause the video. Even if you already know this stuff, just do it real fast. Make sure you got it. I'm gonna use the left hand rule here because this is an electron and the electron is moving down. The election is moving down feet and the B field points left. So this is my B. Lines left hand. I have to make my left hand point left and notice how this gets kind of weird. Now I gotta do this and you can't see me. But I'm sort of contorting here. And if you try to do something like this, you sort of struggle as well. Right? So something like this. But notice that now my fingers up here, that's a problem. My V. Is down. So what I gotta do is sort of do this weird contortion. And if you're doing this the way I'm doing your all kinds of weird now. Right? Um So this is my body. This is my V. But what you see happens is my poem is up. My poem is up. It's coming out of the page um therefore it's pointing towards me. So I can say that the magnetic force is out of the page which is given by a dot. So if you want you can draw right here that the F. B. Is out of the page. Hopefully you got that right, let's do one more. And then now I have a proton. So we're back at positive right hand rule, positive video. Try it yourself. Okay. Hopefully this is getting easy now protons moving into the page. So the velocity is into the page. If something's going into the page you see the back of the arrow right here. Into the page. Right? So this is the direction of the and the magnetic field is pointing right? So it looks like this B. B. And we want to know what is the direction of the force which is the direction of your home. So let's do this. V. Should be into the field. So I should point my thumb into the page. But then I need I need the magnetic fields to be to the right. So this is really hard for you to see and I'm trying to contort here. But if you do this, okay, there you go. If you do this, hopefully you're saying that the my palm is pointing down on my page. Okay, my poem is going this way my poem is going this way. So this is the magnetic force is going to be down. Okay, so again I have up, down right left. But you also have into and out of the page. Okay, so that's it for this one. Hopefully you got it. The visuals are a little bit tricky here. But you know, hopefully that was enough practice. Let's keep going.
Force on Charge Moving at an Angle
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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.