Magnetic Field Produced by Moving Charges

by Patrick Ford
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Hey, guys. So in this video, we're gonna talk about moving charges, producing a magnetic field. Let's check it out. All right. So remember that a charge. If a charge moves through an existing magnetic field, it's going to feel a magnetic force. And we've seen this before. You have magnetic fields. Be right here and you have a charge, Q that moves through it with a speed V. This charge will feel a force. This is called a Lawrence Force, and you may even remember the equation is Q V b sign of Fada. Super important equation. Gotta know it. What I also need you to know and remember is that the not only will the charge I'm not only will move in charge, feel a force if it goes through an existing magnetic fields, but a moving charge is also going to create its own magnetic fields away from itself. Okay, so moving charge is also going to produce produce a new magnetic fields. Okay, you need to know that these two things happen and you need to know that they happen a same time. It's not one or the other. Um, it's both now I need you to know that. But I also I also need toe have a disclaimer here. Big disclaimer that this topic is much less popular than, for example, being asked to find the force that I'm moving charge feels okay. In fact, most professors in most textbooks skip this all together. And the reason why I'm including this video across all of the textbooks recover even though a lot of the textbooks don't don't have this topic is because it's a really big point. And I think it's very helpful for you to remember that's a moving charge, can feel of force and produce a magnetic field that you have to know the matter what. What you may not need to know is what follows, which is how to actually use this equation to solve a problem for this specific kind of questions. Okay, so here's the equation I'll give you, and what you need to do is you need to get this equation. Go talk to your professor. If you're not sure if you need to know this and ask him Hey, do I need to know this? And if they say no, then problem solved or if they look really confused or they don't know where you got this equation from or what are you talking about then Now you know that you don't have to know this. Okay, so the equation, it's an ugly one, but it's pretty straightforward. It's relatively straightforward to plug stuff in B equals. Uh um, you not mu knots is a constant right here. Times q v Sign of theta divided by four pi r square meter lots of Constance He was the charge visas Speed, Sign of theta. I'll talk about fate over here. Four pi r Square R is the distance. Okay, now these two points here talk about how to properly use at this point here talks about how to properly, how to figure out data to properly use this equation. And this point talks about how to find the direction of the magnetic field. I'm gonna just jump straight into this example because rather than talk about this, it's much better to just show you how they work in action. Okay, so I have a three column chart, so let's draw a little Q equals three columns, and it's moving to the right with the speed V equals 4 m per second and we wanna know the magnitude in the direction of the magnetic fields. So what is be and what is its direction? That a charge produces two centimeters directly above itself. So here's a charge. I wanna know what is the magnetic fields. If this is point p at a distance, two centimeters, distances are so r equals 20.2 m. I wanna know what is the magnetic field at this point p produced by this charge here and obviously the equation. We're gonna uses this be equation right here. And I'm gonna write that b equals mu knots, which, by the way, if you want, you can already we can already replace with this. So let's go ahead and do that. You're not gonna be four pi times 10 to the negative seven. You always want to write the left version, not the right version, because the left version you're going to cancel out with the floor pie in the bottom of that equation right away. Quote and then I have q v sign of data. Q is three the is four and sign of data will talk about data in just a second. Um, divided by four Pi already can so that times are square. So 0.2 you can also write. This is two times 10 to the negative to square. I think this makes it a little easier to manipulate the numbers. So the only question here that's kind of tricky is what is your theta? Okay, what is your feta? And it says here theta is the angle between the V vector and the our vector and the our vector is a vector between the charge and the location of the produced fields. You can think of the location to produce field as the targets Target's location. So what the heck does that mean? So it are is a vector between the charge. Their charges right here. Vector just means an arrow and the location of the produce fields. I want to know what is the magnetic fields here? That is my target location. I want to know what is the magnetic field there. So I'm gonna draw a line from the charge it says right here from the charge to the target location. So I'm gonna draw this line here. This is my our vector. And this are vector is Onley useful s so that I can figure out what is the angle between the blue arrow and the Red Arrow. And this angle is, of course, 90 degrees. So this is gonna be sign of 90. A whole lot of work for nothing, because sign of 90 is just one. But obviously you have to figure that out. Um, and now we can simplify some stuff here, so I'm gonna leave three and four by themselves. Times 10 to negative seven. And then this, too is gonna be squared, which becomes a four. And then the 10 to the negative to square 10 to the negative for the force. Cancel and I end up with three times 10 to the You've got to combine the exponents. It's negative. Seven minus negative. Four. So that's negative. Seven plus four, which is negative. Three. Tesla Because we're talking about magnetic field. Okay, so that's the field strength, the field magnitude. What about the direction now to solve for direction? It says right here we wants to use the right hand rule. And by the way, we would have used the left hand rule if Q was negative. So if Q is negative, which in this case, it isn't. And what we wanna do is we want to grab the line of motion. We wanna grab the line of motion. So the best thing for me to do here is to just show you how this works. So let's move over here and we're gonna do that. So I wanna grab the line of motion. So Q is moving this way to the rights and the line of motion is just, ah line formed by the direction of the So what we can do is you can think of the line of motion as sort of like this, right? And what this does the slide of motion does It separates the page into a top part and a bottom part. Okay, by the way, if the if the V was moving up, what it would do is it would separate this line. Um, it would separate the page into left and right. So that's the line of motion. Okay, so we've got a line of motion there and what we wanna do, we wanna grab it, and we want to grab the line of motion in such a way since we're talking about the right hand rule right in such a way that my thumb points to the right. Why? Because if you remember, on the right hand rule your thumb is your velocity Direction is the direction of velocity. So I'm gonna grab this this way and imagine that I can lift this here so that I can grab it. And the only way there's two ways I could grab this, I could grab it like this, right? I'm gonna wrap my fingers around the this line of motion. I can grab it like this, or I could grab it like this and we're going to choose to grab it like this because we want a point. We want our thumb, which is our velocity to point to the right so that it's consistent with the problem. When I do this, the way to grab it is to go under. This is super important is to go under the marker over here and then come back up here. So in the bottom half of this page, I'm going into the plane to grab under the market. And then in the top half, I'm coming out of the page and towards myself towards my face and I have to do that. It's the only way that I could grab in the direction I'm supposed to grab. So what that means is that everything here is going to be into the page, and everything here is going to be out of the page popping towards my face so you can put a bunch of little gods and access everywhere. Anything here right now, we point PTO is somewhere over here, which means which means that the magnetic fields at Point P is going to be out off the page que out of the page. And that is the answer for direction. What if i What if this was point P one and I wanted to know the magnetic fields for a point p two and maybe it was over here? Doesn't even matter, right? Theme magnetic field for a point, P two here would be into the page into the page because it's on the bottom. Because when I grab this thing, my hand goes in and then back out, okay? Three only difference from this is the last point. The only difference between, uh, into the page, which is the X right, Um, s o the only difference between, for example, this point. And this point is the magnitude, because they're different distances in different angles. But all of these points here are have a direction that is into the page. Cope hopeful. This makes sense. This is actually gonna come back later again. When we talk about wires, when we talk about current flowing through wires, we're gonna grab the wire just like how I grabbed this line of motion. Alright, that's it for this one. Let's keep going.