28. Magnetic Fields and Forces

Magnetic Force on Current-Carrying Wire

# Find Force on Current-Carrying Wire at an Angle

Patrick Ford

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Hey, guys. So in this example, we have a wire that sits on a magnetic field and it has a current, and we want to know what is the force on that wire in three different scenarios. So let's see. The wire has a length of 2 m. L equals to the magnetic field. Strength is three. B equals three, and it's directed in the negative y axis the magnetic field. And we wanna know what is the magnitude of the magnetic force, which, in this case, because it's in a wire, it's going to be given by Bill. Sign of data be I'll sign of data, by the way, were also given that the current is for okay, little Why a big guy doesn't matter. Current is four amps. That's a really ugly 44 amps. Cool. So let's get to it. So the magnetic fields I like to draw multiple lines, so let's just do too, is going down right right there. And the The wire is also or the current rather is flowing the negative y axis, which means that the wire goes down this way and then the current is going down in this direction. Here So the equation is F B B. I sign of data, and then these questions. The tricky part is the angle, because I'm given B i n l. So it's just plug and chug. Now the angle is going to be the angle between be and I they're both going down, so they're parallel to each other. So the angle is zero, and the sign of zero is zero the sign of which means there is no force here because they're going parallel to each other. Remember, encouraged to use the right hand rule always, Um, and this is a reminder you can think of. This is a reminder that you're supposed to have a 90 degree angle between your B and your eye, right, 90 degree angle between your being your eye. And here they're like that, and that's not it's supposed to be. In this situation, you have maximum force. If you have an angle like this, you have less than maximum force. But you still got some force. And as you keep going this way, the force and it goes from Max max, 90 degrees to smaller, smaller, smaller, and you get here and you get zero. Okay, So if the angle is zero because they're parallel or if the angles 1 80 which is anti parallel, opposite directions, there will be no force. So no force on this one here. What about here? So be again is down. And the current is in the positive X axis, which means the wire, this horizontal and the current is going in this direction. Theatrical between these two guys is 90 degrees. So FB is Bill sign of 90. Sign of nineties. Just one. So, really, we only have built so three eyes. Four l is too. So this is 24. Newton's very easy. What about the What about the direction of the force? What is the direction of the force? Well, right can rule because it's a wire B is going down. I is going to the right. So you gotta do this, right? You gotta do this. Okay. Away from me. Bees down. So my poem, even though it's pointing at your face, you gotta lose yourself, right? It's not my poem. It's your poem. Your poem is pointing away from you, which means it's going towards your page. So it's into the plane okay or into the page into the page. Make sure your master, your right hand rule into the pages direction. And the magnitude is 24. Okay, so this one's a little more complicated because it's got an angle on Dhere. We have the be this way. Um and we have a wire in the direction that makes 53 with the Y axis. So here is the positive y axis is up here. This makes 53. Now, this is a little tricky because it's ambiguous. It's not totally clear whether it's 53 with the y axis this way or 53 with the Y axis this way. But what you will see is that it actually doesn't matter when it comes to calculating this. Okay, so we're gonna think of this as two possibilities that the current could be going this way or it could be going that way. And then we're gonna calculate that. So the equation is f B equals bill sign of data, and the angle is the angle between the direction of the current and direction of be so B is pointing down. So if you want, what you can do is you can draw. Be over here. Okay. And what is the difference between these guys? So if you go counterclockwise here, this is 90. And then this here is a 37. So 37 plus 90 is 37 plus nineties, 1 27 degrees, 1 27 degrees. Or you can go another. Or you can go in this direction here, which would be negative. Negative 1 27 degrees. Or it could go all the way positive. And you can say that it's 90 plus another 90 plus which is 1 80 plus 53 1 80 plus 53 which is 2 30 three 2. 33. That I got that rights. Yeah. 2. 33 away from this. Um, and the sign off all these numbers will be the same. They may have different signs what might be a positive or negative? But here we're just looking for the magnitude of this thing. So you can pick your choosing. I'm gonna write that B equals B equals 34 eyes for Ellis to sign of 1 27 positive again. Whatever we get here, just think of this is an absolute value because we're just looking for the magnitude of this force on. But if you do this, you get that. The answer is, uh, uh, four is that a 14 can't read my own handwriting. Um, no. 19 point to the answer is 19. Newton's. Okay, so that's the force. And it would work whether you're going this way or this way. What about the direction? Right hand rule bees down. So let's do this. And I want this guy to be going in this direction, okay? I want this guy to be going this direction. So in case of in this case here where I won, right, if you weren't going that way, you'll be going down and you would have the I like this right? Which means my palm is full pointing towards me, which means it's away from the page. So, for in the case of I one, if it was going in that direction on, by the way, a question a question on your test would tell you exactly which one, right? I just wanted to talk about both cases here. Um, so in this case, you would be What do we say we was? We said it was out of the plane out of the page. What about for I to what if you were actually talking about this direction? Well, if you try to do beat down in this I hear you can't put this thumb all the way over here, right? Like not without breaking it. And don't do that, because now you're just you're just messing yourself up in and you're breaking the right hand roll anyway, right? Eso what can we do? Well, you have to do this right. You have to do this. Where now your fingers air still down following B and this guy is up like that. So this looks all kinds of weird, but my palm is away from me, which means it's going into into the page. So in this case, the direction of those two wires, um, actually made a difference in terms of different in terms of direction. Okay, doesn't make a difference in terms off of the force, but it does in terms of the not the magnitude, but it does make a difference for the direction. Cool. It's like this one. Let's get going

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