Torque on a Loop at an Angle

by Patrick Ford
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Hey, guys. So let's check out this example. So here I have a wire arranged in a loop on That's this blue line here. This is the loop current loop on. Do we want to know what must be the currents running through that loop? Given all this information. So I wanna look for the currents. Cool. So it says here that it is arranged as a rectangular, um, to arrange the rectangular 4 m wide and 2 m deep. I forgot to say that this is a loop, but these two pieces of information 4 m and 2 m will allow you to find the area so right away. I know that the area is eight square meters. It is placed in the plane. Shown were a constant five t magnetic field exists. B equals five. It says the wire loop is parallel to the plane. Parallel means side by side. So imagine the X axis right here. And I'm gonna do this just to sort of try to support that image. Imagine the X axis your parallel. So you're sitting on the plane. If it's a horizontal plane, which it is here, it looks like it is, um then you're essentially on the floor. So the cable is on the floor. Imagine that This is the floor of the X Y plane, and this is sort of the height here, So it's parallel to the plane and the magnetic field is directed 30 degrees above the plane. So if this is your plane, then the magnetic field are lines that go like this. So instead of it going like this, they're going like that. Okay, so it's a little weird to draw this here, but basically you're gonna have lines, magnetic field lines that look like this and they make an angle of 30 degrees. This is like the positive X axis. It says you have to make an angle of 30 degrees above the plane. Okay, above the plane theme. The loop experiences a network of 10 and we want to know what is the current. So how do we do this? There's two equations for torque. You can use n ba I sign of data, or you can use theme magnetic moments. Be a sign of theta. Okay, um, here we don't have the magnetic moment, we can calculate it, but there's no point in doing that it's easier to just plug everything here. I'm looking for. I I equals torque. Divided by N b. A sign of data. I have torque, which is 10 and it is the number of loops. It didn't specify how many loops we have, so we're gonna assume that is one. That's what we're supposed to do. B is five. Area is eight, and as usual, the tricky part is finding the angle. So which angle should we use? Well, remember, the definition is that it's the angle between A and B. Now, whatever we talk about, um, the direction oven area, it's always the normal of that area, meaning if you have an area, it's the direction that is perpendicular to that area, the direction that makes a new angle of 90 degrees with its Okay, So it's this Okay, this area. So if this is the area here in the area enclosed by the wires that is sitting on an X on the on the floor, the perpendicular to that will be going up like this. Okay, going up like this. In other words, the A vector points in this direction. Here, this is the normal of the surface. Okay, normal. The surface Diego I want is between the normal of the surface and be and this is be right here. Okay, so they sort of cross over here. So what I want is I want this angle here. This definition, By the way, you might have noticed that I almost always give you the wrong angle, because I want you to be, uh I want you to be very careful. I want to be, um, paranoid about this stuff. But just know that it's not the case that it's all that you're always going to get the wrong angle, right? You could very well just get looking at the right angle. Or maybe some sort of like, you know, backwards. Tricky question that you actually get the right angle. And maybe you changed it. So the angle here is 16. Because that's the one that I want. Onda. We're gonna put it here 60. So if you do all of this and I have it here, the answer will be 0.29 or just 0.30. Our 0.3 amps, co. Uh, that's it for this one. Do we want to know the direction of the current? Um, we're not. We're not told the direction of the torque we can find out. Never mind. So that's it for this one. Let's keep going.