In this problem were asked to find out the magnetic forces that are acting on each side of a triangular shape that is made out of wire that carries a particular current. Now it's gonna look something like this where we have a triangle, a made out of wire. We have a constant current going through that train. Give a wire were also given an angle Phi here and the length of this side here. Now we're gonna label the corners A B and C So this four, therefore the side on the bottom here decide a B, and we can label it the length of Syed A B, and that is given as two meters. Now, we also know that there is a magnetic field directed directly to the right like this. And of course, that is gonna, uh, bring about the magnetic forces that are acting on the charges moving through this wire or because the current dislike the way. Now, if we're in order to figure out the forest on every particular side, we just have to follow our force equation. The magnitude of our force will be given by the current flowing through the particular part of our triangle. How long that side of the triangle is? The magnetic field magnitude in sine of the angle between the magnetic field in the current direction. So we just need to apply this equation for every side of this triangle and then just keep track of both the magnitudes of the forces on each side, on each wire each side of triangle, and think about the right hand rule to figure out the direction of that force. So let's first start with the bottom part of the triangle or what we call side A B. No, it was Think about how this force equation here works for this particular side of our triangle. So the magnitude of the magnetic force is going to be the current I going through that wire times the length of the wire length a B. We know that value. I believe it is two meters, and then we know the magnitude of the magnetic four magnetic field through which the wire is do the white that the wire suspended in. Sorry. And we need to figure out the angle that is between the current carrying direction in the magnetic field direction in the bottom part of this triangle. So just highlight. Decide right the bottom side of the triangle. We see that the current is heading to the left and that our magnetic field is heading directly to the right. So the angle between two completely opposite vectors so directors that in the opposite direction the angle between those two is 180 degrees and sign of 100 degrees is actually zero. And this makes sense because the current or the charge slow. The motion of the charges is directly anti parallel to the external magnetic field, and therefore there's gonna be no magnetic force acting on the bottom part of the wire. So that's one part. So it's only one part of our force. And, of course, since the Forces zero, that means really has no direction. Now let's think of the other side's Let's think about the other sides of this triangle. First, let's think about the vertical side, the vertical part war side A. C. And so that means we're gonna be thinking about this side right here for now. Just a highlight it. So it's right out our equation again, actually will quit before we read on equation. We notice right that we're gonna need the length, but we're only given the length 80 not the links a c So we need to use some trigonometry to figure that out. If you look at this triangle, we have the angle phi which is in the corner. Be so if we know this length a B as well. We can just use a tangent function to figure out the side the length a c So just doing a little strong trigonometry length a C divided by length A B gives us the ratio, the economic function of tangent. And we know the angle here is given as 55 degrees if you two years, 55 degrees. So we now know how to express the length of side A C in terms of length of Syed A B, which we know, and in terms of this angle phi. So when we go on right out the magnitude of the force that's acting on this vertical side, we get the current times the saut length of side a C times the magnetic field strength times sine of the angle between the current direction and the magnetic field direction now it was easy up top to the bottom side. The side of way just made it zero. We don't plug in any new numbers, but now we're gonna have to put those in. So our current value, the current flowing through the wire is 4.70 amps. The length of the side is gonna be the length of sight a B or two meters multiplied by tangent of 55 degrees multiplied by the magnitude of the magnetic field 1.8 Tesla's multiplied by sine of the angle between the current direction and the magnetic field direction. If we go up to our drawing, we'll see that the current is heading up in this part of the wire and the magnetic field direction is heading to the right. So the angle between those two is actually just 90 degrees. So we can plug a 90 degree in here and we remember 90 degrees turns into signing. Made agrees. It's one. So we just plug all this into our calculator and they end up getting that The magnitude of the force acting on the side. A sea of this triangle is 24.2 24.2. Munitz, The question is, is what is the direction of this force? So we have to use the right hand rule. So we put our pointer finger along the direction of the current like this, we twist our wrist to make sure our middle finger points in the direction, man, it field toe left. And when we do that, we see there a thumb is gonna be pointing. Well, you drive a bigger It's a circle with an accident. So it's into the screen. So the direction of this force is actually going to be into the screen. Okay, so what I'm gonna do is keep this diagram. I'm just going to real quickly a race, our work for the bottom part and replace that for our work for side A B, and then they can continue on with the problem. So we're gonna find the magnitude of the force on the slanted side or side A B. C. Now, again, we're gonna need it the length of side BC. So when I use a little bit of trigonometry, But since we know side, uh, a be let's use our coastline function because it's adjacent to our angle Phi and you want to find the value of our iPod news. So if we look at our trigonometry function, we confined the length of science a C by looking at this ratio here, sign right. So the length of side A C is going to be given by the length of side A be divided by co sign. So when we gonna go, will they go plug in our values for the force acting on this side, we take the current multiplied by length of side A C multiplied by the magnitude of making the field multiplied sine of the angle between the two. Now what's plug these things in that we know, right? So we know that the current is 4.7 amps. The length of side A C is the length of Syed A B or 2.2 meters divided by co sign of five. Then we're gonna have this, uh, multiplied by the value of the magnetic field or 1.8 Tesla's and multiplied by sine of the angle between the current the magnetic field. So if you look at that, that's gonna be this angle right here. This angle right here, which is actually the same as angle Phi. So we can actually just plug in the same angle phi into our sine function right here. So after we do a little bit of simplifying, make some room here. Since we already talked about this stuff do a little bit of simplifying and we see that the magnitude the force is gonna be given by 4.7 amps multiplied by the two meters. You see, we have a co son and the denominator and a sign in the numerator that becomes tangent of ah five, which is tangent of 55 degrees, again multiplied by 1.8 Kessel's. We see that mathematically, this ends up being the exact same statement as this. So the magnitude of the force on side B. C is the exact same and magnitude 2.4 mutants. But we have to figure out the direction. So if we put our point of using the right hand right, So if you put our pointer finger along the direction of the current, and then we put our middle finger along the direction of the magnetic field like so Oops, let me do that one direction. The magnetic field like this completely to the right. Then the direction of our thumb actually points outward. That's the only way that we can get those to be situated by rotating our wrist and our thumb points out. So the direction of the force on the side, the magnetic force on side B C, is actually out of the screen. The screen so we have no force on Side A. B affords the magnitude of 24.2 Newton's into the screen on site A. C and that force of magnitude 24.2 Newton's out of the screen, four side C B or B C. Whichever you want to say that. So the next part that was all for part A that was off a part of this problem. The next part actually deals with finding the Net force acting on this object, which we don't need the diagram for this anymore. So I'm gonna clear this out there. We're gonna talk about net forces, right? So remember, we have a force. The magnetic force Onside A B was actually being zero. The force onside A C was 24.2 newtons into the screen, and the force on Side B C was 24.2. Newton's out of the screen. So when we add all these together, add all these together to get the net force right, we add all these up. We have to think about the directions. While zero Force, of course, is gonna have no contribution, let's say let's call into the screen as negative. So we're gonna have a negative 24.2 Newton's being contributed from Side A C and then if into the screen is negative, will consider out of the screen is positive. And so we're gonna have a total of 24 positive. 24.2 Nunes being contributed from the side BC You'll notice that when we add all these together, we end up just getting a net force of zero, which is something that happens when we have a current carrying loop it suspended inside a uniform magnetic field. You'll see that we have a zero net force acting on this. That means this loop is not gonna translate in space anywhere. Move around. But you'll learn that there's gonna be a net Twerk on this thing. So generally current carrying loops in external magnetic magnetic fields like to twist around and spin because they have a non zero network. But they will generally not translator, move around in space linearly because they have no net force, and that is our answer. An explanation.