 Pass current through a galvanometer and the stick turns. If you increase the amount of current passing through the galvanometer, the stick turns even more, showing more current, indicating more current. But how does passing current through something make a stick turn? Well, that's exactly what we want to find out in this video. The principle behind this moving coil galvanometer is if you take a coil and pass current through it, then it will start producing a magnetic field. And this field resembles that of a bar magnet. And so we can pretty much assume that this current carrying coil behaves like a bar magnet. Now, keep this between the two poles of an actual magnet. You can imagine this is a part of a horseshoe, large horseshoe magnet. Then what will happen? Well, if you imagine this current carrying coil to be a bar magnet, it's not really okay, but you're imagining it this way. Then you can see that the north gets attracted by the south pole towards the right. The south gets attracted by the north pole towards the left. And therefore the coil tends to turn. And there you have it. Current is making the coil turn. Now, all you have to do is attach a stick to it as an indicator, put some markers, and we see as you pass current through it, that torque is going to make this thing turn, turn, turn, turn. And this is where there's a problem. This turning will not stop. You see, as long as there's a current over here, the torque exists, and the torque will keep on making it turn. And so this is a problem for us. You see, what we would want is that turning to stop at some point. We would ideally want that for small currents, it'll only turn by a small angle. And for large currents, they should turn by a large angle. That's what a galvanometer does, right? But that's a problem over here. That's not happening. For any current you put, this thing will keep on turning until it gets stuck somewhere. So that's problem number one for us. And if we get rid of that current, if we stop the current, it'll stop behaving like the magnet, so torque disappears. And nothing happens. Now it just stays there. It doesn't come back. So this is a terrible galvanometer. This is problem number two. It doesn't spring back. So the question now is, what do we do? How do we improve this? So can you think of how do we solve this? There are two problems. Problem number one is, let me bring this back. First problem is, we would want the pointer, the coil to stop turning at a particular point, depending upon how much current we have. For more current, we would want it to turn more before stopping. That's problem one. And the second problem is, when you get rid of the current, we would want that thing to snap back. How do we ensure that? Can you pause and think a little bit about this? All right. Have you given us a thought? Well, here's the solution. We want this to snap back, right? What object comes to your mind when it comes to that? Springs. When you stretch a spring, it tends to snap back. But the springs like these are useful for linear motion. Here, we would want it to snap back, turning motion. So we would want not normal springs, but we would want to use coil springs. So these are the two coil springs that we are attaching, two because we want this thing to remain stable. These ends are fixed. And the other end is attached to the coil. Now, again, if we run a current, we now know this acts like a magnet. And as a result, there is a torque acting on it. And this thing tends to turn this way. But now as this turns, these springs, they get coiled. Look at the springs carefully. And as a result, the springs tend to uncoil themselves. In other words, they put a torque in the opposite direction. We can call this the counter torque. And at one particular point, the torque due to the magnetic field and the counter torque balances out and the pointer stays stationary. So we've solved our first problem. Now think about what would happen if we were to increase the strength of this current. Now the coil will act like a stronger bar magnet. And as a result, the forces between these pole pieces of magnet increases. In other words, the torque, the turning force, the torque increases. And so the coil now turns more. Again, eventually until the counter torque equals the torque of the magnetic field. So for more currents, we get more deflection. Exactly what we wanted. And of course, if we get rid of the current, the torque due to the magnetic field disappears. The counter torque brings the coil back. And the coil comes back to zero. So yay, we have our galvanometer. We just now have to put this together in a box and construct it. And we can start selling it, right? Well, not quite. There's one last challenge that we need to solve for. We need to make sure that this is a linear device. What do I mean by that? See, now we know for more currents, we get more deflection. But we need to make sure that the amount of deflection is proportional to the current. That means if we were to double the current, we need to make sure that the deflection doubles. Only then we will have a linear galvanometer. Only then this measuring system will work. So to put it in other words, if you pass current through it and say the coil comes to equilibrium in this position, let's say by making an angle theta. Let's imagine that it turned by an angle. Let's not use theta. I will need theta for something else. By turning an angle phi, mathematically, we need to make sure that the angle phi is proportional to current. Does that make sense? Otherwise, we don't have a good galvanometer. So that if my current were to double now, it should show 10. That means the deflection should become twice. This angle should become twice. So how do we ensure this is the question? And so how do we ensure this? Well, we can do that mathematically. We can start by building equations. But again, how do I start? Where do I start? Well, I know we're talking about turnings. And turnings is about torques. We already have torques over here. And we know that at equilibrium, the torque due to the magnetic field exactly equals the counter torque in magnitude. So we can start over there. So we can say at equilibrium, the counter torque, I'll just call that as the TC, that's the counter torque, must be exactly equal to the torque due to the magnetic field. The torque due to the magnetic field. I'll use B for magnetic field. All right. So what does the counter torque depend on? Well, the counter torque depends upon how much the spring twists. More the twisting, more is the torque. And in these springs, they are proportional to it. So we can say the torque is proportional to the angle of twist, which is phi. All right. Or we can also write it is equal to some constant C, which that constant will completely depend upon the spring, some constant C times phi. So this is our counter torque. And that at equilibrium should equal to in magnitude. They're in opposite direction, of course, should equal to the torque due to the magnetic field. Now comes the question. What is the torque due to the magnetic field equal to? This is something that we've talked about in previous videos. So I'm not trying to derive this over here. So I would like to pause the video and see if you can remember this. What is the torque due to the magnetic field depend on? All right. If you recall, the torque is equal to the magnetic moment of this coil, M. The magnetic moment tells you how strong a magnet behaves like times the magnetic field B times the sign of the angle between the two. Let's call that angle as theta. So the angle between the magnetic field strength. So here is our magnetic field strength B. And the angle theta is the angle between that magnet. Let me bring back that magnet. If we assumed, yeah, if you assume the coil to be a magnet, then whatever is the angle between the magnet or the pointer and the magnetic field. So this is the angle theta. And hopefully that makes sense because as the angle becomes smaller and smaller, the torque becomes smaller and smaller. Think about it. When the angle becomes zero, your bar magnet will be completely horizontal and there'll be no more torque acting on it. All right. So what is that equal to? Well, what is M equal to the magnetic moment of this particular, you know, this coil? Well, that is equal to again something we did right before. So I'm not going to try and derive this over here. It's going to be equal to the number of magnetic number of turns of the coil times the strength of the current. How much current is passing through the coil times the area. So this is our magnetic moment times the magnetic field times sine theta. And now let's see is our phi. So here's our C times phi is our phi proportional to current. So we just have to think about whether the rest of the stuff are constants. Well, this is a constant. N is a constant. I for a given current, I is a constant. It does not change. B is a constant. But theta is not a constant as the thing turns as the thing turns theta keeps changing. So what we are getting is that for a given current five is proportional to I times sine theta. In other words, this is not a linear device. I is not proportional to I but times sine theta. So we have a problem. We need to fix this. And again, just to be clear that we are on the same page because this can be confusing. What exactly is the problem? In our case, more current gives us more deflection. But we want to make sure if we double the current, the deflection should double linear proportionality. And right now we are not getting that. So in our case, doubling the current is not doubling the deflection. That's a problem. So to fix this mathematically, at least, we have to make this a constant, which means theta needs to be a constant. But how can you do that? As the thing turns, theta definitely changes. So how do we solve for it? How do we make sure that this stays a constant? The secret is we produce not a linear uniform magnetic field but a radial field. So here's what I mean. The first change we'll do is we'll change the surface of the poles to make it concave. Next, instead of just coiling the wire around itself, we're going to wind it on a cylinder made of soft iron. And just so that we can visualize, this is what it looks like from the side. These are the pole pieces of the magnet. This is the cylinder made of soft iron. I'll clarify that in a second. And this is how we are winding the coil around that. And these are the springs and the indicator just as before. All right. So how does this help? Well, it helps in forming a radial magnetic field, meaning all the magnetic field lines point towards the center or appear to be coming from a center. Of course, again, more questions. First of all, why does it happen? You see, the magnetic poles, now that since they are concave, the magnetic field at least start out radially, right? Perpendicular to the surface, they start out radially. And this soft iron core, think of it as a material that gets magnetized very easily. So the moment there is a current running in this coil, it gets magnetized super easily and it starts sucking the magnetic field. And that's why the magnetic field sort of gets sucked into it. Think of it that way. And that's why because of this soft iron core and the concave pole pieces, we end up getting a radial magnetic field. And if you're interested in looking, how does the magnetic field lines look like inside? Inside they look like this. Of course, the magnetic field lines are not in reality radial because they will not, otherwise they'll end up intersecting with each other. That cannot happen. So yes, the magnetic field lines will sort of curve like this. You can kind of see they're getting sucked in. But for all purposes, if you look at outside, then the magnetic field is radial. Now, okay. Second question is why does this solve the problem over here? Well, think about the magnetic field right now, passing through the coil, the wires of the coil. Remember, the coil is wound on the outside of that cylindrical core. And so I don't care about the magnetic field inside because there are no wires inside. So I only have to care about the field that is touching the wire, which is over here and over here. None of these field lines are touching the wire right now. And therefore currently the field that is exerting a torque on this would be this. And if you look at the angle between the magnetic field that is exerting the torque and this needle, that angle is now 90 degrees. So theta at this position is 90 degrees. But what happens when this thing turns? Let's say it starts turning now. It turns, turns, turns. And let's say it comes in this position. What happens now? Well, now notice this is no longer the magnetic field that is going through the coil. And so that field is no longer producing a torque. The torque is produced by now this field. This is the field that is in line with the coil. And again, notice what's the angle between the pointer and the magnetic field line 90 degrees. And so hopefully you will now agree. It doesn't matter what the orientation of this pointer is. It doesn't matter where it goes. We will always find that the magnetic field that is producing the torque will always be perpendicular to this pointer. And therefore theta will always be 90 degrees. And so sine 90 will be one. But more importantly, this thing will become a constant. And so the radial field, when the field is radial, radial field ensures theta is always 90 degrees. And therefore this thing becomes a constant. And we get what we want. We get phi proportional to i. That means the deflection is proportional to current. We have built ourselves a linear galvanometer. All right. So let's quickly summarize what we learned. Long story short, the whole idea is when you pass current through a coil, it behaves like a magnet. And when you keep it in an external magnetic field, it experiences a torque that twists this coil. Putting coil springs produces counter torque. And when the counter torque equals the torque to the magnetic field, the needle comes to equilibrium. This ensures that for more current, we get more deflection, precisely what we wanted. But then we saw that this is not a linear device because the torque produced depended on the angle between the needle and the magnetic field, which kept changing. So to keep the angle constant, we introduced concave pole pieces and a cylindrical core of soft iron. This ensured that the field was radial, making sure that the angle between the field and the pointer always remained 90 degrees. This now is a linear galvanometer. The deflection is proportional to the current.