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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 tongue 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 you'll 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 the 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 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 will 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 you get 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 this a thought well here's the solution we want this to snap back right what 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 to because we want this thing to remain stable these ends are fixed and the other end is you know 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 spring 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 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 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 we'll see 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 i if my current will 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 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 to the magnetic field equal to this is something that we have 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 sine of the angle between the two let's call it angle is 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 uh um you know this coil well that is equal to again something we did derived 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 a 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 5 is proportional to i times sine theta in other words this is not a linear device i is not proportional to y 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 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 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 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 the software encode and the concave pole pieces we end up getting a radial magnetic field and if you're interested in looking how how does the magnetic field look 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 are getting sucked in but for all purposes if you look at outside then the magnetic field is radial now okay second question is why why how 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 ex you know 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'll now agree it doesn't matter what the orientation of this pointer is it doesn't matter where it goes we'll 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 1 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 introduce 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