Hysteresis & magnetic retention

a current carrying solenoid generates a magnetic field now let me call that magnetic field b naught and let's address that as the vacuum field because there's nothing kept inside the solenoid it's vacuum inside the turns but what if i keep say a piece of ferromagnet say a piece of iron then we've seen before the magnetic field inside the iron is going to be way stronger than the field outside because iron is a ferromagnet it gets magnetized and we wrote a relationship between the two we saw that the magnetic field inside any material can be written to be equal to mu r called the relative permeability times the magnetic field outside now what i want to show you in this video is that although the relationship works for paramagnets and diamagnets it does not work for ferromagnets for ferromagnets the relationship is actually quite more complicated to truly understand this relationship we need to study something called the hysteresis graph and that's the goal of this video hysteresis graph so history says graph is basically the graph between these two things what we want to study it's a graph between the vacuum field and the magnetic field inside the ferromagnet and it's called hysteresis because the name it basically says something is lagging behind something we will see once we understand the graph that this magnetic field inside the ferromagnet actually lags behind the vacuum field that's where the name comes from all right so let's do that let's try to study that and for that we're going to draw a graph so here's our x-axis on the x-axis we're going to draw b naught and we know how to change b naught just by changing the current through the solenoid increase it decrease it you can even flip the battery and you can reverse the current so you can do all of that and then we will see how does that change the magnetic field inside the ferromagnet and we'll call that b and just to keep our attention on the ferromagnet imagine our in our sonar is invisible it's just there but let's imagine we've made it invisible okay so how can we understand what's going to happen inside the ferromagnet how do we understand that for that we need to recall the domain theory remember we said that ferromagnets have magnetic domains which are groups of atoms that are all completely aligned in one direction so what we'll do is we'll keep track of what happens to these magnetic domains as we change the vacuum field and that's going to help us understand what happens to the magnetic field inside the ferromagnet and just to you know keep things simple instead of drawing all these gajillion atoms i'm just going to draw one arrow mark representing the direction in which the atoms inside the domains are all oriented all right so let's get started so how do we start well let's imagine right now there is no current running through our invisible solenoid so we are at zero and let's imagine we are going to slowly increase increase increase increase that back current so the magnetic the vacuum field starts increasing what's going to happen inside well we have seen before that when you expose a ferromagnet to the magnetic field the domains tend to get domains tend to turn and get aligned in the direction of the field and so as we make the magnetic field stronger and stronger more and more domains get lined up so in essence the magnetic domain is becoming bigger and bigger these three have now become one giant domain okay and as a result the magnetic field inside the ferromagnet starts increasing it becomes orders of magnitude larger than the field outside because there are billions of atoms all of their magnetic domains align in magnetic dipole aligned in the same direction so as we make the magnetic field stronger and stronger more and more domains get aligned eventually eventually all the domains are aligned in the same direction all of the magnetic domains there are millions of domains billions of them actually and i've only drawn six for simplicity but eventually we reached this point now what happens if i make the my magnetic field even stronger the vacuum field i increase the current more in my solenoid i increase it even more what's going to happen well now since all the domains are already lined up you can't have a stronger field inside this means there is a saturation point so let's say this is that point this means eventually we hit a saturation basically it means maximum and so now based on this i want you to pause the video and think about can you draw a graph for this of what happens as you go from zero the vacuum field and keep increasing we know eventually you're going to hit a saturn so can you guess what that graph is going to look like all right so let's see because i know it's going to hit a saturation after this point it's going to be straight i can make a guess that the magnetic field the magnetic field inside should keep increasing but not linear eventually it's going to saturate and this means increasing the vacuum field further will not increase the magnetic field inside saturated it's reached the maximum and at this point you might say okay the relationship is not not that bad it's not a straight line but it's a curve and that's not a big deal we read this far in physics curves don't you know we're not afraid of curves right wait for it what if now we decrease the magnetic field say the current in the solenoid we reduce it and we take it all the way to zero what do you think is going to happen to the magnetic field inside what do you think is going to happen to all these domains i want you to pause the video think about that and think about what the graph is going to look like as i take it back do you think it's going to follow back okay if it has to follow back reverse that means all the domains have to go back and become random and that's not what's going to happen because ferromagnets have this property of retention which basically means that the domains once they're all aligned they tend to stay aligned so even when i reduce my magnetic field most of the domains don't flip back maybe some of them do so i'm going over here let's say one of these domains they flip back so some of them say flip and become random but a lot of domains still stay aligned that means the magnetic field inside is still very strong very strong in towards the right so the field will not go all the way to zero it might come somewhere over here as the vacuum field goes to zero and so now we can predict what the graph is going to look like so our graph from here as i come back will not follow this it'll not go reverse but it'll go somewhere over here and this point shows the property of error magnets even when the magnetic field outside the vacuum field is zero i can take this outside the solenoid now we have permanent magnetism okay so you can immediately see things are starting to get a little bit interesting but wait for it what if now i start increasing the magnetic field in the leftward direction i'm going to call that as the as the negative b naught and we can easily do that by flipping the battery what do you think is going to happen so i'm going to increase it in the leftward direction again pause and ponder upon this all right so as i increase the magnetic field in the left direction now it's going to force the domains to flip in the leftward direction so some of the domains oops sorry so let's say this domain gets flipped to the left maybe this gets flipped to the left and as a result as more and more domains get flipped to the left notice they start cancelling the domains which are flipped to the right and as a result the net magnetic field starts decreasing inside so as i go towards the left the magnetic field starts decreasing so it sort of like goes here and then comes a very interesting point somewhere when half the domains are to the right and half the domains are to the left that's when all the domains cancel out pretty much and the magnetic field inside is pretty much zero so that means as i make it more and more negative eventually there comes a point where the magnetic field goes to zero this is turning out to be really interesting so now the graph continues and eventually goes to zero so this is that point where pretty much half of the domains are to the left and half of them are right and the magnetic field inside has gone to zero but we won't stop there we won't stop there we're gonna increase our magnetic field even further what if i make that field even stronger to the left well then the story continues more and more domains oops more and more domains are going to start getting flipped to the left and eventually it will saturate in the leftward direction so what will the graph look like well the graph will continue now the magnetic field inside will become negative and so the graph will go like this and just like what we saw on the other side it's going to hit saturation so now we are saturated pretty much the same value as we had earlier but now in the leftward direction so this will be again b saturation and now increasing the magnetic field even further is going to be useless because we know it's going to be straight so we're going to decrease that magnetic field and make it zero and again what do you think is going to happen again would be a great idea for you to pause and see if you can now complete this graph well just like before we will find that not all of them will turn back in fact most of the domains will stay aligned in the leftward direction it's kind of like they have inertia right they stay in tend to stay aligned some of them will flip back maybe this is that notorious domain that you know tends to flip back once the magnetic field is gone so maybe it flips back and so the graph is gonna look pretty similar to what we got over here it's gonna come back but not all the way to zero a lot of magnetization is there over here again retention that's what we see over here and then what we can do well we can again flip the direction of the current in our solenoid and make the magnetic field stronger and stronger to the right and something very similar is going to happen we will now find that more and more domains more and more domains are gonna start flipping to the right there come a point where half the domains are to the right half the domains are to the left and that's where we are over here we can now speed up our explanation because very similar to what we saw earlier this is the point half the domain are to the left and halfway to the right and eventually if i make my magnetic field even stronger the vacuum field even stronger finally i will find that all the domains all the domains have turned to the right and we now go back to that saturation so eventually we will find this thing goes all the way back and this means that the initial graph which we got when we had a fresh ferromagnet where its domains are all randomly aligned that is no longer we no longer get that that's gone that innocent looking ferromagnet you can see once you magnetize it it's going to go along this path you will never get back that path and so this graph is called the hysteresis graph and every ferromagnet will have its own graph and depending upon that graph they can be used for different applications which we'll talk about in a separate video but let's summarize a few things from this graph first of all can you see what why can you see why the magnetic field inside is lagging behind the vacuum field you can see when we reduce the vacuum vacuum field to zero the magnetic field inside did not go to zero because of the retention property it's only when i made it negative then the back then the field inside became zero then i make the vacuum field even more negative then the field inside becomes negative so you can kind of see that the field is yield inside is lagging behind the vacuum field the second thing you can see immediately is not that this this relationship doesn't work and i can show you in a very simple way you take a specific point on this graph let's say this point and i ask you for this amount of vacuum field what is the magnetic field inside the ferromagnet so here's what i'm saying i'm going to give you what is the current running inside the solar solenoid from that you know what the vacuum field is and i ask you what the magnetic field inside this ferromagnet is going to be and you have two answers you can either have this much positive value or you can have this negative value both of them are possible i'm neglecting this one because this you only get initially you don't get it later and so this means that the magnetic field inside the ferromagnet not only depends upon the vacuum field it also depends upon the history how it went through cycles of magnetization so just if just by knowing the field outside the vacuum field you can't tell what the magnetic field is inside and that's the whole idea behind the hysteresis that's the whole idea behind this complication and finally increasing or decreasing the magnetic field requires energy and you know that energy is eventually dissipated as heat in the ferromagnet what's happening is every time these dipoles are turning there's heat generated and it turns out that the amount of heat generated is given by the area under this hysteresis curve so this area represents hysteresis heat we can say or mostly we call that hysteresis is loss because you know it's kind of an energy loss so it's in the form of heat so ferromagnets that have a very fat hysteresis curve that means that you know it's harder to take them through that cycles of magnetization it takes a lot of energy and ferromagnets that have very slim hysteresis curve it means that it's easier to take them through that cycles of magnetization because it takes less amount of energy and in the future video we are going to use the hysteresis graph to understand retentivity and something called the cohesivity of ferromagnets based on which we're going to decide whether to use the ferromagnet as a permanent magnet or electromagnet we'll talk about those in future videos