 Okay, so let us proceed. So the next topic is magnetization and magnetic intensity, right down. See what happens is that just like you have dielectric, right, when you talk about electric field, you put a dielectric medium, electric field gets modified, fine. So electric field can change depending on what medium it is, okay. Similarly magnetic field also changes depending on what medium we are talking about, okay. So that is what we will be discussing here, okay. Now one way the medium affect the magnetic field which is completely different from the way medium affects the electric field is that, you know, the medium can support the external magnetic field. So if you change the medium, suppose you take a soft iron core, if magnetic field before soft iron core was suppose 10 raise to power minus 4 Tesla, then if you put a soft iron core, magnetic field can grow 100 times, 1000 times, fine. So the substance can actually increase the magnetic field just by putting the substance. But that will never happen when you talk about electric field. Electric field in a dielectric medium will always reduce by a factor of K, fine. So this is the basic difference between how the medium affect the magnetic field and how medium affects the electric field, okay. So now you will see that ultimately magnetic field B depends on magnetic field B depends on magnetic moment, right. So it depends on magnetic moment. So I will try to see how the external magnetic field B gets affected by the medium, okay, because of the magnetic dipole moment, because ultimately if magnetic field changes, then there has to be magnetic dipole moment that is getting changed, okay. So we will talk in much, you know, micro level. So let us try to proceed further, you know. So if total magnetic dipole moment is let us say m, okay, m is a total magnetic dipole moment. So if total magnetic dipole moment is not equal to zero, then the substance will have some magnetic field. What happens is this magnetic dipole moment, it get developed because of the electron revolution, fine. When electron revolve, it will create some magnetic dipole moment, fine. So let us say that this is the magnetic dipole moment due to one electron. So if like that randomly everywhere, these magnetic dipole moments, they are arranged in a random direction, then net dipole moment will get cancelled out, fine. So you will not find magnetic dipole magnetic property in every material because on all the materials usually the electrons are randomly revolving and because of that, the net magnetic dipole moment get cancelled out, okay. And if you have a permanent magnet, if you have a permanent magnet, then the magnetic dipole moments of the electron that are revolving, they are not completely canceling out, okay. But one thing remains here is this, if you take a small magnet, okay, or if you take a bigger magnet, fine. Since I am talking about the property of the matter, I am talking about the property of matter like how matter affect the magnetic field, right. Automatically, if you take the same matter, let us say this is iron and this is also iron, okay. But just because this is bigger in size, just because the lower one is bigger in size, the dipole moments will be more in the bigger one, isn't it? So dipole moment, let us say this is M1 dipole moment and this is M2 dipole moment. So M1 will automatically be more than M2 but then M1 is more than M2 not because the material is different. M1 is more than M2 because the size is different, okay. So rather than finding everything with respect to what is a total magnetic dipole moment, I am trying to find now with respect to magnetic dipole moment per unit volume now. Getting it, if I divide, let us say volume of this block is V2 and volume of this block is V1, fine. And then if magnetic dipole moments are aligned similarly, I can say that M1 by V1 is equal to M2 by V2, fine. So the density of dipole moment, the density of net dipole moment will depend on what material it is. All of you clear about it because this is very critical in this topic. Just type in yes or no, the magnetic dipole moment per unit volume, this only depends on what is the material, okay. So if I say that if there is a magnetic field due to a bar magnet, then can I say that bar magnet is magnetized, isn't it? Initially there was no magnetic field because of the bar magnet, because it was not magnetized. Now if there is a magnetic field because of the bar, because of the iron bar, it means iron bar is acting like a permanent magnet, so it is magnetized, okay. It is behaving like a magnet, so it is magnetized. So there is a net magnetic dipole moment now, okay. So if it is magnetized, there is a variable, there is a term called magnetization, okay. Write down, this is magnetization. How much it has magnetized? Magnetization, this will be different for different material, okay. This will be different for different material and it only depends on material. This magnetization will be total magnetic dipole moment divided by the volume of the bar magnet, getting it? So like this, I can talk about magnetization, all right. It is like this, that if I put, if I put 2 tesla of magnetic field on iron, okay. On iron, if I put 2 tesla of magnetic field, it does not matter what is the shape and size of the iron, it will get magnetized or it will have the same magnetization if it is iron. So total magnetic moment divided by volume will be same. But if I take, let us say other material, let us say I take steel, okay. Steel will get magnetized differently. So magnetization of steel will be different. Total magnetic dipole moment divided by volume for steel will be different than total magnetic dipole moment per unit volume for iron, okay. So that is why we define magnetization which only depends on material not on shape and size of the substance, okay. Now this is a very important term. Right now let us just write it as equation 1 and let us proceed further. Let us see that first of all, a very common way to magnetize is what? A common way to magnetize is to put the matter, to put the bar inside the solenoid. Yes or no? So this is a very common way of magnetizing the substance, okay. So let us try to visualize that particular scenario because it is a very common thing. So you have a solenoid, draw this solenoid, guys. Let us say this has a current I, it has a radius of let us say A, number of turns per unit length is N and the length of the solenoid, let us say is L, okay. Now first of all tell me what is a total dipole moment of this solenoid? M net is what? For the solenoid M net, is it equal to number of turns current into area which is equal to N small n into length into current into pi into r square which is a square. All of you getting it? Now M net will come out to be equal to pi a square L into N into i, okay. This is M net, fine. Now if that is M net then this is M net, can I write M net as equal to volume times N i? This bracket term, this bracket pi a square into L is the volume of the solenoid, isn't it? So since it is volume I can write it like this. So magnetic dipole moment of a solenoid per unit volume is equal to N into i, getting it? Now this is the magnetic dipole moment which is affecting the iron. Are you getting it? So this thing is magnetizing the iron, okay. So you can say that okay it is solenoid that is magnetizing the iron but if solenoid there is no current it cannot magnetize the iron and because of the current only the solenoid has a dipole moment and it is a dipole moment which is magnetizing the iron, okay. So if there is no dipole moment in the solenoid it cannot magnetize iron. Are you getting it all of you clear? So let's call it as capital H. So H is creating capital M, H is creating capital M. This magnetization is the effect of H, okay. So since this is an effect of H let us write down everything in terms of capital H and capital M. Are you guys understanding any doubt? Just let me know. I am taking a pause here. Message me. Are you able to understand? Yes or no? Please. This is very important derivation. Okay, Ritwik. Okay. Fine. So I will assume that all of you are on the same page. Okay. Now H is creating M. So it is H that is creating M. So there has to be a name for H. H is called magnetic intensity. Magnetic intensity. How intense the magnetic field is that is creating magnetization. How intense the magnetic field is. How will you find out if there are so many dipole moments per unit volume as in the density of dipole moments is very large. Lot of dipole moments are there per unit volume. It means that magnetic intensity is high. Okay. So it can create higher magnetization. Fine. Now let us try to write down magnetic field in terms of magnetic intensity. We know that magnetic field is mu naught n i. Okay. So this can be written as mu naught H because n into i is H getting it. Okay. So this thing is coming out clearly that if magnetic dipole moment per unit volume is X. This implies magnetic field due to this X should be equal to mu naught X. Fine. So this is magnetic field due to the solenoid. Now tell me what will be the magnetic field because of magnetization. How much it will be when the material get magnetized. What will be its magnetic field. Okay. So Shweta is asking M by V should be magnetization. Why it is magnetic intensity. See M net by volume is nothing but dipole moment per unit volume. Okay. Now if dipole moment per unit volume is getting created. If it is getting created because of external field we say that magnetization is happening. Then we say M net by V is magnetization which is M. Okay. Now if M net by V is dipole moment per unit volume that is created in a solenoid which is creating magnetization. Okay. So if it is a cause of magnetization then we call it magnetic intensity. Is it clear now Shweta. So it is I mean we don't call anything M net by volume. If M net by volume is a cause. Okay. If it is a cause we call it magnetic intensity. It is causing. What it is causing magnetization. Okay. So if M net by volume creates dipole moment per unit volume inside a material then whatever dipole moment are getting created inside the volume per unit volume the created dipole moment per unit volume is magnetization which is created inside the material. Okay. And the cause of creation there should be some external field which is creating this magnetization. Right. So this external field also has a magnetic moment per unit volume. So this external field that is creating magnetization that magnetic moment per unit volume is called magnetic intensity. So cause is magnetic intensity and affect is magnetization. Now tell me what will be the magnetic field due to magnetization. This is magnetic field due to magnetic intensity. So this magnetic intensity has created magnetization of M value. So what will be the value of magnetic field due to magnetization what will be the magnetic field. See if magnetic dipole moment per unit volume is H magnetic field is mu not H. So if magnetic dipole moment per unit volume is M the magnetic field should be mu not into M. Isn't it simple. We have found out magnetic field in terms of the density of magnetic dipole moment. Now that could be magnetic intensity or that could be magnetization. Okay. And if there are both there will be magnetic field due to both. This is the magnetic field because of magnetic intensity and this is the magnetic field because the material is getting magnetized. All of you with me type in yes or no. Okay. So now total magnetic field will be what? Total magnetic field will be the sum of B1 and B2. And so total magnetic field is the sum of magnetic field due to solenoid plus magnetic field due to the material. Material creates a magnetic field because it also gets magnetized. So total magnetic field will be mu not M plus mu not H. Okay. So this will be equal to mu not M plus H. See M depends on what material we are talking about. So value of M will be different for different materials. Now since M is because of H, okay. Since M is because of H, M cannot exist without H because M is a cause of H. It's like excision cannot be there without a force. It's like that. So M is like the effect of H. So I can say that M is a fraction times H. Right. M is a fraction times X where this fraction is called magnetic susceptibility. Okay. It is a dimensionless quantity because M and H has the same dimension. Value of X determines how sensitive M is with H. If X is very less like 0.0001 then M does not get affected by H too much. Okay. But if X is very large like if X is 100 okay then M gets affected by H very much. So that is why it is called susceptibility, magnetic susceptibility. Fine. So if I use this equation, let's say this is equation 2 and this is equation 1. So if I use both of them then I can write total magnetic field is equal to mu naught H plus X H. So this will be equal to mu naught 1 plus X times H. Fine. So this is also mu naught mu R H. All right. Where mu R is relative magnetic permeability. Mu R write down is relative. These are just names okay. This is relative magnetic permeability. Okay. You can also write this as just mu into H. Okay. Now what was H? We have found the value of H to be N into I. So this you can write it as mu naught mu R N into I. Okay. This mu R depends on what material it is. Mu R value is 1 plus X. Okay. So you can have a solenoid. Okay. You can have a solenoid in which if current I is flowing, magnetic field will be equal to mu naught N I. Okay. But if you put an iron bar inside, if you put an iron bar inside, magnetic field will become mu naught mu R N I. Okay. Where mu R, why mu R is coming? Because there will be dipole moments inside this material also that is that are contributing to the magnetic field. Fine. So I hope this is clear to you. Any doubt please ask anything. Okay. So I'll assume no doubts. So we'll take up a question on whatever we have done till now. I hope you have copied it down.