 okay welcome everyone waiting for everybody else to join in wait for a minute anybody has any doubt in whatever questions you might have solved one okay your utes are going on but it's over which one is tomorrow Monday okay all right so I guess we should start now others will probably join meanwhile so you know that modern physics is over now all right we are done with the entire modern physics and very important section nuclei dual nature atoms all those chapters are very simple easy to score and that's why it is very very important okay so we are done with that and we are getting into this chapter which we had left earlier this chapter name is magnetism and matter okay so this is what we will be studying today and today we will be done with the done with this chapter and then I will require maybe one or one and a half more classes to complete the entire syllabus okay so in next maybe another one or two classes physics curriculum is going to get over okay so make sure that you know whatever we are doing towards the end be it modern physics magnetism and matter or communication system and EM wave all those chapters you must do very very properly because we may not get time to you know revise that too much okay so that's Rajdeep anyways so we are going to start this chapter today we are going to complete it also today only because it's a simple and a small chapter okay let us proceed write down perfect mute magnetism and matter yes later on so in this chapter we're going to discuss about magnetism due to the material like permanent magnets okay and we are going to discuss how these material will behave when they are put under the external magnetic field okay so these are the two things that we are going to discuss very similar to a moving charges and magnetism scenario in which our focus was magnetic field due to the current and what happens to the current if it is inside already existing magnetic field similarly here magnetic field due to the matter and what will happen if the matter is kept in already existing magnetic field okay so these things we are going to discuss in this particular chapter and naturally you might be knowing it and it is quite obvious that the first time the magnetism was discovered was not from the current okay so magnetism was discovered first in the form of matters magnetic field as in there will be some material which has its own magnetic field that got discovered in Greece place called Magnesia long long back okay so people I think we have already you know talked about it but then just I'll repeat it again so these guys were they used to wear the wooden shoes and their souls lot of nails were there so they could not walk very easily on the floor of particular place so later on they found out that the place is attracting the nail and it has some mysterious property which is what we are calling magnetism okay so because of the magnetic field of the floor it is attracting the shoe so hence they used to get tired very soon and then they discovered that these are some special kind of rocks which are having magnetic property and the first thing they do is they started worshipping it thinking that it's God so they have that is how it all started and it was very precious at that time when it got discovered these stones were considered to be very very unique precious so the ladies used to wear jewelry made up of magnets thinking that's a unique and very very very you know unique property but then later on of course it was well known later on that it is abundantly available most of the places so that there it loses the importance where in all the super belief were gone based on it but then you know nobody thought of any proper systematic or scientific usage of the magnet which was discovered okay it was you know very very late when people thought of a proper usage of the bar magnet what what do you think that usage is anyone for the compass compass compass navigation okay for the navigation purpose so how people are using for navigate navigation purposes what happens is that when you I mean it was found out very quickly it was found out that if you hang a piece of bar magnet with a thread like this which is which enables the bar magnet to freely rotate okay so the bar magnet is free to rotate about this axis every time they found out that this portion this end is always aligning in a unique direction and this automatically so whichever that is suppose this direction is north so they will write north on this end and south on that end so wherever you go however it is as in you can give it some you can have some disturbance you can rotate it randomly but when it stops it'll always align in a unique manner so you will know where is your north and south and then you can easily find out where is your east and west so just need one direction other directions will be very easily found out okay for example if you stand facing the east your backside will be west what will be your right hand south okay so you know it was used for navigation purposes and the thing is that when we are sitting at home we know the direction we know you know which direction is east which direction is south and north but then when you are in a ship okay or in a barren land wherein you don't see the maybe in the nighttime okay it becomes extremely difficult to find out which direction is north which direction is south like that okay so before the compass came in people used to have stargazing for the navigation purposes have you heard of stargazing the constellation not the constellation actually but have you heard of stargazing using stars for navigation like you look at the pole star and that will be the south direction always okay so there are few stars which are very very far away for them entire solar system is just a point okay so it doesn't matter where the earth moves how it is rotating it doesn't even matter to those stars so relatively the star location is fixed so if you can look at a particular star and if you know that the star is in the south direction whose position won't be changing so you can find out which direction is south which direction is northeast west okay so this was a very popular way of navigating in the sea but then of course it has its own limitation right it is very easy to misjudge the direction probably this way you're looking at the star maybe slightly this way the star is so rather than going this way you're tilted by 10 degrees so you will end up going somewhere else if stargazing is this way the actual star is in this way but then you are gazing in this direction but anyways it was at least it gave some idea about it the another limitation was that during the cloudy weathers it was very difficult to use the star navigation and hence there this particular discovery that you can use the magnet for navigation purpose was a game-changer during that time okay in fact there was this Chinese Emperor with whom people many many tell stories of so what they used to do is that they have a chariot like this they designed a chariot okay on top of the chariot there is you can put a man like this I mean not the living man just a small thing statue of the man and you can put a magnet over in this direction put an arrow like that and this thing is able to rotate freely about this axis so whichever direction the hand points to that will be a definite direction maybe a north direction so on a chariot moving chariot on a runtime you can find out which direction the north and south is and then you have your bow and arrow and you you can accordingly you know target your enemies now this thing is basically utilized in a low visibility areas where in for example during late night where in the light or the visibility is very less okay or maybe in a foggy situation when the visibility is very less then the enemy will basically take the rest camp or the enemy might be moving very very slowly but if you have a navigation device like this you can move very fast and attack your enemy from various directions and you can win wars and that is how the story is regarding Chinese Emperor winning many wars you know wars like that and this Chinese Emperor called this guy who has created this kind of chariot this guy is called as craftsman of course it was not in English he might have meant it in Chinese but little trans translation of that is craftsman and later on this craftsman they are called engineers which is what you guys will be if you go and do your engineering okay so this is just a brief of how the magnetism got evolved but then you know this was the only usage of magnetism for a very very long time so only in past 300 to 400 or maybe two to 300 years ago only people have understood that magnetism can be utilized or magnetism already exists in various facets of their lives okay so then they started recognizing it and more and more importance magnetism has gained and the importance of magnetism now is no less than the importance of the current or electricity okay you can for you can you cannot think of any instrument without any let's say instrument without magnetism for example anything that rotates has a motor in it inside the motor there will be a magnet okay then you have your AC generator generation of the current itself is when you current the magnetic energy you when you convert the magnetic energy into the electrical energy or utilize it to create electricity out of it so there are various like the medical devices also MRIs and stuff all those they they utilize the magnetism to analyze various things so now though I mean you cannot imagine a life without magnetism you right now you're attending classes the the memory of the laptop or your mobile phone all those memories hard disk and everything is made up of a magnetic property of the matter only okay so hence that's the reason why we are studying this chapter and we should know the basics of it at least in class 12th okay so like I said this was very very well known that magnetism exists and for thousands of year nobody has this idea of how to utilize it but then based on their experiences they have understood few things about the magnetism so which we will not debate in the chapter we will take it as it is okay we will be taking these things as facts fine so write down commonly known ideas regarding magnetism again this chapter is like semiconductor chapter okay there will be theoretical stuff mainly in this chapter that is the reason why I was avoiding this chapter this chapter is not in the J advanced okay at least for many years J advanced it was not there this year not sure whether they will keep it or not you have to check it but it was not there for long okay somebody asking did our seniors write J mains that happening now yeah your seniors are writing it definitely they are writing it the I think yesterday first shift Shreya one of our students she wrote her comment was that maths came easy chemistry was mainly inorganic chemistry she said and physics was more of calculation based that that is what she said it took time at least those numeric times numeric types it took time because it was having lot of calculations that is what she said okay so yeah J is exam of elimination they are trying to eliminate you they are not trying to test you okay find how much you know how much you don't know okay anyways commonly known ideas regarding magnetism write down the first one is earth when I say J I mean neat also I is there anyone who is writing neat critique I writing near neat that I know anybody else sig sig critica Rajdeep and and who else Anush sig critica Rajdeep Anush okay I don't earth behaves earth like a magnet okay that was established where the magnetic field magnetic field pointing approximately to geographic south to geographic north now do you know what is geographic south and north what it is anyone has any idea select the magnetic north attracts the geographic south others how geographic south and north are defined anybody else geographic north is like the north pole geographic south is Antarctic I don't know geography need particular because that's isn't that I mean it could be that but how it is defined you just explained it what it is but then no you're not getting it what I'm asking I'm asking how it is both of the points it this is what I was looking for so if this is the axis of rotation of the earth okay your north and south pole is one top point and one down point so one of the point is assumed to be top that you can call north and this is south this is geographic so ngsg you can say okay of course you can debate that the axis of the earth is tilted fine it is tilted but I have not made it tilted okay let me put it straight like this this is geographic north geographic south okay so now basically the first point is pointing towards a fact that the earth behaves like a magnet and a bar magnet okay as if there is a bar magnet inside the earth alright and it may sound funny but it is true that in earlier days people used to think that there is a bar magnet hidden inside the earth okay a giant bar magnet but they never found it because it never existed so there is an angle between the magnetic north and magnetic south this is this you can say an M this is SM magnetic north and south fine but approximately for practical purpose you can say both of them coincide fine and there was one more thing I wanted to huh so the my the magnetism of the earth okay magnetic field of the earth is such that as if there is a bar magnet inside and this magnetic field of the earth is something which is very important for the human lives okay if it doesn't exist then the lot of harmful radiation from the sun will be reaching the earth and destroy the this thing destroy the living organisms and everything so you can see earth magnetism I'll just show you why it is taking so much time look at this I mean this is just artistic impression of what it is actually see this is the earth magnetic field trying to repel the harmful radiations okay exactly what kind of harmful radiation how the repulsion happen and everything I'm not getting into all that I'm just showing it to you that the magnetic field of the earth which is there it is helping us protect the life in it okay so every planet has a magnetic field and Jupiter has the strongest magnetic field and the weirdest magnetic field also so Jupiter if you read the magnetic field of the Jupiter it's very unique I forward actually what it is what is a unique thing and look at this look at this this is a geographic North Pole geographic South Pole and this is the dotted line is the axis the angle between magnetic North South and the geographic is eleven point five degrees right now and this angle is changing and this angle is also very finely balanced there there are some benefits because of this angle if this angle changes the some disturbance will be there okay and yes slowly and slowly it is changing how does it measure this angle exactly I mean you just check the magnetic field lines identify how it is exactly like this okay then you find out okay fine where is North and South Pole it is based on observation there is no formula or concept as such here they just observe it and yes of course there is no bar magnet inside the earth so from where the magnetic field is coming from nobody has a proper answer to that okay the most convincing answer yet is that the the molten iron is there inside the earth which has the the ions which are moving and when ions are moving inside the core that movement of ions is like the current and that current will have some magnetic field so that is the explanation of the I mean just it is an approximate explanation nobody exactly can explain exactly how it is similar to a bar magnet embedded inside the earth like that okay but yeah second point is right done if we suspend which test you had today a computer bio okay it is not that all NPS have the same test right different NPS have different test yes if we suspend a bar magnet in air it will orient it will orient itself in north south direction it is obvious isn't it it is obvious that this will happen because earth behaves like a giant bar magnet so if you suspend a magnet let's say this is your magnet just give me a second guys someone at door just give me one second guys one okay sorry about that yeah so what I was saying was that if you suspend a bar magnet like this okay which direction the north pole of the magnet will orient itself suppose the north pole of the magnet which direction it will orient towards the south right because north pole will attract the south so whichever is a north pole typically s is written on it so that you will understand that it will show the south direction okay and whatever the south pole of the magnet on that north is written okay so that you understand it has oriented towards the north alright third point right down I mean these are obvious even you have experienced it north and north south and south they will ripple okay and north and south poles they will attract so like poles ripple unlike will attract just like the charges like the charges but the story of magnetism starts from dipole can you separate north and south pole Rajdeep no sir no magnetism is about dipoles monopoles don't exist okay they don't fourth is the same point the point is we cannot write down we can't separate north and south pole if there is a north pole there will be a south pole can you think of the simplest of the dipole simplest dipole that exists in the nature hydrogen atoms electron do you have learned it right magnetron magnet on name have you heard of it yes so electron revolving in a circle one side will be south other side will be north pole okay that is the simplest magnet or the basic the thing that exists in nature even that has both north and south pole so that's a reason okay and the fifth point is that it is possible to create magnet okay like you know for charges it was not possible to create or destroy the charges right but then over here it is possible to create magnetic magnets possible to create magnets out of iron and it's over so these are the commonly accepted things as a fact and we will not debate on it will be accepting yes this is what happens okay we will not debate why north north ripple north south attract you never asked why positive and negative charge will attract right same way here also these are the facts now let us proceed so in case of the this thing in case of moving charges and magnetism we had Beosauer law which has given us a very powerful equation which is this may not by 4 pi i dl cross our unit vector divided by distance square okay this ideal is the current element okay now this formula even though it is very useful and you can find out the magnetic field due to various current elements and try to integrate and get it for the wire circular wire for the you know different shapes as in circular straight wire and finite wire infinite wire part of the circle okay all those things we have done while integrating this we have found out those okay but then the basic thing okay basic thing in magnetism is dipole moment m okay so our idea here should be that can I find the magnetic field can I find the function can I find a function which will give me magnetic field in terms of m okay if I get magnetic field in terms of m then my m can be due to anything okay it does not matter I'll just substitute the value of m and I'll get the answer because m is the most basic thing in magnetism so I can you know there are experiments experimentally you can find out easily and more so over for example a permanent magnet how can you use this particular definition for permanent magnets in permanent magnet what you will substitute I as what is dl okay so this formula you cannot hope to use in a permanent magnet setup so that's the reason why we will be trying to find out magnetic field in terms of m so that I can get the value of m for a permanent magnet and substitute that value over here and experiment it is very easy to find out why you might have learned this formula torque is equal to m cross b you have seen it before or not yes so experimentally you can have a device which could measure the torque value and magnetic field you'll get the value of m okay using this expression so get the value of m that m can be from bar magnet or could be anything could be from a wire which has current or anything as long as you know the value of m you can use that formula because that is a basic formula so we are now trying to find out the magnetic field in terms of m okay now first thing that will come on our mind is a bar magnet right so we will try to find out magnetic field of a bar magnet in terms of m now what I am trying to do over here I should make it very clear that what is known to us what is known to us I am trying to correlate with what is unknown okay so basically what is known to me magnetic field because of the solenoid magnetic field because of the circular wire magnetic field into a straight wire all these things we have already derived and we will be treating as if we know it okay so can I use the formula of something which I already know modify that formula and make it appear as if it is in terms of m this is what we are trying to do but before we do that for a bar magnet I need to understand a similar scenario as in is there a scenario in which the current and wire is there which will create similar magnetic field as that of bar magnet can you tell me which scenario creates similar magnetic field as that of bar magnet right so right down solenoid has a similar magnetic field similar looking magnetic field as that of bar magnet okay so what we will do is that we will we will try to find magnetic field of a solenoid as a function of m okay then this m can be due to a bar magnet also okay it is like you are trying to find acceleration in terms of force force is equal to mass emigration and that force could be any force could be spring force or a tension force could be from friction could be anywhere as long as net force is 10 Newton is does not matter from where this 10 Newton is coming from it will create same acceleration okay same thing here also we are trying to find in terms of M and then that M can be from anything okay so let us first you know just to revisit can you draw the magnetic field to a solenoid draw a small solenoid and just quickly draw the magnetic field because of it will it be like this yes yes it will be like this okay it looks like a bar magnet bar magnets magnetic field okay so let us draw this and find out the magnetic field in terms of M okay so just to make sure there is you know clarity in the picture or drawing we will be representing solenoid as a cylinder so draw a small cylinder like this a few fine so this is the axis of the solenoid and when we talk about the bar magnet usually we talk about the magnetic field of a bar magnet in front of its pole right so that is why our interest is to find out the magnetic field along the axis at a point P let's say this is the point P which is at a distance of R from the center of the solenoid I'll draw a center line also this distance is R okay and the radius of the solenoid is given to me this radius is a okay the length of the solenoid is also given total length is 2L so this is L this is L okay of course it is a solenoid so other things are also given number of turns per unit length is N current is I current in the solenoid is I okay now tell me how will you proceed to find out magnetic field at a point P due to the entire solenoid any guesses no one we can just take one like ring and you can say that this is just rings going from this side to this side so you'll take a ring like this rings thickness is DX okay you're taking a ring like this whose thickness is DX and since we are measuring all the distances from the center only so I'll keep X this only from the center this is your X this thickness is DX okay this is DX now do you remember the formula for magnetic field due to the ring along the axis what was it mu naught ni R square by 2 into X square by 2 into X square plus R square to the power 3 by 2 where X is what so the distance to the point okay you can do it as why because you can you may confuse X from here to there huh now tell me what is a magnetic field due to this thin ring DB is what write down first all of you write down and then you can tell once you're done that you know done okay Ruchir Singh is done others Akansha you are absent last class make sure you go through the videos through everything fine one of my relative also got Corona now he's in Bombay he traveled came back with Corona okay DB DB is mu naught and number of tons will be what and into DX and DX and is number of tons per unit length capital is and DX that I into R is a so a square divided by two times of R is a square Y is what what should I write instead of Y R minus X L minus yeah yeah minus X what R minus X yeah Param is confusing me sorry this okay now do you remember in the case of electrostatic dipole we had assumed that the distance between the two poles is very less compared to wherever we are finding the electric field yes or no okay because we were dealing with small small dipoles like for example the dipoles because of HCL molecule and so on and so forth here also we are going to assume that we are dealing with small bar magnets or you're dealing with let's say one electrons dipole fine so we can assume that the length L is very less compared to sorry that should be opposite R is very large compared to L as well as the radius a okay so this is the thing that we are going to assume over here similar thing we have assumed in the electrostatic dipole also fine so you will get total magnetic field by integrating this right your limits will be for X from where to where you'll integrate minus C to E minus L by 2 minus L to plus L yeah minus L Param you're getting very innovative doing silly errors no sir I thought he was yeah that's what I'm saying you get innovative okay so don't start assuming things look at the facts you should not assume no length is my radius that is what I thought that is it will destroy you in the test which you write okay so tell me if R is very large compared to L and A can I say X is negligible in terms of R no matter how it is changing can I write R minus X as R only yes right I can do that so it'll become a square plus R square right then even is very less compared to R then a square plus R square connects can I say it become R square only yes okay so it'll become N DX current into a square divided by denominator will be what then two times but I'm what it will be R cube integral minus L to plus L okay now only variable left is DX so that you'll integrate how much DX will become when you integrate 2L right this will be equal to I will have zone may I and into 2L I a square divided by 2R cube now this is your magnetic field B I want you to modify this and write this might be filled in terms of dipole moment of the solenoid do it okay I can see some of you got it Param what is your answer did you get it so you multiply and divide by pi right yet you have to do so that denominator will become like this and 2L I pi a square divided by 2R cube now any into 2L is what number of turns this is N I into a right can I say this is my dipole moment N I a that's a definition of dipole moment right for a current loop this can be written as mu naught by 4 pi into 2M anyone has any doubt clear to everyone yes so this is your actual magnetic field actual magnetic field due to a magnetic dipole okay now we are going to see something very interesting interesting to me I don't know how much interesting it is to you so magnetic field along the axis is mu naught by 4 pi into 2M by the way is this chapter done in your school no sir what are they doing just finishing up questions of moving charges so my head very very far or little bit ahead only quite so I can as well cancel still I'll be ahead okay but I won't do it this is a magnetic field in terms of dipole moment the class 12 physics is very simple right compared to 11th it get over quickly and not many details are there as many as an 11th did you feel that way all of you yes more details there's a lot more details in class 12 yes so that you didn't pay attention so an 11th creative is just like five equations everything on 11th I'm talking about if I collect all the numericals of 11th and all the numericals of 12th which one do you think is easy to master 12th 8 12th Param did not pay attention to 12th so that's why Param is busy with something what is something that you're doing Param nowadays practically used in the real world 12th physics is more practically used how can you say that have you seen electric field and magnetic field from your eyes I can say that these things are something which you can you have seen devices of in your lab but mechanics is something which you use in a your day-to-day life you're so used to it that you start taking you for granted also devices yeah because your devices are mainly electrical instruments isn't it your devices in your lab is mostly electrical or optical in nature so electrical device electrically so if you take let's say mechanical or civil then you'll see the mechanics the kind of okay anyways this is actual magnetic field do you remember actual electric field you do a dipole how much it was formula do you remember the same or is that 1 by 4 paps or 2 p by 2 p by rq 2 p by rq similar looking okay we had derived the equatorial electric field also what was it 1 by 4 piter not into minus p by rq okay this is the equatorial electric field similarly I don't need to derive the equatorial magnetic field I can just correlate and it will be this minus m by rq okay the electric dipole will go the direction of the electric dipole moment is from positive to 9 from negative to positive this is the direction of the electrical dipole moment what do you think that direction of the magnetic dipole moment is not to south no not to south no south to north what do you think others so south to north this is your magnetic dipoles direction okay everything okay it will be same m is a vector p is also a vector you have seen numericals in which the dipole electrical dipoles were added like vectors same thing can be there for a magnetic dipole also I can have a bar magnet like this okay curved bar magnet so you can divide it into different small small pieces and then vectorally add the net dipole moment I'm just telling you in numericals you may see something like that very similar to the way you're dealing with the electrical dipole magnetic dipole also you have to deal with it okay now again I'll just tell you again these things because I can send some of you might have this confusion they go m is represented by the arrow this arrow is m this arrow could represent solenoid this arrow could represent the bar magnet this arrow can represent the electron a current loop could be anything I don't care as long as m is m it doesn't matter from where it is coming okay now this line perpendicular to m this line is equatorial this line is axial axial I put another color blue line is the axial okay this is distance r this is the when you talk about the equatorial you measure the distance perpendicular to m vector when you measure the axial one you measure the along the vector distance r okay magnetic field along the actual direction will be in the direction of m it will like this only magnetic field on the equatorial will be in opposite direction like this getting it why opposite direction there's a minus sign minus represents the direction in the case of vectors okay anyone has any doubts till now anyone no one has any doubt okay fine write down died since it boils down to a dipole okay let's discuss few more things about the dipole so dipole in a uniform magnetic field how much time remain before you write your j means have you do are you aware of it five right now four months and the even one month will be gone before you complete your class 12 so after you're done with 12th probably two and a half to three months will be remaining okay so things have become very very serious all right don't take this slightly two months is two to three months around 60 to 80 days and you are dealing with 140 chapters 140 chapters 80 days I think it is not as easy as it you might be taking it okay so right now your top priority should be doing well in January G means if you do well in January J means you'll be very very relaxed okay suppose you get 99 or 98 percentile in January J means itself imagine how much relax you will be okay you will not have lot of worry going into the second phase of J means do yourself a favor and give your best shot in January J means even though you might be lesser prepared so are everybody else so it's a relative ranking that matters anyways I think I've repeated many times this thing first thing is torque a dipole moment of m experiences a torque of m cross B okay very similar expression that of the electric dipole moment which is p cross okay and you know the best part about these torques these torques are couple how the couple torque is different from any other torque about anything about any point you will have the same torque so the torque equal to i alpha equation is valid about the center of mass axis okay so same torque will be about the center of mass also okay so you can equate this talk to i alpha easily fine now very similar you know situation over here why I am keep on repeating myself that for example you remember you had let's say electrical dipole moment like this okay this is electrical dipole moment P and electric field is also like that e if you rotate your dipole moment little bit like this what will happen to this electrical dipole moment P it will try to go back or what it will try to go back the direction is p cross e so alpha direction is into the screen so it goes inside okay very similar thing happens for the magnetic dipole moment also so suppose this is the magnetic dipole moment this is the magnetic dipole moment okay so if you rotate it a bit like this where in external magnetic field like this then again it will try to go back okay so whether it is magnetic dipole moment or electric dipole moment what they will do they will try to align in the direction of electric or magnetic field okay now the other situation torque is zero at what angles between magnetic dipole moment and magnetic field zero and 180 right torque equal to zero for an angle of zero and 180 degrees same thing over here also now net force so anyway is zero right so equilibrium net force is zero because we are talking about uniform magnetic field okay equilibrium implies that torque is also zero so even you know if angle is 180 degree then also it is in equilibrium only but do you remember what happened to the electric dipole moment when it was making an angle of 180 degrees with the electric field like this if you displace it slightly like this what will happen to it it will rotate like this it will just flip it over it will not go back okay so even though it is an equilibrium but then this is an unstable equilibrium and usually unstable equilibrium's are the point of max potential energy the slope is slope of potential energy is zero but it is maximum there here also slope is zero but it is minimum over here and theta is zero so over there all as well if magnetic dipole moment makes 180 degree with the magnetic field and if it rotates little bit it will go back like that okay so this is also unstable equilibrium only fine no doubts right so theta equal to zero and theta equal to 180 both are equilibrium but zero is stable one and 180 is unstable one okay then we need to define the potential energy also over here so change in potential energy is negative of the work done let's say okay not let's say this is the formula for the potential energy so magnetic potential energy can magnetic field do any work but how come it is doing here the BW is integral of tau d theta how come it is doing work so it can't do work on any single particle you work on the electrons inside magnetic field cannot do work on a moving charge but it can do the work on dipoles okay so we are generalizing it in our head when we say that magnetic field doesn't do work that's not correct okay you take two magnets one magnet will attract the other magnet other magnet will gain the kinetic energy from where it gained the kinetic energy because the other magnet is doing work pulling it towards itself okay so we are trying to define the potential energy for that case so suppose it goes from theta 1 to theta 2 now when you're leaving it as it is when you rotate like that and you leave it the magnetic field will do the positive work or negative work what do you think it tries to go back magnetic field is doing positive work or negative work positive positive work right all of you yes it is doing positive work but what about d theta is it a positive quantity or negative quantity negative negative so overall it is what mb sin theta d theta is a negative quantity work done should be positive so multiply minus one with it so it will become class outside this minus is in the formula so minus will come from here also this will be equal to mb integral of sin theta d theta theta 1 theta 2 okay when you integrate you will get delta u and magnetic potential energy is equal to minus of mb integral sin theta is minus cos theta mb cos theta 2 minus cos theta 1 so u2 minus u1 is equal to minus of mb cos theta 2 minus of minus mb cos theta 1 can I say u2 is this and u1 is that this is u1 and this is u2 can I say that I have already asked you such kind of questions before if 5 minus 3 is equal to 4 minus 2 5 doesn't become equal to 4 differences are equal individually they need not be equal okay so when theta 1 is 90 degree let's say take theta 1 to be 90 degree you'll get u2 minus potential energy when angle between magnetic field and dipole is 90 degree to be equal to minus of mb cos theta 2 then if we assume every time you define a potential energy you need to assume which one has the zero potential energy here if we assume u90 is zero when angle between the magnetic field and the dipole if it is 90 degree we say potential energy is zero okay then the definition of potential is equal to minus of m dot b mb cos theta this is the magnetic potential energy no one has any doubt fine let us take few questions from your school textbook first one is this all of you let's say you have a magnet like this there is a magnetic field uniform magnetic field of B like that this is north and this is south okay what you did is that you have slightly tilted the magnet like that and then you have observed the movement of the magnet and it is found out that magnet is doing SHM okay magnet has started to do the SHM it swings like this and then goes back like that you need to find out the time period of the SHM time period of SHM is what you have been given magnetic dipole moment of the magnet m moment of inertia I okay you know right how to deal with the angular SHM scenario you rotate it by a small angle theta then you look at the restoring torque and you have the direct formula with you which is mb m cross B which is mb sin theta this torque should be equal to i alpha and it is a restoring torque it tries to go back so minus sign will also be there so alpha is equal to minus of mb by i into sin theta theta is very small otherwise it will not remain simple harmonic motion it will be oscillation but not simple so if theta is very small sin theta will be theta okay then you compare it with the angular SHM equation omega square theta so omega comes out to be root over mb by i this is your omega the time period is 2 pi by omega 2 pi root over i by mb okay now using this relation you can also determine magnetic field you know for sometimes time time period is easy to calculate by stopwatch moment of inertia suppose known to you and magnet dipole moment is known you want to find out B from this relation so be will come out to be how much then 4 pi square i divided by m into t square right so it can treat it like a relation this relation can be utilized to find a magnetic field as well as time period both but time period though you can calculate by using the stopwatch as well this relation will be useful in calculating the magnetic field more than anything else everybody understood anyone has any doubt has any doubt okay Krithika you're writing still having the issue you're not writing so doctor said what till when this will continue okay Jay need goes ahead okay fine okay I'll just give you questions from your textbook right now alright let's take it one by one you don't need figure here okay find out you may know exactly how to do it nobody cares about that get the right answer that is what matter knowing just knowing how to do it is not enough okay tell me the answer Param got the answer something he got something what do you think Param is that correct yes no you might hate it but then I keep on reminding you that you're taking it lightly calculations are very very important in any exam like Jay only Richard Parik got it correct till now only one person Rahul Mishra close Abhiram Abhiram using calculator okay the answer is no Mahith not that I think you guys are approximating that is why close to the answer you're you guys are getting but let me tell you the final answer first answer is B equal to point zero one Tesla okay now I mean do I need to show you how to get the answer Magda field is 4 pi square I get a divided by M into T square you can use this if you don't remember it you can derive it quickly not a problem what is pi square equal to everyone then 10 so 10 I'll keep it as 10 moment of inertia 7.5 into 10 is power minus 6 divided by what is M M is what here 6.7 into 10 is power minus 2 time period is how much 0.6 10 complete oscillation in 6.7 seconds so one oscillation in 0.67 this 0.67 square now I'll just show you quickly how to get the answer over here so 4 into 7.5 divided by 6.7 0.67 you can write it as 2 by 3 so it become 4 by 9 when you square it 2 by 3 is 6.67 right so that into 10 this power minus 5 minus 2 so it become minus 3 okay then this 4 is gone then 7.5 divided by 6.7 slightly more than 1 when you multiply with 9 you'll get close to 10 okay so after this you can look at the options also and get the correct answer so roughly it is 10 into 10 is power minus 3 which is 10 is power minus 2 that is 0.01 tesla everyone got this error see catching silly error won't help you because every time you'll make a new silly error catching it will not help you at all you need to just stop making silly errors by being more careful and respectful to the question okay here is another chance to not to make silly error those who did not get the previous one do this see questions from this chapter will be like this only in J also that is the best part it will be simple when I say J I automatically mean neat also what is G G is goss it's another unit of magnetic field one minus 4 tesla yes Rajdeep is smart tensor minus 4 tesla okay just like electron volt is a smaller unit of energy you have a smaller unit of magnetic field also because one tesla is huge very very large magnetic field one tesla so what's the unit of magnetic moment you tell me magnetic moment is ni a right current into area ampere meter square okay first part first part everybody should get it richer that is wrong is equal to it's not those simple enough torque is equal to MB sine theta work is point 016 this is equal to M which we have to find out into B that is 800 into 10 is power minus 4 you to convert in SI units MB sine theta which is 1 by 2 so from here you'll get M as point 4 Newton meter not Newton meter what I'm saying ampere meter square okay B part everyone there are two ruchers when I say richer got it correct I could mean richer sing or richer park both good to create some confusion also B part without my answer just tell me the B part right now I don't care about the C part okay okay richer Parik got it Kirtana G KTG got it Param Pradhyat okay work done will be negative or positive what do you think some of you are telling negative positive positive why positive so because you would you have to push it you don't need to stop it from moving so you have to do positive work so what then is positive that is clear okay Prathit understood yes I was thinking about the field okay so what then is simply U2 minus U1 work then Kirtana KTG is 0 you are slowly moving it it should be written it should be written that it is slowly moving otherwise you should write U2 plus K2 minus U1 plus K1 but it is not written so we'll assume changing kiting edge is 0 this is equal to U2 U2 is equal to minus of U1 right U2 is the most unstable position minus of M into B into cos of 180 degree that is M into B and U1 is minus of Mb cos of 0 which is minus of M into B so U2 minus U1 is simply 2 times U1 2 times U2 which is 2 Mb 2 Mb is 0.064 joules C part Ruchir got it correct Vika Shaitanya param Pradyut Raju okay others he also got it Prabhupada Akansha Akansha Akshit Advik Mahit why are you keeping quiet Krithika also got it without writing anything and she got it correct oh left hand you're using left hand that the bar magnet is replaced by a solenoid of this but same magnetic moment determine the current simple NIA is the magnetic dipole moment number of turns is 1000 current is I area is 2 into 10 is a power minus 4 this should be equal to 0.4 so current will come out to be 2 amperes okay simple straightforward there is a very nice table which is there in your textbook which I wanted you to see how electrostatics and this thing is compared look at the comparison here dipole moment this constants of electrostatics one by some not and this is for mu not for the magnetism 4 pi is there in electrostatic as well as in magnetism then look at the other formulas energy torque axial field equatorial field everything looks so similar isn't it so if you remember one formula other formula is you automatically tend to remember okay so like that you can try to remember you'll not make silly rest solve this question also see you just need to find one of the field other one is half or double of the other isn't it direction also changes though equatorial magnetic field will be half of the actual magnetic field richer here because nobody else what do you think param correct there won't comment this time that's correct the moment you become humble about these numericals you stop making silly errors you should give them due respect that's all all right so axial magnetic field mu not by 4 pi is 10 is power minus 7 into 2 into m 0.4 divided by r cube kange by r r is 50 centimeters 0.5 cube why do you think length of a magnet is given to us any idea yes just to make a point here that you can use that formula which in which you have made a lot of approximations so axial magnetic field will be 6.4 into 10 this power minus 7 tesla equatorial will be half of it isn't it look at the formula it'll be half of it 3.2 into 10 is a power minus 7 tesla you have written only the magnitudes remember direction of actual is along the dipole moment direction of equatorial is against the direction of the dipole moment okay so this is a question from the book again which i like one of those questions do it yourself guys i mean the moment you refer to anything you're wasting time effort cheating yourself don't do all that do it yourself if you get it wrong that's fine one by one you answer answer for the first one which configuration is not in equilibrium okay one and two everybody so that's correct why it is one and two everyone theta is not zero i guess 90 please it's 90 so elect the magnetic field due to due to p over q2 it is in which direction downwards here also downwards isn't it it's like this that's why solve the b part b part first one stable equilibrium which one stable equilibrium for stable equilibrium what should be theta where all it is zero is it zero at q3 180 at q3 q3 is down magnetic field is what which direction due to p what is downwards downwards only q3 is correct what about q5 what is the angle between q5 and magnetic field 180 so that's not what about over here q4 which direction the magnetic field is upwards you have to think before you say something now okay magnetic field is along the axis when you talk about the axis axis is vertical over here q6 which direction it is up or down upwards upwards okay so clearly q3 and q4 where the angle is zero okay then unstable equilibrium where angle should be 180 you can easily identify which one it is q5 and q6 right q3 and q3 and q6 and the other one q5 and q4 q4 c part so the stable equilibrium c part lowest potential energy means it should have largest negative quantity right angle should be zero only lowest potential energy angle should be zero or not if angle is 180 degree the potential energy become positive it has to be negative we are talking about lesser potential energy so 180 degree is there are only couple of scenarios one is this 180 degree other one is this which one out of two will have least potential energy but both of them will have equal what is the formula for potential energy minus of what i said so it should be stable right q3 and q5 this and this now tell what you're saying chadanna you're saying something nothing so i was just saying that it should be these ones not okay so out of these two which one has the least potential energy minus of m dot b angle is zero so it is minus of mb right so m is same but b is different whose b is more b along q6 is more or along q3 along q6 so q6 is the answer so that's how you do this next since we are talking about equivalence a lot so let us discuss the analog of the Gauss law also here okay Gauss law was for the charges till now isn't it so let us try to see whether something like Gauss law can be there for the magnetism also no no no ampere circuit law is not analogous to Gauss law did i say that during that time yes but do you have anything recorded so we can check don't waste your time i would not have told you that it is exact analog i might have told you something similar to that okay like that we are talking about analog analog as in in Gauss law we discuss about the electrostatic flux electric flux fine but did we find the flux in ampere's law no sir it was not a flux it was a line integral flux is always through an enclosure okay so so we are going to find out or we are going to discuss can we we find out a law related to magnetic flux magnetic flux will be defined exactly like how the electric flux is defined through a closed enclosure which is b dot d now Gauss law i hope you guys remember integral of e dot da to an enclosure is equal to q enclosed divided by epsilon not remember this now at the start we have discussed the analog of a positive charge north okay analog of a negative charge is south analog of a dipole is north south together okay so if i create a magnetic enclosure and find out the magnetic flux what do you think it should be equal to this should be equal to what should be zero you need to have equal north and south right all of you agree with param when you include both north and south it is like including both positive and negative charges together so net charge enclosed will be zero so electric flux would be zero similarly the magnetic flux should also be zero that is how analog works right so if you include lot of electric dipole dipole moment net charge is zero if you include thousands of the dipole moment also inside enclosure still net charge will be zero so that's the reason why magnetic flux will always be equal to zero through an enclosure magnetic flux an enclosure is zero can you defend this logic as in for example if i have a bar magnet like this it has one pole here one pole there but my enclosure includes only part of it i'm not including north pole including north pole then how come the flux should be zero i'm including only one pole you can take small small dipoles inside infinite dipoles inside which are aligned from south to north correct so this is the when you say north and south pole this is the net effect of dipoles this is a net effect when you're including a portion of it you need to go inside and see the individual dipoles individual dipoles are already aligned these aligned dipoles are creating net effect of a bar magnet very net net this is the north pole and the backside is the south pole okay so when you include only portion of it you need to see how many actual dipoles which are in the form of electron spins are getting inside okay fine i think this is clear right so we have we have to start another topic now on the chapter we'll take a break now because that topic will be completely different from whatever we have been discussing till now okay so we'll take a break right now itself and after the break we will continue with whatever is new okay i don't want to take a break starting something new for two minutes and immediately okay so right now it is no it is not six already it is five fifty five we'll meet after 15 minutes six ten come back after the break okay stopping the