Free Physics NEET Video Lectures for Magnetism and Matter

00:00:00 e [Music] [Applause] a very good morning to all of you we are discussing magnetic dipoles and uh let me recall in the last lecture we had looked at uh torqus and energy of a magnetic dipole so we had defined a magnetic dipole by considering a a loop of wire carrying a current I and of radius R so the Magnetic Moment so magnetic dipole having a Magnetic Moment m is equal to I * a vector a area area Vector in this case the current is propagating like this so the area Vector is pointing up and the magnetic dipole

00:01:34 moment is pointing up we also calculated the magnetic field due to a dipole and we had done this for uh field along axis B is equal to Mu M by 2 piun * Z Cub where Z is much much greater than the radius of the of the of the of the coil so we are this magnetic field is on the axis far away from this dipole and it has the same direction as the Magnetic dipo Moment similarly we had done a calculation for field in the plane and B was equal to minus mu M by 4 pi x Cub for X much greater than R so this is we had assume this is a z

00:02:51 Direction This is X Direction and so we far away from the dipole the magnetic dipole uh field along the axis is Mu M by 2 pi Z Cube It's parallel to the magnetic field it's parall to the magnetic dipole moment and the field in the plane isus mu M by 4X Cube so if I were to draw a figure here if this is the dipole M then this is the axis of the dipole and this is the plane perpendicular to the dipole so here the magnetic field is like this here the magnetic field is like this B is parallel to m

00:03:31 and here the magnetic field is downward here the magnetic field is downward so B in the plane is U minus of m and b in the axis is along the M Direction so we had obtained these magnetic fields of a dipole far away from the dipole and also we had calculated the torque on a dipole due to an external magnetic field b f to is equal to M cross B so the torque is M crossb and the torque on the dipole tends to align the dipole along with the magnetic field so the torque tries to align the magnetic dipole along the direction of

00:04:35 the magnetic field we also calculated the potential energy of the dipole in an external field U is equal to minus M dob that the potential energy and the zero of the potential energy is assumed to be when m and b are perpendicular to each other and the external field tends to align the dipole parall to the magnetic field and where the potential energy is minimum and equal to minus MB when m and b are parallel the potential energy is minimum that is minus MB and when M and an anti parallel the potential energy is

00:05:32 maximum and that is plus MB so as the dipole goes from anti parallel to parallel so if the magnetic field is pointing up and the magnetic dipole is pointing down maximum potential energy and as it twists and comes in this direction parall to the magnetic field the potential energy is minimum when the dipole is oriented along the magnetic field so whenever you have a dipole magnetic dipole the external field tends to apply a torque on the dipole tending to align the dipole along the magnetic field

00:06:00 we started looking at one example in the last at the end of the last class and that is let me recall the example again we have a a loop Curr caring current I let me assume this is the xaxis this is z axis and so the rightand system Y axis is like this Y axis is going inwards uh let me assume there is a magnetic field uniform magnetic field in this direction so it's given that the radius of the coil is 5 cm the current through the loop is 5 amp and the magnetic field the external magnetic field

00:07:00 p is equal to .1 Tesla and oriented along the X Direction so I'm given a loop carrying current a loop of radius 5 cm carrying a current of 5 ampers and placed in an external magnetic field of strength point on Tesla so first let's calculate the Magnetic Moment of this Loop mag Magnetic Moment of this Loop m is equal I * a and because the loop is carrying a current in this Direction with the right handed rule the area Vector points along the Z Direction so this is equal to I into P Pi r² into K

00:07:52 cap and so we can substitute this so 5 amp into Pi into r Square which is 25 10- 4 K cap and that is equal to 1.25 Pi into 10us 2 a cap amp M Square so the Magnetic Moment dipole moment of this Loop is 1.25 Pi 10us 2 K cap AMPM Square so the moment dipole moment is pointing upwards along the Z axis and this is now placed in a magnetic field pointed along the X Direction so as we have seen before the torque will be to M cross B so m is pointing upwards B is pointing this way so if you look at M cross B the torque will be oriented

00:08:47 along the Y Direction so we can calculate the torque on this Loop torque on the loop to is equal to M cross B which is equal to we have just calculated M 1.25 Pi 10us 2 K cap cross1 I cap so this is equal to 1.25 Pi into 10us 3 JC K crack K cap cross IAP is jcap and as you can see there is a torque which is acting along the jcap direction so jcap is in this direction so the torque is tending to align the DI the the loop along the x-axis the the area of the loop to be along the x-axis so there is

00:09:46 a torque acting on this on this Loop which is tending to align this and along the and the torque is oriented along the jcap direction now I can also calculate the potential energy change so when change in potential energy when the coil when the loop goes from this position to a position which is minimizing the potential energy so the loop is like this now it gets uh the torque will try to align this and the the loop will get aligned perpendicular to the x-axis so initial potential energy now is equal to 0 because in this

00:10:37 orientation m is along Z axis B is along xaxis and M do B is zero the final potential energy minus M dob which is equal to minus MB where M becomes parallel to B which is equal to -1 .25 Pi into 10us 3 juw now the stock has a unit Newton meter and this is 1.25 Pius 1.25 pi-3 Jew that means the potential energy decreases as the loop gets aligned along the direction of the magnetic field and similarly if you have to I leave it a problem to you what is the work to be done to align the dipole not from this orientation to this

00:11:34 orientation that means the dipole moment pointing along the minus X cap Direction so I must as you will see that whether I have to do work on the dipole or the field does not work on the dipole you can calculate what is the work to be to be done in rotating the loop from this orientation to an orientation in which the magnetic dipole moment is pointing along the minus X cap Direction so I leave this as a simple problem to you to calculate what is the energy required or the change in potential energy in this

00:12:02 process now we have done all this calculation for torqus ETC to finally understand what happens to the magnetic field in the presence of matter now in the case of electrostatics remember we had discussed initially we looked at electric fields in free space and then we introduced the concept of dialectric and said that when you place a dialectric inside in an electric field the electric field polarizes the dialectric that means creates small electric dipoles within the material and these small electric dipoles create

00:12:38 their own electric field and what You observe is the sum of the electric field that you have applied and the electric field that the dipoles are generating so in a similar fashion we need to understand what will happen if I place a medium in a magnetic field what is the effect of a magnetic field on the medium and whether the medium affect the magnetic field inside the medium outside the medium Etc so in for this we must recall that all matter consists of atoms and these atoms are actually made

00:13:10 up of electrons and protons and neutrons and in all these atoms the electrons are uh in the simplest picture revolving around the the nucleus and these orbital motions of electrons constitute a current so you have in the simplest picture I can assume that I have a nucleus in which the electron is revolving and this revolving electron has a uh constitutes a current in the in the system and that current will have its own Magnetic Moment and so this Magnetic Moment will then try to generate a magnetic field

00:13:44 outside so please remember that this current is different from a current that you will flow in a wire if you have a wire if you have a conducting wire carrying current there are actually electrons flowing from one end of the wire to the other end that's something called conduction current so electrons are actually flowing from one end to the other end in an atom the electrons are revolving within the atom itself they are not freely flowing within the atom and within the system and these Atomic

00:14:10 currents also constitute dipoles and these dipoles also create their known magnetic fields and what you need to understand is the total magnetic field generated by the conduction current as well as the bound Atomic currents so these currents bound currents do not uh actually uh get transported from one end to the other and they are just circulating around each of the nuclei and but they still constitute currents now in many materials these currents are producing magnetic dioles which are randomly oriented and so the

00:14:44 material does not produce a a magnetic field outside the material there's no magnetic field generated because they're all randomly oriented now because you can represent each um magnetic dipole as a current which is flowing going like this and we can Define so we have magnetic dipoles small small dipoles miniature dipoles each atom represents a dipole and so in the case just like in the case of dialectric we had introduced a concept called polarization so if you have take a medium recall if you take a medium and

00:15:19 put it in an electric field external electric field the electric field generat small small dipoles each atom becomes a dipole electric dipole and we then find the total dipole moment per unit volume electric dipole moment per unit volume which we had called polarization similarly we will introduce A New Concept here which is called magnetization magnetization is the dipole moment this is magnetization M Vector M Vector is the dipole magnetic dipole moment per unit volume so you take a small element uh

00:16:13 infinite esal volume of the material the small volume should contain thousands of atoms and then you calculate the total Magnetic Moment of the small volume so I take a volume Delta v i sum up all the magnetic moments of all the constituting atoms to get the total Magnetic Moment please remember Magnetic Moment is a vector so I must add all the magnetic vectors vectorially so I get the total Magnetic Moment of the small volume and find out the limit as the volume tend to zero so we will get a magnetization and

00:16:46 then magnetization implies that the material has a Magnetic Moment per unit volume and a material which is uh which has this magnetic type of moment is is called magnet ized magnetized medium so when you place a medium in an external magnetic field the external magnetic field Alters the magnetic structure of the atoms within the material and magnetizes the medium just like an external electric field polarizes a dialectric which means creates electric dipoles within the material a material placed in

00:17:34 an external magnetic field also magnetizes the material the medium and the medium is said to be magnetized in the presence of an external magnetic field so we will consider a very simple model to understand the Magnetic Moment of atoms this is the model which was proposed by Neils bore and in um 1911 an atomic model in which the propos proposal was I have a nucleus and I have electrons revolving around the nucleus please remember um to describe the atoms I need a quantum mechanics which is beyond the scope of

00:18:22 this course here but in a simple picture I can assume that the atom consists of nucleus at the center POS charge nucleus and the electron are revolving around the nucleus so this electron motion like this constitutes a current and I can calculate what is this current and once I have a current I can also calculate the magnetic dipole moment of this so let me assume this is an orbit is circular of radius R so and let me assume the velocity of the electron is equal to V radius of the orbit R so I have an electron circulating

00:19:17 around the nucleus hro distance are from the nucleus and let me assume that the orbit is circular so the time taken for one revolution of the electron T is equal to so if if the electron starts from here and goes one full circle it has traveled a distance 2 pi r with a velocity B so the time taken is 2i R by V so the time taken for one reolution is 2 pi r by V so I can calculate the number of revolutions per unit time is equal to 1 by T which is equal to V by 2i R it takes a Time t for one revolution

00:20:24 so the number of revolutions per unit time is 1 by T which is V by 2 r so this that means if I'm positioning myself at a point here so many times the charge will cross B and because the charge of the electron is e this will constitute a constitute a current so I can calculate the current as the charge multiplied by the number of Revolution per second so the charge crosses this point any point on the circle 1X T * per second each time the charge crosses the charge Crossing is e so the current is essentially the charge

00:21:07 Crossing per unit time which is e by T so this is nothing but e v by 2i R so that's a current let we call it I so this electron orbiting around the nucleus constitutes a current given by EV by 2i R now if you have a current in a loop like this we know that this also constitutes a magnetic dipole so I can immediately calculate the dipole moment magnetic dipole moment m is equal to current into area I'm calculate the magnitude of the dipole moment so at every Point there's a current which is I and the current has a

00:22:00 it's a loop of radius R so the magnetic dipole moment is I * PK R square which is equal to e b by 2 pi r into < r² which is equal to e v r by 2 pi cancels over R cancel over EVR by 2 so that is the magnetic dipole moment of the of this Loop here so this dipole moment will then generate a magnetic field and we've already seen what is the magnetic field generated by a dipole along the Axis or in the plane perpendicular and in in principle you you should be able to calculate the magnetic field generated by the dipole

00:22:40 at all points but so this magnetic dipole will generate its own electric field it's magnetic field and I can relate this dipole moment to the angular momentum of the of the DI of the spinning electron so what is the angular momentum L is equal to mass of the electron which I call me into V * R MVR is the angular momentum that is equal to mass of the electron so me is the mass of the electron here please note m is representing the dipole moment and me represents the mass of the electron so I can use these two

00:23:36 equations to write relationship between dipole mement and angular momentum so m is equal to e by 2 m e * l so I have replaced I have replaced VR by L by m e and I get e by 2 me into L now magnetic dipole moment is a vector angular momentum is a vector so let me convert this into a vector equation so now see here the electron is spinning like this in this direction and electron is a negatively charged particle so actually the current is going in this direction so when the current goes like this dipole moment is pointing

00:24:25 downward a con a current constituted like this will will cons will constitute a magnetic dipole moment which is pointing downward but the electron is spinning like this so the angular momentum is pointing upward please note electron is spinning like this so it has an angular momentum pointing upward electron spinning like this constitutes a current which is in this direction in the opposite direction and a current going like this will produce a magnetic dipole moment which is pointing downward which means in this case the

00:24:55 dipole moment and angular momentum are in opposite directions so in the vector form I can write m is equal to - e by 2 m * L Vector so dipole moment and the angular momentum are related to this equation and this equation we have obtained classically by U looking at the atom to be consisting of electrons which are revolving around the nucleus and I get a relationship connecting the dipole moment and the angular momentum now I need to uh bring in a little bit of quantum mechanics here it is found

00:25:36 using quantum mechanical principles that angular momentum cannot have arbitrary values now this is not obtained classically by this argument but if I use quantum mechanics I find that the angular momentum cannot have arbitrary values but so according to quantum mechanics L can have only L be can only be multiples of this quantity which is equal to n by 2 pi and N is an integer that means the Dio The angular momentum can only be integral multiples of this H cross which is H by 2 pi H is the Plank's

00:26:36 constant which is equal to approximately 6. 626 10us 34 JC now this is a relationship from quantum mechanics that the angular momentum of the electron can only be multiples of H cross and that is NH H cross and so I also find now here that if L can has to be of the form this I can write down the smallest value of magnetic dipole moment the fundamental unit of magnetic dipole moment m is equal to so I had e by 2 m into into L till smallest value of L is H by 2 pi so I will have l e by 2 me into H by 2 pi which gives me

00:27:44 e by 4 Pi fundamental unit of magnetic dipole moment is eh by 4 Pi me this is called the bore Magneton so you can substitute so I can write the B magnetron as MB you can substitute the electronic charge the planks constant and the mass of electron and you will find this approximately 9.27 4 into 10us 24 amp met squ so what we find is the dipole moment is a multiple of this quantity which is the fundamental unit of dipole moment and so the I can associate with the orbital motion of the electron in an

00:28:44 atom an orbital dipole moment which is represented by the bore Magneton so orbiting electrons electrons which are orbiting around the nucleus have their own Magnetic Moment which is also referred to as has orbital Magnetic Moment this are called orbital Magnetic Moment each of the circulating electrons within the atom has an orbital angular moment and the total moment can be obtained by adding the vectorially the orbital magnetic magnetic moments of each of the individual atoms now it is also found that apart from

00:29:32 this Magnetic Moment electrons also possess another very important quantity which is called the spin angular moment spin Magnetic Moment now spin is is an intrinsic inic quantity much like much like charge and mass of the of the particle and associated with this spin is a magnetic moment and the Magnetic Moment spin Magnetic Moment has a magnitude of almost one B Magneton so in an atom you have electrons which are orbiting the nucleus we associate a magnetic moment with the orbital motion called the

00:31:08 orbital Magnetic Moment each of the electron is characterized by a spin an intrinsic quantity called spin and along with this spin we associate another Magnetic Moment called the spin Magnetic Moment so the total Magnetic Moment of the atom will actually be obtained by vectorially adding the orbital angular momentum of all the electrons and the spin angular momentum of moment of the all the electrons to get the total Magnetic Moment of the atom so it is these magnetic moments of the atom which constitutes which constitute

00:31:41 the dipole inside the material and these dipoles May produce their own magnetic field so when you place a a medium inside a magnetic field we are actually modifying the magnetic property of the atoms and that leads to a uh and the medium itself magnetic property of the medium and that leads to a generation of magnetic field by the medium and what You observe total magnetic field is the sum of the applied magnetic field and the magnetic field generated by this magnetized medium now I want to look at physical

00:32:12 interpretation of this magnetization so what is the physical picture of a uniformly magnetized medium remember in the case of electrostatics we had a physical picture of what is the meaning of a uniformly polarized medium we showed that a uniformly polarized medium uh is equivalent to generation of surface charges uh at the surface sures of the medium and those surface charges essentially generate bound charges though they they generate a magnet electric field and we calculated at the total electric field and use them in

00:33:08 Gus's law in a similar picture I want to understand what happens what is a physical mechanism what is a physical understanding of a magnetized U uniformly magnetized medium now so let me consider a uniformly magnetized medium with magnetization M so what it implies is that the medium consists of small atomic dipoles magnetic dipoles and so let me try to represent these dipoles so I have a let me take a a medium like this and so let me look at I'm looking at the top picture of the medium and I have Atomic

00:34:03 dipoles so let me assume that magnetic magnetization is pointing towards me so there are Atomic dipoles like this highly magnified picture I'm trying to draw here so the these are all Atomic currents they are circulating currents and each one of them is a small magnetic tiny magnetic dipole so the material consists of a large number of these magnetic dipoles and because it uniformly magnetized what what you can see is at any point inside for example this point you have a current flowing like this because of the

00:34:42 upper Loop and a current flowing in the reverse Direction because of the lower loop and the currents are equal so the net current at any point inside the medium is zero at any point you see there is a current flowing clockwise and there is a current flowing in the reverse Direction at the same point with a net current being zero so in in a uniformly magnetized medium there seems to be no effective current within the medium but look at the surface at the surface there is a current flowing like this being this

00:35:10 there's a current flowing like this here there's a current flowing like this here so this becomes equivalent to a current flowing in the outside in the surface like this I am picturez a magnetized uniformly magnetized medium a uniformly magn mag ized medium means that there are tiny dipoles in the medium and if the magnetization is pointing up these tiny dipoles constitute current flowing like this in small loops and it's uniformly magnetized medium so these currents are all equal and at any point if you see here

00:35:47 there is a current flowing to the right and there's also a current flowing to the left because of the lower loop so the net current Crossing this point is zero similarly if you take any point within the medium you will find that the net current passing through that point is zero so this cancellation is there within the volume of the medium but at the surface for example on this surface you see that there is a current flowing like this here there is another loop there's a current flowing like this here

00:36:12 there's a current flowing like this here so this becomes effectively equivalent to current flowing on the surface so a uniformly magnetized medium is sort of equivalent to a a medium in which there is a surface current current flowing on the surface of the medium so let me try to relate this surface current let me try to find out what is the surface current what is the relationship of surface current to the magnetization so to do this we will take a cylindrical sample of area a and thickness t t

00:37:00 polarized sorry magnetized uniformly magnetized along its axis so it is like this something like this magnetization is pointing up this thickness is T and this area is a so let me draw the uh side picture there is this medium here this thickness is T and magnetization is pointing upwards uniformly magnetized P so I have a cylindrical sample uniformly magnetized parallel to the axis the axis of the cylinder is vertical of thickness T and cross-sectional area a now remember magnetization is the magnetic dipole moment per unit

00:38:06 volume this sample has a volume a * T so the D magnetic dipole moment of the sample of the sample is equal to M * a * T magnetization is dipole magnetic dipole moment per unit volume so magnetic dipole moment per unit volume into volume of the sample gives me the magnetic dipole moment of this sample now I have just now shown you that a uniformly magnetized sample is equivalent to a current passing on the surface so this must be equivalent to so if I have a uniformly magnetized sample like this this must be equalent

00:39:06 to current going like this please remember this is not an actual current which is Flowing this not a conduction current these are bound currents these are current generated by the bound electrons in the atom so let me recall here these are currents which are current generated within the medium with the part of the part of the atoms it is not that one single electron is Flowing like this or in the other direction it is made up of tiny currents and net the net effect is effect is is to have a current in on the

00:39:40 surface of the sample so if I look at my problem which I'm considering this sample of radius a of thickness T is equivalent to a sample of thickness T and area a in which the current is Flowing like this remember there will be Loops like this these Loops are canceling off everywhere inside the medium except on the surface so there seems to be current flowing like this so I can write the Magnetic Moment also as current into area the area of the sample is a magnetization is like this this is magnetization into volume is the

00:40:30 magnetic dipole moment the magnetized sample is equivalent to a surface current flowing like this magnetic dipole moment is also sub the current into the area the current is Flowing like this area is in this direction here and so I can equate these two quantities to find out M * a * T must be equal to I * a and this gives me this implies magnetization is equal to I by T so magnetization is nothing but current per unit length on the surface please note that this surface is perpendicular to magnetization if you go back to the

00:41:32 earlier picture here uh this picture here here the there is no current in the upper and lower surfaces the current is only on the side surface because the currents are in this orientation and if you uh if you can imagine the current is actually the net effective current is Flowing on the surface and there's no effective current on the upper surface so please remember the surface along which the equivalent current is Flowing is perpendicular to magnetization here so magnetization is nothing but

00:42:07 current per unit length so in this example of a magnetized sample which is magnetized like this this is the magnetization here and the effective current is like this and this magnetization corresponds to a current per unit length of I BYT now this gives me a very nice way to u to imagine uh to calculate the to estimate the magnetic field of this and let me go back and recall a solenoid solenoid having n turns per unit length and carrying current I so let me draw the solenoid here so you had we had considered this

00:42:54 earlier so these are current carrying where current current is going like this this is my Z axis and we had calculated the magnetic field B is equal to Mu n i k uniform magnetic field within the solenoid is inside and zero outside an infinitely long solenoid creates a uniform magnetic field within the solenoid of mu ni K cap outside the solenoid the magnetic field is zero we had calculated this now this solenoid is assumed to be very closely bound so I can imagine as if the solenoid has a current going like

00:43:56 this these are wires carrying actual actual current so if you take a unit length what will be the current per unit length in a unit length there will be n turns each turn carrying a current I so current per unit length will be n i please note if I take unit length of the solenoid there will be n turns each turn carrying a current I so the total current crossing a unit length in this direction is n * I so this n * I is nothing but current per unit length of the solenoid so the magnetic field produced

00:44:47 by solenoid is Mu time current per unit length into K cap inside and zero outside now this gives me an idea that because a uniformly magnetized sample suppose let me take a uniformly magnetized cylinder magnetized in this direction this magnetized sample is equivalent to a uh a current per unit length of M so comparing with a solenoid this is very similar to a solenoid in a solenoid I had a current per unit length of Ni produce a magnetic field which is Mu * n into K cap a uniformly magnetized cylinder

00:45:45 magnetized parallel to the axis is equivalent to a solenoid because both of them have a current passing along the surface in a solenoid the current per unit length is n in a uniformly magnetized cylinder the current per unit length is M so I can immediately write for the current the magnetic field of a magnetized magnetic field of a uniformly magnetized cylinder magnetized parallel to the axis b equal to Mu * m * K cap which is nothing but mu * m because m is along the KC Direction M K cap is M Vector

00:46:50 so first of all I have tried to show that a uniformly magnetized object is equivalent to a current on the surface the current per unit length is simply magnetization just remember the surface is perpendicular to magnetization I'm considering so I have I have equated a magnetize sample to a surface current and these currents again let me emphasize these currents are not conduction current these are bound currents these are currents which are bound to the atoms each atom has its own current it's like the bound charges in

00:47:27 polarization the dialectric these are bound currents so I first showed you that magnetized magnetization gives me a surface current uniformly magnetized sample has a surface current then I showed that the surface current is actually nothing but magnetization so a MAG uniformly magnetized sample has a surface current which is M on the surface which is perpendicular to M Vector then I'm having an analogy of this problem with a solenoid because for a solenoid I know the magnetic field I know the magnetic field of a solenoid is

00:48:03 given by this equation and I can interpret this quantity n * I as nothing but the current per unit length because if I take a unit length of the solenoid in a unit length I have n turns and each turn carrying a current I so the current per unit length is n * I so all I need to do to calculate the magnetic field of a uniformly magnetized cylindrical sample magnetized parallel to the axis is I know that this is equivalent to a surface current of M and that gives me a magnetic field which is B is equal to Mu * m

00:48:44 Vector so this particular sample this cylindrical sample which is magnetized parall to the axis creates a magnetic field mu M inside and is equal zero outside I'm assuming a effectively infinitely long magneti sample so inside the sample the magnetization the magnetic field is Mu M and outside the sample it is zero now I can extend this argument to look at the following problem I have a sample and I W wires on it I found wires on a sample now so this is now a solenoid containing a medium inside

00:49:42 now so this is the medium so I have current flowing in like this and flowing out like this so uh solenoid n terms per unit length carrying current I now I wish to calculate what is the magnetic field inside now this external magnetic field generated by the solenoid will magnetize the medium that means it will generate a magnetic dipole moment per unit volume inside the medium and that magnetic dipole moment will be equivalent to a magnetization and so let me call the magnetization M the magnetic field is parallel to the

00:50:47 axis in the simplest example the magnetization is also parall to the axis and so what is the total magnetic field inside p is equal to now the magnetic field because of the conduction current is Mu * n i * K cap the magnetic field due to the magnetization is Mu M please note there are two components of magnetic field now the conduction current which is flowing in the wire is actually producing magnetic field mu n k inside this magnetic field magnetizes the medium which means it makes we will come to more discussion of the

00:51:40 properties of the media magnetic properties of the media but the magnetic field external magnetic field when magnetize the medium just like an electric field polarizes the medium by polarizes the dialectric an external magnetic field magnetizes the medium and I get a magnetization m so the total field is given by the sum of the field generated by the conduction current flowing in the wire and the magnetization so I can write this equation as B by mu minus m is equal to n i k now I introduce a new

00:52:16 Vector we Define H is equal to B by muus m we Define a new Vector H Vector which is B by mu minus M so I can substitute H Vector into this equation and I get H is equal to n i * K now please remember H Vector contains the properties of the medium through the magnetization and on the right hand side there is no medium there is no uh aspect of the medium at all on the right hand side I've have defined a new Vector H Vector which contains the medium property of M Vector I get a new form of ampers law which is integral h.

00:53:15 DL if is equal to free current so we this is a new form of amp slope we will discuss some examples with this and this is very similar to modification of Gus's law from U electric field form to displacement current form and this is a very very interesting form of ampus law we will discuss some a few examples and then discuss about magnetic properties of different kinds of materials thank you [Music]