"st Class:-B.tech 1 yearChapter- MAGNETIC PROPERTIESMagnetic dipole moment: A system having two opposite magnetic poles separated by a distance dis called as a magnetic dipole. If m is magnetic pole strength and l is the length of the magnet thenits dipole moment isMagnetic induction (or) Magnetic flux density(B)=The magnetic induction in any material isthe number of lines of magnetic force passing through unit area perpendicularly.Its nits is weber/ or teslaMagnetic field intensity(or)strength(H)=Magnetic field intensity at any point in the magnetic fieldis the force experienced by an unit north pole placed at thet point.Its units is ampereThe magnetic induction B due to a magnetic field of intensity (H) applied in vaccum is related byWhere is the permeability of free space (vaccum)= HInstead in vaccum if the field is applied in a medium the magnetic induction in the solids is givenbyB=µH where µ is permeability of the solid material through which the magnetic lines of forcepass.Magnetic permeability(µ)=magnetic permeability of any material is the ratio of the magneticinduction in the sample to the applied magnetic field intensity.relative permeability( )=it is the ratio between the permeability of the medium to permeability ofthe free spaceMagnetization (or)intensity of magnetization(I)=the term of magnetization is the process ofconverting a non magnetic material into a magnetic material .it measures the magnetization of themagnetizedIt is also defined as the magnetic moment per unit volumeIts units is ampere Magnetic susceptibility(x)=the ratio of intensity of magnetization (I) produced to the magneticfield strength (H) in the which the material is placedClassification of magnetic materials:By the application of magnetic field some materials will not show any effect that are called nonmagnetic materials and those which show some effects are called magnetic materialsAll magnetic materials magnetized in an applied external magnetic field.Depending on the direction and magnitude of magnetization and also the effect of temperature onmagnetic properties,all magnetic materials are classified into dia,para and ferromagnetic materials.Two more classes of material have structure very close to ferro magnetic materials, but possesquiet different magnetic properties. They are anti-ferro magnetic and ferromagnetic materials.The number of orientations of electronic orbits in an atom be such that vectoe sum ofmagnetic moment is zeroThe external field will cause a rotation action on the individual electronic orbits this produces aninduced magnetic moment which is in the direction opposite to the field and hence tenda todecrease the magnetic induction present in the substance. Thus the diamagnetic is thephenomena by which the induced magnetic moment is always in the opposite direction of theapplied field.Properties of diamagnetic materials1 Diamagnetic material get magnetized in a direction opposite to the magnetic field.2 Weak repulsion is the characteristic of diamagnetism3 permanent dipoles are absent4 Relative permeability is less than one but positive5 The magnetic susceptibility is negative and small. It is not effected by temperature.6 Diamagnetism is universal i.e all materials when exposed to external magnetic fields,tendto develop magnetic moments opposite in the direction to the applied field.7 When placed inside a magnetic field, magnetic lines of force are replaced asParamagnetismThe number of orientations of orbital and spin magnetic moments be such that he vector sum ofmagnetic moment is not zero and there is a resultant magnetic moment in each atom even in theabsence of applied field.The net magnetic moments of the atoms are arranged in random directions because of thermalfluctuations ,in the absence of external magnetic field.Hence there is no magnetization. If we apply the external magnetic field there is an enormous magnetic moment along the fielddirection and the magnetic induction will be increase.Thus induced magnetism is the sourceof paramagnetism.Preperties of paramagnetism materials:1 paramagnetic materials get magnetized in the direction of the magnetic field.2 Weak attraction is characteristic of paramagnetism3 paramgnetic material posses permanent magnetic dipoles.4 Relative permeability is greater than one but small i.e this indicate that when paramagneticsubstance is placed in a uniform magnetic field the field inside the material will be more thanthe applied field.5 The magnetic susceptibility is small and positive the magnetic susceptibility of paramagneticsis inversely proportional to absolute temperaturei.e x=C/T this is called curie law ,c is calles curie constant6 Paramagnetic susceptibility is independent of the applied field strength.7 Spin alignment is random 8 When placed inside a magnetic field it attracts the magnetic lines of force9 Some of the material which exhibit the paramagnetism are aluminium,manganese ,oxygen.Ferromagnetism:Ferromagnetism arises when the magnetic moments of adjacent atoms are arranged in a regularorder i.e all pointing in the same direction .The ferromagnetic substance thus posses a magneticmoment even in the absence of the applied magnetic field ,this magnetization is known as thespontaneous magnetizationThere is a special form of interaction called “exchange “coupling occurring between adjacent atoms,coupling their magnetic moment together in rigid parallelism.Properties of ferromagnetic materials1 In ferromagnetism materials, large magnetization occurs in the direction of the field.2 Strong attraction is the characteristic of ferromagnetism.3 They posses spontaneous magnetization.4 The relative permeability is very high for Ferro magnetic.5 The magnetic susceptibility is positive and very high.6 Magnetic susceptibility is fairly high and constant up to a certain temperature accordingthe equation X= C= curie constant Curie temperature7 Ferromagnetism is due to the existence of magnetic domains which can be spontaneouslymagnetized.8 Exhibit hysteresis.9 Spin alignment is parallel in the same direction10 When placed inside a magnetic field it attracts the magnetic lines of forces very strongly11 Permanent and electro magnetic are made using ferromagnetic materials.12 Example iron, nickel, cobalt.Antiferro magnetismAnti ferromagnetism arises when the spin magnetic moment of neighbouring atoms are oriented inan antiparllel orderIn the absence of external external magnetic field the magnetization of anti ferro magnetic specimenwill be zero,because of anti parallel and equal spin magnetic moment.By the application of the external magnetic field a small magnetization in the direction of the appliedmagnetic field takes place this magnetization varies with temperature as shownThe susceptibility increases with an increase of temperature upto called as neel temperatureAt neel temperature the magnetization or susceptibility is maximum and above it the magnetizationdecreases with increasing temperature according to the relationX= ,C =is curie constant ?=paramagnetic curie temperatureThe decrease of magnetization with an increase of temperature is a property of of the paramagneticsubstance,therefore the specimen becomes paramagnetic aboveExamples Mno,Nio,Feo,Mns etc XTFerrimagnetism and property of ferromagnetic materials(ferrites) Ferrimagnetic substance are those in which the atomic or ionic dipoles in one diection are ofunequal magnitudes ,this alignment of dipole gives a net magnetization and is the property ofthose magnetic substance which have two or more different kind of atoms.In ferri magnetic materials there may be large net magnetization as compared to anti Ferro magneticmaterials, due to the resultant of anti parallel alignment of neighboring dipoles of unequalmagnitudes.Ferrimagnetic materials generally known as ferrites consist of two or more different kind of atoms— their formula is Where stands for a suitable divalent metal ion such as , , , , etc, isa trivalent ferric ion. The magnetization of ferromagnetic material material can be understood by taking one of the materials as an example say ferrous ferrite(i) In ferrous ferrite we have two types of ions i.e.(ii) here iona has six electrons in 3d sheels out of 6 electrons two electrons are paired witheach other and hence left with 4 unpaired electrons Therefore gives rise to 4 Bohrmagneton(iii) ions has five electrons in 3d shell and hence all these 5 are unpaired electrons Therefore give rise to 5 Bohr magneton Since we have two ,totally the give rise to 2x5=10 bohe magneton Therefore total magnetization of + =4+10+14 bohr magneton. Theoretically we get 14 µB(bohr magneton) but experimentally the total magnetic moment is only4.08µB.The reason is if all the spins are aligned parallel then we get the total magnetization as 14µBBut in ferrites half of the magnetic spins of ions are parallel to one direction and the remaining halfof ions are parallel in opposite direction as shown in fig hence they cancel each other.Therefore net magnetic moment is only due to ions alone i.e .hence we get the totalmagnetization as 4µB which is a good agreement with the experimental value.Application of ferrites(ferromagnetic substance)1 They are used to produce ultrasonics by magnetization principle.2 Ferrites are used in audio and video transformers.3 Ferrites rods are used in radio receivers to increase the sensitivity.4 They are also used for power limiting and harmonic generation.5 Ferrites are used in computers and data processing circuits6 ferrites are used in switching circuits and in storage devices of computers.7 Ferrites are not metals but their resistivity lies in the range of insulators or semiconductors.Explanation of hysteresis curve based on domain theory of ferromagnetism:Domain theory of ferromagnetismAccording to Weiss a virgin specimen of ferromagnetic material consist of a number region ordomains which are spontaneously magnetized .In each domain spontaneous magnetization is dueto parallel alignment of all magnetic dipolesThe direction of spontaneous magnetization varies from domain to domainThe resultant magnetization may hence br zero or nerly zeroWhen an external field is applied there are two possible ways of alignment of domains(i)By motion of domain walls: the volume of domains that are favourably oriented with therespect to the magnetizing field increases at the cost of those that are unfavourably oriented fig(b) (ii)By rotation of domains:when the applied magnetic field is strong rotation of the direction ofmagnetization occurs in the direction of the field.fig(c)H H Fig(a) fig(b) fig(c)Hysteresis curvesHysteresis : lagging of magnetization behind the magnetizing field(H)We know when the ferro magnetic material is subjected to external field ,there is increase inthe value of the resultant magnetic moment due to two process(i)the movement of domain walls(ii)rotation of domain walls When a weak magnetic field is applied the domains are aligned parallel to the field and in the easydirection of magnetization grow in size at the expense of the less favourably oriented domains.This result in the bloch wall (or)domain wall movement and when the weak field is removed thedomains reverse back to their original state .this reversible wall displacement is indicated by OA themagnetization curve.When the field becomes stronger han the domain wall movement continues and it is mostlyreversible movement .this is indicated by path AB of the graph .the phenomena of hysteresis is dueto the irreversibility.At the point B all domains have got magnetized along their easy directionApplication of still higher field rotates the domains into the field direction indicated by BC.Once the domains rotation is complete the specimen is saturated denoted by C.Thus the specimen is said to be attain the maximum magnetization .at this position if the externalfield is removed (H=0),the magnetic induction B will not fall rapidly to zero ,but falls to D rather thanO this shows that even when the applied field is zero the material still posses some magneticinduction(OD)which is called residual magnetism or retentivity.Actually after the removal of the external field the specimen will try to attain the originalconfiguration by the movement of domain wall .But this movement is stopped due to the presenceof impurities, lattice imperfections.Therefore to overcome this a large amount of reverse magnetic field ( ) is applied to the specimen.the amount of energy spent to reduce the magnetization (B) to zero is called“c oe r ci t i v i t y ” represented by OE in the fig.HSTERESIS: lagging of magnetization (B) behind the magnetizing field (H) is called hysteresis.Hysteresis loss: It is the loss of energy in taking a ferromagnetic body through a complete cycle ofmagnetization and this loss is represented by the area enclosed by the hysteresis loop.Hard and soft magnetic materials: Based on the area of hysteresis, magnetic materials canbe classified into hard and soft magnetic materials.Hard magnetic materials Soft magnetic materials(i) Hard magnetic materials have large hyster- (i)Soft magnetic materials have low hysteresis lossdueesis loss due to large hysteresis is loop area to small hysteresis loop area.(ii)in these material the domain wall movement (ii) in these materials the domain wall movement isrelati-76is difficult because of presence of impurities vely easier .even for small changes in themagnetizing and crystal imperfection and it is irreversible field magnetization changes by large amount.in nature (iii) The coercitivity and retentivity are large (iii) )the coercitivity and retentivity aresmall .theseHence these materials cannot be easily magne- materials can be easily magnetized anddemagnetized.Tised and demagnetized(iv)In these materials because of the (iv)since these materials free from irregular themagnetpresence of impuroties and crystal imperfection ostatic energy is very small.the mechanical strain is more hence magnetostatic energy is loss .(v)these materials have large values of permeability(v)these materials have small values of permeaandBility and susceptibility. Susceptibility. (vi)they are used to make permanent magnets. (vi)there are used to make electromagnets. (vii)eample copper nickel iron alloys,copper (vii)examples:iron silicon alloys,ferrous nickel alloys, nickel Cobalt alloys. Ferrites. (viii)applications:for production of magnetic (vii)mainly used in electromagnetic machinery and Detectors ,microphones,damping devices. And transformer cores.used in switching circuits,microwave isolators.Origin of magnetic moment.In atoms the permanent magnetic moments can arises due to the following.1 the orbital magnetic moment of the electrons2 the spin magnetic moment of the electrons.3 the spin magnetic moment of nucleus.Orbital magnetic moment of the electrons and bohr magneton:77 We know that in an atom electrons revolve round the nucleus in different circular orbits.let m be themass of the electron and r the radius of the orbit in which it moves with angular velocity wWe can calculate the electric current due to the moving electron.Current I=charge flow/unit time= -e/TWhere T is the time taken for one revolutionI = ( )We know that the current flowing through a circular coil produces a magnetic field in a directionperpendicular to the area of the coil and it is identical to a magnetic moment produced by such adipole is= I.A= = = = LWhere L= mw is the orbital angular moment of the electronThe possible orientation of the angular momentum vector when placed in an external magnetic field=== == - = bohr magneton. 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