10. Magnetism. ) it is. S G appropriate to call the magnetic pole

Transcription

1 10 agnetism The wor magnetism is erive from iron ore magnetite (Fe 3 O 4, which was foun in the islan of magnesia in Greece It is believe that the Chinese ha known the property of the magnet even in 000 BC an they use magnetic compass neele for navigation in 1100 AD But it was Gilbert who lai the founation for magnetism an ha suggeste that Earth itself behaves as a giant bar magnet The fiel at the surface of the Earth is approximately 10-4 T an the fiel extens upto a height of nearly five times the raius of the Earth 101 Earth s magnetic fiel an magnetic elements A freely suspene magnetic neele at a point on Earth comes to rest approximately along the m geographical north - south irection This shows that the Earth behaves G like a huge magnetic ipole with its magnetic poles near its geographical poles ince the north pole of the magnetic neele approximately points towars geographic north ( G it is G appropriate to call the magnetic pole m near G as the magnetic south pole of Earth m Also, the pole near G is the magnetic north pole of the Earth ( m (Fig101 Fig 101 agnetic fiel of Earth The Earth s magnetic fiel at any point on the Earth can be completely efine in terms of certain quantities calle magnetic elements of the Earth, namely (i Declination or the magnetic variation θ (ii Dip or inclination δ an (iii The horizontal component of the Earth s magnetic fiel B h 173

2 Causes of the Earth s magnetism The exact cause of the Earth s magnetism is not known even toay However, some important factors which may be the cause of Earth s magnetism are: (i agnetic masses in the Earth (ii Electric currents in the Earth (iii Electric currents in the upper regions of the atmosphere (iv Raiations from the un (v Action of moon etc However, it is believe that the Earth s magnetic fiel is ue to the molten charge metallic flui insie the Earth s surface with a core of raius about 3500 km compare to the Earth s raius of 6400 km 1011 Bar magnet The iron ore magnetite which attracts small pieces of iron, cobalt, nickel etc is a natural magnet The natural magnets have irregular shape an they are weak A piece of iron or steel acquires magnetic properties when it is rubbe with a magnet uch magnets mae out of iron or steel are artificial magnets Artificial magnets can have esire shape an esire strength If the artificial magnet is in the form of a rectangular or cylinrical bar, it is calle a bar magnet 101 Basic properties of magnets (i When the magnet is ippe in iron filings, they cling to the ens of the magnet The attraction is maximum at the two ens of the magnet These ens are calle poles of the magnet (ii When a magnet is freely suspene, it always points along north-south irection The pole pointing towars geographic north is calle north pole an the pole which points towars geographic south is calle south pole (iii agnetic poles always exist in pairs (ie isolate magnetic pole oes not exist (iv The magnetic length of a magnet is always less than its geometric length, because the poles are situate a little inwars from the free ens of the magnet (But for the purpose of calculation the 174

3 geometric length is always taken as magnetic length (v Like poles repel each other an unlike poles attract each other orth pole of a magnet when brought near north pole of another magnet, we can observe repulsion, but when the north pole of one magnet is brought near south pole of another magnet, we observe attraction (vi The force of attraction or repulsion between two magnetic poles is given by Coulomb s inverse square law ote : In recent ays, the concept of magnetic poles has been completely change The origin of magnetism is trace only ue to the flow of current But anyhow, we have retaine the conventional iea of magnetic poles in this chapter Pole strength is enote by m an its unit is ampere metre agnetic moment ince any magnet has two poles, it is also calle a magnetic ipole The magnetic moment of a magnet is efine as the prouct of the pole strength an the istance between the two poles If m is the pole strength of each pole an l is the istance between the poles, the magnetic moment = m ( l agnetic moment is a vector quantity It is enote by Its unit is A m Its irection is from south pole to north pole agnetic fiel agnetic fiel is the space in which a magnetic pole experiences a force or it is the space aroun a magnet in which the influence of the magnet is felt agnetic inuction agnetic inuction is the funamental character of a magnetic fiel at a point agnetic inuction at a point in a magnetic fiel is the force experience by unit north pole place at that point It is enote by B Its unit is It is a vector quantity It is also calle as magnetic flux Am ensity 175

4 If a magnetic pole of strength m place at a point in a magnetic fiel experiences a force F, the magnetic inuction at that point is F B = m agnetic lines of force A magnetic fiel is better stuie by rawing as many number of magnetic lines of force as possible A magnetic line of force is a line along which a free isolate north pole woul travel when it is place in the magnetic fiel Properties of magnetic lines of force (i agnetic lines of forces are close continuous curves, extening through the boy of the magnet (ii The irection of line of force is from north pole to south pole outsie the magnet while it is from south pole to north pole insie the magnet (iii The tangent to the magnetic line of force at any point gives the irection of magnetic fiel at that point (ie it gives the irection of magnetic inuction ( B at that point (iv They never intersect each other (v They crow where the magnetic fiel is strong an thin out where the fiel is weak agnetic flux an magnetic flux ensity The number of magnetic lines of force passing through an area A is calle magnetic flux It is enote by φ Its unit is weber It is a scalar quantity The number of magnetic lines of force crossing unit area kept normal to the irection of line of force is magnetic flux ensity Its unit is Wb m or tesla or A 1 m 1 agnetic flux φ = B A Uniform an non-uniform magnetic fiel agnetic fiel is sai to be uniform if the magnetic inuction has the same magnitue an the same irection at all Fig 10 Uniform agneticfiel 176

5 the points in the region It is represente by rawing parallel lines (Fig 10 An example of uniform magnetic fiel over a wie area is the Earth s magnetic fiel If the magnetic inuction varies in magnitue an irection at ifferent points in a region, the magnetic fiel is sai to be non-uniform The Fig 103 on-uniform magnetic fiel magnetic fiel ue to a bar magnet is non-uniform It is represente by convergent or ivergent lines (Fig Force between two magnetic poles In 1785, Coulomb mae use of his torsion balance an iscovere the law governing the force between the two magnetic poles Coulomb s inverse square law Coulomb s inverse square law states that the force of attraction or repulsion between the two magnetic poles is irectly proportional to the prouct of their pole strengths an inversely proportional to the square of the istance between them If m 1 an m are the pole strengths of two magnetic poles separate by a istance of in a meium, then 1 F α m 1 m an F α mm 1 F α mm 1 F = k where k is the constant of proportionality an k = 4 µ π permeability of the meium where µ is the But µ = µ o µ r 177

6 µ r = µ µ o where µ r - relative permeability of the meium µ o - permeability of free space or vacuum Let m 1 = m = 1 an = 1 m µ o k = 4π In free space, µ o = 4π 10-7 H m -1 F = F = m m F = 10-7 Therefore, unit pole is efine as that pole which when place at a istance of 1 metre in free space or air from an equal an similar pole, repels it with a force of agnetic inuction at a point along the axial line ue to a magnetic ipole (Bar magnet is the bar magnet of length l an of pole strength m P is a point on the axial line at a istance from its mi point O (Fig 104 Accoring to inverse square law, F = µ o mm 1 4π agnetic inuction (B 1 at P ue to north pole of the magnet, µ o m F B 1 = along P B= 4π P m µ o m = 4 π along P ( l agnetic inuction (B at P ue to south pole of the magnet, µ o m B = 4π P along P P O Fig 104 agnetic inuction along the axial line 178 l

7 µ o m B = 4 π ( + l along P agnetic inuction at P ue to the bar magnet, B = B 1 B µ o m µ o m B = - 4π ( l 4π ( + l along P µ B = m o π ( l ( + l B = µ o m ( + l ( l 4 π ( l µ o B = m 4 l 4 π ( l µ o B = m l 4 π ( l µ o B = 4 π ( l where = ml (magnetic ipole moment For a short bar magnet, l is very small compare to, hence l is neglecte µ o B = 3 4π The irection of B is along the axial line away from the north pole T B 1 P 104 agnetic inuction at a point along the equatorial line of a bar magnet B is the bar magnet of length l an pole strength m P is a point on the equatorial line at a istance from its mi point O (Fig 105 O l Fig 105 agnetic inuction along the equatorial line 179

8 agnetic inuction (B 1 at P ue to north pole of the magnet, µ o m B 1 = 4π P = 4 ( l along P µ o m π + along P ( P = O + OP agnetic inuction (B at P ue to south pole of the magnet, µ o m B = 4π P = 4 ( l along P µ o m π + along P Resolving B 1 an B into their horizontal an vertical components Vertical components B 1 sin θ an B sin θ are equal an opposite an therefore cancel each other (Fig 106 The horizontal components B 1 cos θ an B cos θ will get ae along PT Resultant magnetic inuction at P ue to the bar magnet is B = B 1 cos θ + B cos θ (along PT µ o m B = 4π + l µ o = 4 B ml π 3/ ( + l µ o = 4 3/ π ( + l l + l µ o + 4 π O O cos θ = = P P, (where = ml For a short bar magnet, l is neglecte µ o B = 3 4π The irection of B is along PT parallel to B 1 B 1 cos T B cos B m l ( + l + l B 1 sin P B sin Fig 106 Components of magnetic fiels 180

9 105 apping of magnetic fiel ue to a bar magnet A bar magnet is place on a plane sheet of a paper A compass neele is place near the north pole of the magnet The north an south poles of the compass are marke by pencil ots The compass neele is shifte an place so that its south pole touches the pencil ot marke for north pole The process is repeate an a series of ots are obtaine The ots are joine as a smooth curve This curve is a magnetic line of force Even though few lines are rawn aroun a bar magnet the magnetic lines exists in all space aroun the magnet (i agnet place with its north pole facing geographic north A sheet of paper is fixe on a rawing boar Using a compass neele, the magnetic meriian is rawn on it A bar magnet is place on the magnetic meriian such that its north pole points towars geographic north Using a compass neele, magnetic lines B H B H P P / of force are rawn aroun the B B magnet (Fig 107 The magnetic lines of force is ue to the combine effect of the magnetic fiel ue to the bar Fig 107 eutral points - equatorial line magnet an Earth It is foun that when the compass is place at points P an P along the equatorial line of the magnet, the compass shows no eflection They are calle neutral points At these points the magnetic fiel ue to the magnet along its equatorial line (B is exactly balance by the horizontal component of the Earth s magnetic fiel (B h Hence, neutral points are efine as the points where the resultant magnetic fiel ue to the magnet an Earth is zero Hence, at neutral points B = B h µ o 4π 3/ ( + l = B h 181

10 (ii agnet place with its south pole facing geographic north A sheet of paper is fixe on a rawing boar Using a compass neele, the magnetic meriian is rawn on it A bar magnet is place on a magnetic meriian such that its B south pole facing geographic north h Using a compass neele, the magnetic P lines of force are rawn aroun the B magnet as shown in Fig 108 The magnetic lines of force is ue to the combine effect of the magnetic fiel ue to the bar magnet an Earth It is foun that when the compass is place at points P an P along the axial line of the magnet, the B h compass shows no eflection They are P / calle neutral points At these points B the magnetic fiel (B ue to the magnet along its axial line is exactly Fig 108 eutral points - axial line balance by the horizontal component of the Earth s magnetic fiel (B h Hence at neutral points, B = B h µ 4 π ( l o = B h 106 Torque on a bar magnet place in a uniform magnetic fiel mb Consier a bar magnet of length l an pole strength m place in a uniform magnetic fiel of mb inuction B at an angle θ with the irection of the fiel (Fig 109 l Fig 109 Torque on a bar magnet A B 18 Due to the magnetic fiel B, a force mb acts on the north pole along the irection of the fiel an a force mb acts on the south pole along the irection opposite to the magnetic fiel

11 These two forces are equal an opposite, hence constitute a couple The torque τ ue to the couple is τ = one of the forces perpenicular istance between them τ = F A = mb A (1 = mb l sin θ τ = B sin θ ( Vectorially, τ = B The irection of τ is perpenicular to the plane containing an B If B = 1 an θ = o Then from equation (, τ = Hence, moment of the magnet is equal to the torque necessary to keep the magnet at right angles to a magnetic fiel of unit magnetic inuction 107 Tangent law A magnetic neele suspene, at a point where there are two crosse magnetic fiels acting at right angles to each other, will come to rest in the irection of the resultant of the two fiels B 1 an B are two uniform magnetic fiels acting at right angles B to each other A magnetic neele mb place in these two fiels will be subjecte to two torques tening mb 1 to rotate the magnet in opposite irections The torque τ 1 ue to l the two equal an opposite B 1 parallel forces mb 1 an mb 1 ten to set the magnet parallel to B 1 imilarly the torque τ ue to mb 1 A the two equal an opposite parallel forces mb an mb mb tens to set the magnet parallel to B In a position where the Fig 1010 Tangent law torques balance each other, the 183

12 magnet comes to rest ow the magnet makes an angle θ with B as shown in the Fig 1010 The eflecting torque ue to the forces mb 1 an mb 1 τ 1 = mb 1 A = mb 1 cos θ = mb 1 l cos θ = l mb 1 cos θ τ 1 = B 1 cos θ imilarly the restoring torque ue to the forces mb an mb τ = mb A = mb l sin θ = lm B sin θ τ = B sin θ At equillibrium, τ 1 = τ B 1 cos θ = B sin θ B 1 = B This is calle Tangent law Invariably, in the applications of tangent law, the restoring magnetic fiel B is the horizontal component of Earth s magnetic fiel B h 108 Deflection magnetometer Deflection magnetometer consists of a small magnetic neele pivote on a sharp support such that it is free to rotate in a horizontal plane A light, thin, long aluminium pointer is fixe perpenicular to the magnetic neele The pointer also rotates along with the neele (Fig Fig 1011 Deflection magnetometer There is a circular scale ivie into four quarants an each quarant is grauate from 0 o to o A plane mirror fixe below the scale ensures, reaing without 184

13 parallax error, as the image of the pointer is mae to coincie exactly with pointer itself The neele, aluminium pointer an the scale are enclose in a box with a glass top There are two arms grauate in centimetre an their zeroes coincie at the centre of the magnetic neele 1081 En-on (or Tan A position The magnetic fiel at a point along the axial line of a bar magnet is perpenicular to the horizontal component of Earth s magnetic fiel If a magnetometer an a bar magnet are place in such way that this conition is satisfie, then this arrangement is calle Tan A position To achieve this, the arms of the eflection magnetometer are place along East-West irection (ie perpenicular to the 0 0 E magnetic meriian The bar magnet is place along East - Fig 101 En-on (or Tan A position West irection (ie parallel to the arms, as shown in the Fig 101 When a bar magnet of magnetic moment an length l is place at a istance from the centre of the magnetic neele, the neele gets eflecte through an angle θ ue to the action of two magnetic fiels (i the fiel B ue to the bar magnet acting along its axis an (ii the horizontal component of Earth s magnetic fiel B h The magnetic fiel at a istance acting along the axial line of the bar magnet, µ o B = 4 π ( l Accoring to Tangent law, B = B h µ o 4 π ( l = B h Comparison of magnetic moments of two bar magnets (i Deflection metho The eflection magnetometer is place in Tan A position (Fig 1013 A bar magnet of magnetic moment 1 an length l 1 is place at a istance 185

14 1 from the centre of the magnetic neele, on one sie of the compass box ince, the sensitivity of the magnetometer is more at 45 o, the istance of the bar magnet shoul be chosen such that the eflection lies between 30 o an 60 o The reaings corresponing to the ens of the aluminium pointer are note as θ 1 an θ The magnet is reverse pole to pole an kept at the same istance Two more reaings θ 3 an θ 4 are note By placing the magnet on the other sie of the compass box at the same istance, four more reaings θ 5, θ 6, θ 7 an θ 8 are note as above The mean of the eight reaings gives a value θ I The experiment is repeate as above for the secon bar magnet of magnetic moment an length l by placing at a istance ow the mean of 0 0 E the eight reaings gives a value of θ II 1 Applying tangent law, for the first magnet, Fig 1013 Deflection metho µ o 4 π ( l1 = B h I (1 an for the secon magnet µ o 4 π = B ( h II ( l From the above equations (1 an (, we get 1 = ( 1 -l1 ( -l 1 I II (3 pecial case If the magnets are place at the same istance, then 1 = = 1 = ( -l1 ( -l I II In aition, if l 1 an l are small compare to the istance then 1 = tanθ I II 186

15 (ii ull eflection metho The eflection 0 0 E magnetometer is place in Tan A position (Fig 1014 A bar 1 magnet of magnetic moment 1 an length l 1 is place Fig 1014 ull eflection metho on one sie of the compass box at a istance 1 from the centre of the magnetic neele The secon bar magnet of magnetic moment an length l is place on the other sie of the compass box such that like poles of the magnets face each other The secon magnet is ajuste so that the eflection ue to the first magnet is nullifie an the aluminium pointer reas 0 o - 0 o The istance of the secon magnet is x 1 The first magnet is reverse pole to pole an place at the same istance 1 The secon magnet is also reverse an ajuste such that the aluminium pointer reas 0 o - 0 o The istance of the secon magnet is x The experiment is repeate by interchanging the magnets Two more istances x 3 an x 4 are note The mean of x 1, x, x 3 an x 4 is taken as As the magnetic fiels ue to the two bar magnets at the centre of the magnetic neele are equal in magnitue but opposite in irection, (ie B 1 = B µ o 4 π ( l1 = = ( 1 l1 ( l µ o 4 π ( 1 l If the bar magnets are short, l 1 an l are negligible compare to the istance 1 an = 3 187

16 0 108 Broa sie on (or Tan B position The magnetic fiel at a point along the equatorial line of a bar magnet is perpenicular to the horizontal component of Earth s magnetic fiel If the magnetometer an a bar magnet are place in such way that this conition is satisfie, then this arrangement is calle Tan B position To achieve this, the arms of the eflection magnetometer are place along the orth - outh irection (ie along the magnetic meriian The magnet is place along East - West irection (ie parallel to the aluminium pointer as shown in the Fig 1015 When a bar magnet of magnetic moment an length l is place at a istance from the centre of the magnetic neele, the neele gets eflecte through an angle θ ue to the action of the following two magnetic fiels (i The fiel B ue to the bar magnet along its equatorial line (ii The horizontal component of Earth s magnetic fiel B h The magnetic fiel at a istance along the equatorial line of the bar magnet, µ B = o 3/ 4π ( + l Accoring to tangent law Fig 1015 Broa-sie on or Tan B position 0 B = B h E (ie µ o 4 π ( + l 3/ = B h If the magnet is short, l is small compare to an hence l is neglecte µ o 4π 3 = B h 188

17 Comparison of magnetic moments of two bar magnets (i Deflection metho The eflection magnetometer is place in Tan B position A bar magnet of magnetic 1 moment 1 an length l 1 is place at a istance 1 from the centre of the magnetic neele, on one sie of the compass box 0 0 (Fig 1016 ince, the sensitivity of the magnetometer is more at 45 o, the istance of the bar magnet shoul be chosen such that the eflection lies between 30 o an 60 o The reaings corresponing to the ens of the aluminium pointer are note as θ 1 an θ The magnet is reverse pole to pole an kept at the same istance Two more Fig1016 Deflection metho reaings θ 3 an θ 4 are note By placing the magnet on the other sie of the compass box at the same istance, four more reaings θ 5, θ 6, θ 7 an θ 8 are note as above The mean of the eight reaings gives a value θ I The experiment is repeate as above for the secon bar magnet of magnetic moment an length l by placing at a istance ow the mean of the eight reaings gives a value of θ II Applying tangent law, for the first magnet, µ o 1 3/ 4 π = B ( 1 + l1 h tanθ I (1 an for the secon magnet µ o 3/ 4 π = B ( + l h II ( From the above equations (1 an (, we get 1 = ( 1 +l1 ( +l 3/ 3/ I II (3 pecial case If the magnets are place at the same istance, then 1 = = E 189

18 1 = ( +l1 ( +l 3/ 3/ tanθ I II In aition, if l 1 an l are small compare to the istance, 1 = I II (ii ull eflection metho The eflection magnetometer is place in Tan B position (Fig 1017 A bar magnet of magnetic moment 1 an length l 1 is place on one sie of the compass box at a istance 1 from the centre of the magnetic neele The secon bar magnet of magnetic moment an length l is place on the other sie of the compass box such that like poles of the magnets face in the opposite irection The secon magnet is ajuste so that the eflection ue to the first magnet is nullifie an the aluminium pointer reas 0 o - 0 o The istance of the secon magnet is x 1 The first magnet is reverse pole to pole an place at the same istance 1 The secon magnet is also reverse an ajuste such that the aluminium pointer reas 0 o - 0 o The istance of the secon magnet is x The experiment is repeate by interchanging the magnets Two more istances x 3 an x 4 are note The mean of x 1, x, x 3 an x 4 is taken as ince the magnetic fiels ue to the two bar magnets at the centre of the magnetic neele are equal in magnitue but opposite in irection B 1 = B Fig 1017 ull eflection metho E µ o 1 4π ( + l 1 = 3/ 1 1 ( 1 +l1 ( +l 3/ 3/ µ o = 4 π ( + l 3/ 1

19 If the bar magnets are short, l 1 an l are negligible compare to the istance 1 an = agnetic properties of materials The stuy of magnetic properties of materials assumes significance since these properties ecie whether the material is suitable for permanent magnets or electromagnets or cores of transformers etc Before classifying the materials epening on their magnetic behaviour, the following important terms are efine (i agnetising fiel or magnetic intensity The magnetic fiel use to magnetise a material is calle the magnetising fiel It is enote by H an its unit is A m 1 (ote : ince the origin of magnetism is linke to the current, the magnetising fiel is usually efine in terms of ampere turn which is out of our purview here (ii agnetic permeability agnetic permeability is the ability of the material to allow the passage of magnetic lines of force through it Relative permeability µ r of a material is efine as the ratio of number of magnetic lines of force per unit area B insie the material to the number of lines of force per unit area in vacuum B o prouce by the same magnetising fiel B Relative permeability µ r = Bo µ r = µ H = µ µ oh µ o (since µ r is the ratio of two ientical quantities, it has no unit The magnetic permeability of the meium µ = µ o µ r where µ o is the permeability of free space agnetic permeability µ of a meium is also efine as the ratio of magnetic inuction B insie the meium to the magnetising fiel H insie the same meium µ = B H 191

20 (iii Intensity of magnetisation Intensity of magnetisation represents the extent to which a material has been magnetise uner the influence of magnetising fiel H Intensity of magnetisation of a magnetic material is efine as the magnetic moment per unit volume of the material I = V Its unit is A m -1 For a specimen of length l, area A an pole strength m, I = lm la I = m A Hence, intensity of magnetisation is also efine as the pole strength per unit area of the cross section of the material (iv agnetic inuction When a soft iron bar is place in a uniform magnetising fiel H, the magnetic inuction insie the specimen B is equal to the sum of the magnetic inuction B o prouce in vacuum ue to the magnetising fiel an the magnetic inuction B m ue to the inuce magnetisation of the specimen B = B o + B m But B o = µ o H an B m = µ o I B = µ o H + µ o I B = µ o (H + I (v agnetic susceptibility agnetic susceptibility χ m is a property which etermines how easily an how strongly a specimen can be magnetise usceptibility of a magnetic material is efine as the ratio of intensity of magnetisation I inuce in the material to the magnetising fiel H in which the material is place 19

21 Thus χ = m I H ince I an H are of the same imensions, χ m has no unit an is imensionless Relation between χ m an µ r χ m = I H I = χ mh We know B = µ o (H + I B = µ o (H + χ mh B = µ o H (1 + χ m If µ is the permeability, we know that B = µh µh = µ o H (1 + χ m µ µ = (1 + χ m o µ r = 1 + χ m 1010 Classification of magnetic materials On the basis of the behaviour of materials in a magnetising fiel, the materials are generally classifie into three categories namely, (i Diamagnetic, (ii Paramagnetic an (iii Ferromagnetic (i Properties of iamagnetic substances Diamagnetic substances are those in which the net magnetic moment of atoms is zero 1 The susceptibility has a low negative value (For example, for bismuth χ m = usceptibility is Diamagnetic liqui inepenent of temperature 3 The relative Watch glass permeability is slightly less than one 4 When place in a Fig 1018 Diamagnetic liqui non uniform magnetic fiel they have a tenency to move 193

22 away from the fiel (ie from the stronger part to the weaker part of the fiel They get magnetise in a irection opposite to the fiel as shown in the Fig When suspene freely in a uniform magnetic fiel, they set themselves perpenicular to the irection of the magnetic fiel (Fig 1019 Examples : Bi, b, Cu, Au, Hg, H O, H etc (ii Properties of paramagnetic substances Paramagnetic substances are those in which each atom or molecule has a net non-zero magnetic moment of its own 1 usceptibility has a low positive value (For example : χ m for aluminium is usceptibiltity is inversely proportional to absolute temperature (ie χ α 1 m As the temperature increases susceptibility T ecreases 3 The relative permeability is greater than one 4 When place in a non Paramagnetic liqui uniform magnetic fiel, they have a tenency to move from Watch glass weaker part to the stronger part of the fiel They get magnetise in the irection of Fig 100 Paramagnetic liqui the fiel as shown in Fig When suspene freely in a uniform magnetic fiel, they set themselves parallel to the irection of magnetic fiel (Fig 101 Fig 1019 Diamagnetic material perpenicular to the fiel Fig 101 Paramagnetic material parallel to the fiel Examples : Al, Pt, Cr, O, n, CuO 4 etc 194

23 (iii Properties of ferromagnetic substances Ferromagnetic substances are those in which each atom or molecule has a strong spontaneous net magnetic moment These substances exhibit strong paramagnetic properties 1 The susceptibility an relative permeability are very large (For example : µ r for iron = 00,000 usceptibility is inversely proportional to the absolute temperature (ie χ α 1 m As the temperature increases the value of susceptibility T ecreases At a particular temperature, ferro magnetics become para magnetics This transition temperature is calle curie temperature For example curie temperature of iron is about 1000 K 3 When suspene freely in uniform magnetic fiel, they set themselves parallel to the irection of magnetic fiel 4 When place in a non uniform magnetic fiel, they have a tenency to move from the weaker part to the stronger part of the fiel They get strongly magnetise in the irection of the fiel Examples : Fe, i, Co an a number of their alloys 1011 Hysteresis Consier an iron bar being magnetise slowly by a magnetising fiel H whose strength can be change It is foun that the magnetic inuction B insie the material increases with the strength of the magnetising fiel an then attains a saturate level This is epicte by the path OP in the Fig 10 If the magnetising fiel is now Fig 10 Hysteresis loop ecrease slowly, then magnetic inuction also ecreases but it oes not follow the path PO Instea, when H = 0, B has non zero value equal to OQ This implies that some 195 X / H- K B Y L Q R O U T Y / G P +H X

24 magnetism is left in the specimen The value of magnetic inuction of a substance, when the magnetising fiel is reuce to zero, is calle remanance or resiual magnetic inuction of the material OQ represents the resiual magnetism of the material ow, if we apply the magnetising fiel in the reverse irection, the magnetic inuction ecreases along QR till it becomes zero at R Thus to reuce the resiual magnetism (remanent magnetism to zero, we have to apply a magnetising fiel OR in the opposite irection The value of the magnetising fiel H which has to be applie to the magnetic material in the reverse irection so as to reuce its resiual magnetism to zero is calle its coercivity When the strength of the magnetising fiel H is further increase in the reverse irection, the magnetic inuction increases along R till it acquires saturation at a point (points P an are symmetrical If we now again change the irection of the fiel, the magnetic inuction follows the path TUP This close curve PQRTUP is calle the hysteresis loop an it represents a cycle of magnetisation The wor hysteresis literally means lagging behin We have seen that magnetic inuction B lags behin the magnetising fiel H in a cycle of magnetisation This phenomenon of lagging of magnetic inuction behin the magnetising fiel is calle hysteresis Hysteresis loss In the process of magnetisation of a ferromagnetic substance through a cycle, there is expeniture of energy The energy spent in magnetising a specimen is not recoverable an there occurs a loss of energy in the form of heat This is so because, uring a cycle of magnetisation, the molecular magnets in the specimen are oriente an reoriente a number of times This molecular motion results in the prouction of heat It has been foun that loss of heat energy per unit volume of the specimen in each cycle of magnetisation is equal to the area of the hysteresis loop The shape an size of the hysteresis loop is characteristic of each material because of the ifferences in their retentivity, coercivity, permeability, susceptibility an energy losses etc By stuying hysteresis loops of various materials, one can select suitable materials for ifferent purposes 196

25 10111 Uses of ferromagnetic materials (i Permanent magnets The ieal material for making permanent magnets shoul possess high retentivity (resiual magnetism an high coercivity so that the magnetisation lasts for a longer time Examples of such substances are steel an alnico (an alloy of Al, i an Co (ii Electromagnets aterial use for making an electromagnet has to unergo cyclic changes Therefore, the ieal material for making an electromagnet has to be one which has the least hysteresis loss oreover, the material shoul attain high values of magnetic inuction B at low values of magnetising fiel H oft iron is preferre for making electromagnets as it has a thin hysteresis loop (Fig 103 [small area, therefore less hysteresis loss] an low retentivity It attains high values of B at low values of magnetising fiel H B oft Iron teel H Fig 103 Hysteresis loop for steel an soft iron (iii Core of the transformer A material use for making transformer core an choke is subjecte to cyclic changes very rapily Also, the material must have a large value of magnetic inuction B Therefore, soft iron that has thin an tall hysteresis loop is preferre ome alloys with low hysteresis loss are: raio-metals, pern-alloy an mumetal (iv agnetic tapes an memory store agnetisation of a magnet epens not only on the magnetising fiel but also on the cycle of magnetisation it has unergone Thus, the value of magnetisation of the specimen is a recor of the cycles of magnetisation it has unergone Therefore, such a system can act as a evice for storing memory Ferro magnetic materials are use for coating magnetic tapes in a cassette player an for builing a memory store in a moern computer Examples : Ferrites (Fe, Fe O, nfe O 4 etc 197