Chapter 25 Magnetism PDF

Magnetism 87 Sm  Nm E3 60 Sg Ng The molecular theory of magnetism was given by Weber and modified later by Ewing. According to this ID theory. Every molecule of a substance is a complete magnet in itself. However, in an magnetised substance the U molecular magnets are randomly oriented to give zero...

Magnetism 87 Sm  Nm E3 60 Sg Ng The molecular theory of magnetism was given by Weber and modified later by Ewing. According to this ID theory. Every molecule of a substance is a complete magnet in itself. However, in an magnetised substance the U molecular magnets are randomly oriented to give zero net magnetic moment. On magnetising, the molecular D YG magnets are realigned in a specific direction leading to a net magnetic moment. (Unmagnetised) On heating/hammering the magnetism of magnetic substance reduces. U Note :  (Magnetised) Bar Magnet. ST A bar magnet consist of two equal and opposite magnetic pole separated by a small distance. Poles are not exactly at the ends. The shortest distance between two poles is called effective length ( Le) and is less then its geometric length (Lg). 2R S N S N Le = 2 l Lg Le  5 6  Lg Le = 2 R and Lg = R 88 Magnetism (1) Directive properties : When a magnet suspended freely it stays in the earth’s N-S direction (in magnetic meridian). Magnetic axis S 60 N E3 Magnetic meridian (2) Monopole concept : If a magnet is Broken into number of pieces, each piece becomes a magnet. This in turn implies that monopoles do not exist. (i.e., ultimate individual unit of magnetism in any magnet is called ID dipole). N U S N S D YG S N S N (3) For two rods as shown, if both the rods attract in case (i) and doesn’t attract in case (ii) then, B is a magnetic and A is simple iron rod. Repulsion is sure test of magnetism. B A A (ii) ST U B (i) (4) Pole strength (m) : The strength of a magnetic pole to attract magnetic materials towards itself is known as pole strength. (i) It is a scalar quantity. (ii) Pole strength of N and S pole of a magnet is conventionally represented by +m and –m respectively. (iii) It's SI unit is amp × m or N/Tesla and dimensions are [LA]. Magnetism 89 (iv) Pole strength of the magnet depends on the nature of material of magnet and area of cross section. It S SS S S S S A – more m – more N N N N N N N S SS SS SS N NN NN N A – less m – less 60 doesn't depends upon length. E3  (5) Magnetic moment or magnetic dipole moment (M) : It represents the strength of magnet.   Mathematically it is defined as the product of the strength of either pole and effective length. i.e. M  m(2 l ) (i) It is a vector quantity directed from south to north. –m S N L = 2l ID (ii) It's S.I. unit amp×m2 or N-m/Tesla and dimensions [AL2] +m  M U (iii) Magnetic moment in various other situations. Current carrying coil M D YG i Magnetic moment M = NiA i N = number of turns, M i= current through the coil, A= Area of the coil Combination of bar magnet M2 M net  S N M net U   S N tan   M 12  M 22  2 M 1 M 2 cos  M 2 sin  M 1  M 2 cos  ST M1 2M M M N N 2M M S 90o N 3M S M S 60o N S S S N M N M Mnet = 2M Revolving charge (a) Orbital electron : In an atom electrons revolve around the nucleus in circular orbit and it is equivalent to the 90 Magnetism flow of current in the orbit. Thus the orbit of electrons is considered as tiny current loop with magnetic moment. M  e A  1 e r 2 e eh ; where,  = angular speed,  = frequency, v = linear speed and  evr  L 2 2 2m 4m 60 L= Angular moment I. (b) For geometrical symmetrical charged rotating bodies : The magnetic moment given by M  QL QI ; where  2m 2m Note :  1 mR 2 , M  QR 2 4 2 I  MR 2 , M  1 QR 2 2 U I ID E3 m = mass of rotating body, Q = charge on body, I = moment of inertia of rotating body about axis of rotation. I 1 mL 2 , M  Q L2 24 12 eh  9.27×10–24 A/m2. It serves as natural unit of magnetic moment. 4m Bohr magneton can be defined as the orbital magnetic moment of an electron circulating in inner D YG Bohr magneton  B  most orbit.  Magnetic moment of straight current carrying wire is zero.  Magnetic moment of toroid is zero. U  If a magnetic wire of magnetic moment (M) is bent into any shape then it's M decreases as it's length (L) always decreases and pole strength remains constant. L/3 ST L –m L/2 +m L/3 R L/3 L = R L/2 M = mL M'  M / 2 M'  M / 3 M'  2M /  M = 0 (6) Cutting of a bar magnet : Suppose we have a rectangular bar magnet having length, breadth and mass are L, b and w respectively if it is cut in n equal parts along the length as well as perpendicular to the length simultaneously as shown in the figure then b b L L L , breadth of each part b '  b n each part m '  m , Magnetic moment of each part M '  m ' L'  , Mass of each part w'  n m  n n w , pole strength of n E3 Length of each part L'  60 Magnetism 91 L  n M n If initially moment of inertia of bar magnet about the axes passing from centre and perpendicular to it’s Note :    then moment of inertia of each part I'  I  n2  ID  L2  b 2 length is I  w   12   Commonly asked question N S  N A/2 D YG S I L w M and I'  3 , w'  , m '  m , M '  n n n n U For short bar magnet b = 0 so L'  L (m, M) S N L A/2  N S L (m, M) m = m/2, M = M/2 S N L/2 L/2 m = m, M = M/2 Various Terms Related to Magnetism. (1) Magnetic field and magnetic lines of force : Space around a magnetic pole or magnet or current carrying U wire within which it's effect can be experienced is defined magnetic field. Magnetic field can be represented with ST the help of a set of lines or curves called magnetic lines of force. N Isolated north pole S Isolated south pole (2) Magnetic flux () and flux density (B) S N Magnetic dipole                                         Inward magnetic field Outward magnetic field 92 Magnetism (i) The number of magnetic lines of force passing normally through a surface is defined as magnetic flux ( ). It's S.I. unit is weber (wb) and CGS unit is Maxwell. 60 Remeber 1 wb = 108 maxwell. (ii) When a piece of a magnetic substance is placed in an external magnetic field the substance becomes magnetised. The number of magnetic lines of induction inside a E3 magnetised substance crossing unit area normal to their direction is called S magnetic induction or magnetic flux density (B). It is a vector quantity. It's m 2  unit is Tesla which N J volt  sec   amp  m amp  m 2 m2 is equal to ID wb SI N and CGS unit is Gauss. Remember 1 Tesla = 104 Gauss. U Note :  Magnetic flux density can also be defined in terms of force experienced by a unit north F. m0 D YG pole placed in that field i.e. B  (3) Magnetic permeability : It is the degree or extent to which magnetic lines of force can enter a substance and is denoted by . or Characteristic of a medium which allows magnetic flux to pass through it is called it's permeability. e.g. ST U permeability of soft iron is 1000 times greater than that of air. In air In soft iron Also  =  0  r ; where  0  absolute permeability of air or free space = 4  10 7 tesla m / amp. and  r  Relative permeability of the medium = flux density in material B . B 0 flux density in vacuum Magnetism 93 (4) Intensity of magnetising field (H ) (magnetising field) : It is the degree or extent to which a magnetic field can magnetise a substance. Also H  N m  Tesla 2  . N J J It's CGS unit is Oersted. Also 1oersted = 80  3  wb m  Tesla m  wb 60 It's SI unit is A / m.  B A/ m E3 (5) Intensity of magnetisation (I) : It is the degree to which a substance is magnetised when placed in a magnetic field. It can also be defined as the pole strength per unit cross sectional area of the substance or the induced Hence I= ID dipole moment per unit volume. m M . It is a vector quantity, it's S.I. unit is Amp/m. A V U (6) Magnetic susceptibility (m) : It is the property of the substance which shows how easily a substance can be magnetised. It can also be defined as the ratio of intensity of magnetisation ( I) in a substance to the magnetic I. It is a scalar quantity with no units and dimensions. H D YG intensity (H) applied to the substance, i.e.  m  (7) Relation between permeability and susceptibility : Total magnetic flux density B in a material is the sum of magnetic flux density in vacuum B 0 produced by magnetising force and magnetic flux density due to magnetisation of material B m. i.e. B  B 0  B m  B   0 H   0 I   0 (H  I)   0 H (1   m ). Also  r  (1   m ) B  H  4I and   1  4 m. U Note :  In CGS ST Force and Field. (1) Coulombs law in magnetism : The force between two magnetic poles of strength m1 and m2 lying at a m m  distance r is given by F  k. 1 2 2. In S.I. units k  0  10 7 wb / Amp  m , In CGS units k  1 4 r (2) Magnetic field (i) Magnetic field due to an imaginary magnetic pole (Pole strength m) : Is given by B  also B  0 m. 4 d 2 (ii) Magnetic field due to a bar magnet : At a distance r from the centre of magnet e  Be B g Equatorial line +  N S 2l a  Ba F m0 94 Magnetism (a) On axial position  0 2 Mr ; 4  (r 2  l 2 )2 If l> B0 induction B where B0 is the magnetic induction in vacuum Magnetic susceptibility  Low and negative ||  1 Dependence Does temperature of  on not depend on temperature (except Bi at low temperature) Low but positive   1 Positive and high   102 Inversely proportional to  1 or T  Tc  C This is called T  Tc temperature  1 T or Magnetism 119   C. T This is called Curie law, where C = Curie Curie Weiss law. Tc = Curie temperature Does Relative not depend Does not independent independent r < 1 r > 1 depend Does not depend independent r >> 1 E3 Dependence of  on H 60 constant permeability (r) r = 102 I is in a direction opposite I is in the direction of H I is in the direction of H (I) to that of H and its value is but value is low and value is very high. ID Intensity of magnetisation very low I-H curves Magnetic moment (M) Is H D YG –I U +I H Hs The value of M is very low The value of M is very low The value of M is very ( 0 and is in a direction and is in the direction of H high and is in the direction opposite to H.) U Transition of materials (at These do not change. Curie temperature)  ST The property magnetism H of H On cooling, these get These get converted into converted to ferromagnetic paramagnetic materials  above Curie temperature at Curie materials temperature T T of TC T Diamagnetism is found in Paramagnetism is found in Ferro-magnetism is found those materials the atoms those materials the atoms in those materials which of of which have majority of when placed in an external which have even 120 Magnetism number electrons electron spins in the same magnetic field are strongly direction magnetised NaCl, H2O air and and crown glass diamond etc. Distortion effect Orientation effect Hysteresis effect E3 Nature of effect Fe, Co, Ni, Cd, Fe3O4 etc. 60 Cu, Ag, Au, Zn, Bi, Sb, Al, Mn, Pt, Na, CuCl2, O2 Examples (4) Hysteresis : For ferromagnetic materials, by removing external magnetic field i.e. H = 0. The magnetic ID moment of some domains remain aligned in the applied direction of previous magnetising field which results into a residual magnetism. D YG U The lack of retracibility as shown in figure is called hysteresis and the curve is known as hysteresis loop. I or (B) C B A D G H F ST U E O (i) When magnetising field (H) is increased from O, the intensity of magnetisation I increases and becomes maximum. This maximum value is called the saturation value. (ii) When H is reduced, I reduces but is not zero when H = 0. The remainder value OC of magnetisation when H = 0 is called the residual magnetism or retentivity. The property by virtue of which the magnetism ( I) remains in a material even on the removal of magnetising field is called Retentivity or Residual magnetism. Magnetism 121 (iii) When magnetic field H is reversed, the magnetisation decreases and for a particular value of H, denoted by Hc, it becomes zero i.e., Hc = OD when I = 0. This value of H is called the corecivity. 60 (iv) So, the process of demagnetising a material completely by applying magnetising field in a negative direction is defined Corecivity. Corecivity assesses the softness or hardness of a magnetic material. Corecivity E3 signifies magnetic hardness or softness of substance : Magnetic hard substance (steel) High corecvity ID Magnetic soft substance (soft iron) Low corecivity (v) When field H is further increased in reverse direction, the intensity of magnetisation attains saturation U value in reverse direction (i.e. point E) (vi) When H is decreased to zero and changed direction in steps, we get the part EFGB. Note :  D YG Thus complete cycle of magnetisation and demagnetisation is represented by BCDEFGB. The energy loss (or hysteresis energy loss) in magnetising and demagnetising a specimen is proportional to the area of hysteresis loop. ST U (vii) Comparison between soft iron and steel : Soft iron Steel I I H The area of hysteresis loop is less (low energy loss) H The area of hysteresis loop is large (high energy loss) 122 Magnetism More retentivity and corecive force Magnetic permeability is high Magnetic permeability is less Magnetic susceptibility () is high  is low Intensity of magnetisation (I) is high I is low It magnetised and demagnetised easily Magnetisation and demagnetisation is complicated Used in dynamo, transformer, electromagnet tape Used for making permanent magnet. ID Concepts E3 recorder and tapes etc. 60 Less relativity and corecive force  An iron cored coil and a bulb are connected in series with an ac generator. If an iron rod is introduced inside a coil, then U the intensity of bulb will decrease, because some energy lest in magnetising the rod.  Hysteresis energy loss = Area bound by the hysteresis loop = VAnt Joule Time. Examples Example: 39 D YG Where , V = Volume of ferromagnetic sample, A = Area of B – H loop P, n = Frequency of alternating magnetic field and t = A ferromagnetic substance of volume 10 –3 m3 is placed in an alternating field of 50 Hz. Area of hysteresis U curve obtained is 0.1 M.K.S. unit. The heat produced due to energy loss per second in the substance will be (b) 5  10–2 cal (c) 1.19  10–3 cal (d) No loss of energy ST (a) 5 J Solution : (c) By using heat loss = VAnt ; whre V = volume = 10–3 m3; A = Area = 0.1m2, n = frequency = 50 Hz and t = time = 1sec Heat loss = 10–3  0.1  50  1 = 5  10–3 J = 1.19  10–3 cal Example: 40 A magnetising field of 1600 A-m–1 produces a magnetic flux of 2.4  10–5 Wb in an iron bar of crosssectional area 0.2 cm2. The susceptibility of an iron bar is (a) 298 Solution : (b) (b) 596 By using B  H   0  r H and  r  (1   m )   r  (c) 1192 B 0 H    0 HA (d) 1788 Magnetism 123 r  Example: 41 2.4  10 5 (4  10 7 )  1600  (0.2  10 4 ) = 596.8. Hence  m  595.8  596 For iron it's density is 7500 kg/m3 and mass 0.075 kg. If it's magnetic moment is 8  10 –7 Amp  m2 , (a) 8 Amp/m (b) 0.8 Amp/m M Md 8  10 7  7500    0.08 Amp / m V m 0.075 60 it's intensity of magnetisation is (c) 0.08 Amp/m (d) 0.008 Amp/m I Example: 42 The dipole moment of each molecule of a paramagnetic gas is 1.5  10 –23 Amp  m2. The E3 Solution : (c) temperature of gas is 27 oC and the number of molecules per unit volume in it is 2  10 26 m–3. The (a) 3  103 Amp/m ID maximum possible intensity of magnetisation in the gas will be (b) 4  10–3 Amp/m (c) 5  105 Amp/m (d) 6  10–4 Amp/m M  N 1.5  10 23  2  10 26    3  10 3 Amp / m V V 1 I Example: 43 The coereivity of a small bar magnet is 4  10 3 Amp/m. It is inserted inside a solenoid of 500 turns U Solution : (a) D YG and length 1 m to demagnetise it. The amount of current to be passed through the solenoid will be (a) 2.5 A (b) 5 A H = ni  i  Example: 44 The units for molar susceptibility U (a) m3 Molar susceptibility  ST (d) 10 A (c) kg–1 m3 (d) No units H 4  10 3   8A n 500 Solution : (c) Solution : (a) (c) 8 A (b) kg-m–3 Volume susceptibility I/H I/H  molecular weight  M  M  Density of material M /V So it's unit is m3. Example: 45 The ratio of the area of B-H curve and I-H curve of a substance in M.K.S. system is (a) 02 Solution : (c) (b) 1  02 Area of B-H loop   0 (Area of I-H) (c) 0 (d) 1 0