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Pooja M
Pooja M

MAHARASHTRA STATE BOARD CLASS XI AND XII PHYSICS CHAPTER 11 MAGNETIC MATERIAL

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Chapter 11 Magnetic Materials MAHARASHTRA STATE BOARD
Can You Recall? 1. What are magnetic lines of force? Magnetic Lines of Force is a an imaginary line representing the direction of magnetic field such that the tangent at any point is the direction of the field vector at that point. 2. Why magnetic monopoles do not exist? A magnetic monopole does not exist . Just as the two faces of a current loop cannot be physically separated, magnetic North pole and the South pole can never be separated even on breaking a magnet to its atomic size. 3. Which materials are used in making magnetic compass needle? The needle of magnetic compass is made of steel. This material can be magnetised for an extended period. On the other hand, plastic, wood and paper are non-magnetic substances and hence, can not be magnetised in order to indicate directions.
β€’ Toque on a bar magnet in a magnetic field If a bar magnet placed in uniform magnetic field 𝜏 = π‘šπ΅ sin πœƒ Bar magnet will perform rotational motion Due to any displacement Work will be done (Work – Stored in the form of P.E.) We say magnetic Potential Energy. π‘ˆπ‘š = 0 πœƒ 𝜏 π‘‘πœƒ π‘ˆπ‘š = 0 πœƒ π‘šπ΅π‘ π‘–π‘› πœƒ π‘‘πœƒ = βˆ’π‘šπ΅ sin πœƒ
β€’ Toque on a bar magnet in a magnetic field Case I: At πœƒ = 00 π‘ˆπ‘š = βˆ’π‘š 𝐡 Case II: At πœƒ = 1800 π‘ˆπ‘š = π‘š 𝐡 Case III: At πœƒ = 900 π‘ˆπ‘š = 0 Where, m – Magnetic Moment B – Magnetic Field πœƒ βˆ’ 𝐴𝑛𝑔𝑙𝑒 β€’ Two magnet suspended Freely – Mutual Perpendicular to each other
β€’ Two magnet suspended Freely – Mutual Perpendicular to each other At equilibrium: 𝜏 = 𝐼 𝛼 𝜏 = 𝐼 𝑑2πœƒ 𝑑𝑑2 __________ (i) 𝛼 = π‘‘πœ” 𝑑𝑑 = 𝑑 𝑑𝑑 π‘‘πœƒ 𝑑𝑑 𝐼 β†’ π‘€π‘œπ‘šπ‘’π‘›π‘‘ π‘œπ‘“ π‘–π‘›π‘’π‘Ÿπ‘‘π‘–π‘Ž 𝛼 β†’ π΄π‘›π‘”π‘’π‘™π‘Žπ‘Ÿ π‘Žπ‘π‘π‘’π‘™π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› πœƒ β†’ π΄π‘›π‘”π‘’π‘™π‘Žπ‘Ÿ π·π‘–π‘ π‘π‘™π‘Žπ‘π‘’π‘šπ‘’π‘›π‘‘ πœ” β†’ π΄π‘›π‘”π‘’π‘™π‘Žπ‘Ÿ π‘‰π‘’π‘™π‘œπ‘π‘–π‘‘π‘¦ If we rotate magnet in opposite direction: Torque will be opposite 𝜏 = βˆ’π‘šπ΅ sin πœƒ ______________(ii) (-ve sign: Bar magnet is rotating in opposite direction) From equation (i) and (ii) ∴ 𝐼 𝑑2πœƒ 𝑑𝑑2 = βˆ’π‘šπ΅ sin πœƒ
If πœƒ β†’ π‘‰π‘’π‘Ÿπ‘¦ π‘ π‘šπ‘Žπ‘™π‘™ π‘‘β„Žπ‘’π‘› sin πœƒ β‰ˆ πœƒ ∴ 𝐼 𝑑2πœƒ 𝑑𝑑2 = βˆ’π‘šπ΅ πœƒ 𝑑2πœƒ 𝑑𝑑2 = βˆ’ π‘šπ΅ 𝐼 πœƒ Here, π‘šπ΅ 𝐼 β†’ πΆπ‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘ 𝐼 β†’ π‘€π‘œπ‘šπ‘’π‘›π‘‘ π‘œπ‘“ πΌπ‘›π‘’π‘Ÿπ‘‘π‘–π‘Ž 𝐡 β†’ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ 𝐹𝑖𝑒𝑙𝑑 π‘š β†’ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘šπ‘œπ‘šπ‘’π‘›π‘‘ As we studied in Simple Harmonic Motion (S.H.M) 𝑑2π‘₯ 𝑑𝑑2 = βˆ’πœ”2π‘₯ Where, π‘₯ β†’ π·π‘–π‘ π‘π‘™π‘Žπ‘π‘’π‘šπ‘’π‘›π‘‘ 𝑑2π‘₯ 𝑑𝑑2 β†’ π΄π‘π‘π‘’π‘™π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› On comparing, πœ”2 = π‘šπ΅ 𝐼
∴ πœ” = π‘šπ΅ 𝐼 Time period for Bar Magnet, ∴ 𝑇 = 2πœ‹ πœ” ∴ 𝑇 = 2πœ‹ π‘šπ΅ 𝐼 = 2πœ‹ Γ— 𝐼 π‘šπ΅ ∴ 𝑇 = 2πœ‹ 𝐼 π‘šπ΅ Examples A bar magnet of moment of inertia of 500 𝑔 π‘π‘š2 makes 10 oscillations per minute in a horizontal plane. What is its magnetic moment, if the horizontal component of earth's magnetic field is 0.36 gauss? Ans: 𝑇 = 2πœ‹ 𝐼 π‘šπ΅
Examples A bar magnet of moment of inertia of 500 𝑔 π‘π‘š2 makes 10 oscillations per minute in a horizontal plane. What is its magnetic moment, if the horizontal component of earth's magnetic field is 0.36 gauss? Given: Moment of Inertia I = 500 𝑔 π‘π‘š2 Frequency n = 10 oscillation per minute = 10/60 oscillations per second Time period T = 6 sec 𝐡𝐻 = 0.36 gauss 𝑇 = 2πœ‹ 𝐼 π‘šπ΅ π‘š = 4πœ‹2𝐼 𝑇2𝐡 = 4 Γ— (3.14)2 Γ—500 Γ—10βˆ’7 36 Γ— 0.36 Γ— 10βˆ’4 m = 1.524 𝐴 π‘š2
π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘š β†’ π΄π‘‘π‘œπ‘šπ‘–π‘ π‘ π‘‘π‘Ÿπ‘’π‘π‘‘π‘’π‘Ÿπ‘’ β†’ 𝐷𝑒𝑝𝑒𝑛𝑑 Origin of Magnetism in Materials: Electron Revolving around the nucleus ↓ Magnetic Dipole Moment (m = IA) Where, I β†’ Moment of Inertia π‘š β†’ π‘šπ‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘‘π‘–π‘π‘œπ‘™π‘’ π‘šπ‘œπ‘šπ‘’π‘›π‘‘ A β†’ π΄π‘Ÿπ‘’π‘Ž π‘…π‘œπ‘‘π‘Žπ‘‘π‘’π‘‘ 𝑏𝑦 π‘’βˆ’ β€’ Magnetism depends upon atom.
Magnetic Moment of an Electron Revolving Around the Nucleus of an Atom: Intrinsic Angular Momentum Magnetic dipole moment due to current loop is, m = I A Where, m β†’ magnetic Dipole (Orbital Magnetic Moment) I β†’ Current A β†’ Area enclosed by loop Consider, An electron moving in an orbit with constant velocity (v), Having radius r about nucleus Electron covers distance of circumference i.e. 2πœ‹π‘Ÿ in time 𝑆𝑝𝑒𝑒𝑑 = π·π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’ π‘‡π‘–π‘šπ‘’ = 2πœ‹π‘Ÿ 𝑇
Magnetic Moment of an Electron Revolving Around the Nucleus of an Atom: Intrinsic Angular Momentum Current associated with charge π‘’βˆ’ is, 𝐼 = 𝑒 𝑇 _______(i) ∴ πΉπ‘œπ‘Ÿ π‘Žπ‘›π‘”π‘’π‘™π‘Žπ‘Ÿ 𝑠𝑝𝑒𝑒𝑑, 𝑇 = 2πœ‹ πœ” We get from (i), 𝐼 = 𝑒 2πœ‹ πœ” = π‘’πœ” 2πœ‹ 𝐼 = π‘’πœ” 2πœ‹ As 𝑣 = πœ” π‘Ÿ i.e. πœ” = 𝑣 π‘Ÿ ∴ 𝐼 = 𝑒𝑣 2πœ‹π‘Ÿ Now, For orbital magnetic moment: π‘šπ‘œπ‘Ÿπ‘ = 𝐼𝐴 π‘šπ‘œπ‘Ÿπ‘ = 𝑒𝑣 2πœ‹π‘Ÿ πœ‹π‘Ÿ2 = 1 2 evr ________ (ii)
Magnetic Moment of an Electron Revolving Around the Nucleus of an Atom: Intrinsic Angular Momentum For some electron, orbital angular momentum: 𝐿 = π‘šπ‘’π‘£π‘Ÿ Where, π‘šπ‘’ β†’ π‘šπ‘Žπ‘ π‘  π‘œπ‘“ π‘’βˆ’ From equation (ii), π‘šπ‘œπ‘Ÿπ‘ = 1 2 π‘’π‘£π‘Ÿ π‘šπ‘œπ‘Ÿπ‘ = 1 2 π‘’π‘£π‘Ÿ Γ— π‘šπ‘’ π‘šπ‘’ = 𝑒 2π‘šπ‘’ Γ— (π‘šπ‘’π‘£π‘Ÿ) π‘šπ‘œπ‘Ÿπ‘ = 𝑒 2π‘šπ‘’ Γ— 𝐿 Where, π‘šπ‘œπ‘Ÿπ‘ β†’ π‘‚π‘Ÿπ‘π‘–π‘‘π‘Žπ‘™ π‘šπ‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘šπ‘œπ‘šπ‘’π‘›π‘‘ Conclusion: π‘‚π‘Ÿπ‘π‘–π‘‘π‘Žπ‘™ π‘šπ‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘šπ‘œπ‘šπ‘’π‘›π‘‘ ∝ π΄π‘›π‘”π‘’π‘™π‘Žπ‘Ÿ π‘šπ‘œπ‘šπ‘’π‘›π‘‘π‘’π‘š 𝑖. 𝑒. π‘šπ‘œπ‘Ÿπ‘ ∝ 𝐿 Where, 𝑒 2π‘šπ‘’ β†’ πΆπ‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘ πΆπ‘Žπ‘™π‘™π‘’π‘‘ π‘Žπ‘  πΊπ‘¦π‘Ÿπ‘œπ‘šπ‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ πΆπ‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘
π‘¬π’π’†π’“π’ˆπ’š = 𝒏 Γ— 𝒉 πŸπ…
Similarly, From Quantum Mechanics: From 2𝑛𝑑 postulates of Bohr’s theory: Angular momentum of electron is n multiple of β„Ž 2πœ‹ i.e. 𝐿 = π‘šπ‘’π‘£π‘Ÿ = 𝑛 β„Ž 2πœ‹ We know that, π‘šπ‘œπ‘Ÿπ‘ = 𝑒 2π‘šπ‘’ 𝐿 ∴ π‘šπ‘œπ‘Ÿπ‘ = 𝑒 2π‘šπ‘’ . π‘›β„Ž 2πœ‹ = π‘’π‘›β„Ž 4πœ‹π‘šπ‘’ For 1𝑠𝑑 orbit, n = 1 ∴ π‘šπ‘œπ‘Ÿπ‘ = π‘’β„Ž 4πœ‹π‘šπ‘’ The Value π‘’β„Ž 4πœ‹π‘šπ‘’ β†’ π΅β„Žπ‘œπ‘Ÿ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘œπ‘› β†’ 9.274 Γ— 10βˆ’24 𝐴/π‘š2 Example Calculate the gyromagnetic ratio of electron (given 𝑒 = 1.6 Γ— 10βˆ’19 𝐢, π‘šπ‘’ = 9.1 Γ— 10βˆ’31 π‘˜π‘”)
Example Calculate the gyromagnetic ratio of electron (given 𝑒 = 1.6 Γ— 10βˆ’19 𝐢, π‘šπ‘’ = 9.1 Γ— 10βˆ’31 π‘˜π‘”) Ans: Gyromagnetic Ratio = 𝑒 2 π‘šπ‘’ Gyromagnetic Ratio = 1.6 Γ— 10βˆ’19 2 Γ— 9.1 Γ— 10βˆ’31 πΊπ‘¦π‘Ÿπ‘œπ‘šπ‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘Ÿπ‘Žπ‘‘π‘–π‘œ = 8.8 Γ— 1010 𝐢/π‘˜π‘”
Magnetization β€’ Unpaired electron having magnetic dipole moment β€’ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘§π‘Žπ‘‘π‘–π‘œπ‘› = π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘€π‘œπ‘šπ‘’π‘›π‘‘ π‘‰π‘œπ‘™π‘’π‘šπ‘’ π‘œπ‘“ π‘šπ‘Žπ‘‘π‘’π‘Ÿπ‘–π‘Žπ‘™ β€’ 𝑀 = 𝑀𝑛𝑒𝑑 π‘‰π‘œπ‘™π‘’π‘šπ‘’ β€’ M is vector quantity β€’ Unit - 𝐴 π‘š β€’ Dimension - [πΏβˆ’1𝐴]
Magnetization Consider, a rod placed in solenoid ∴ Magnetic field inside solenoid 𝐡𝑂 = πœ‡0𝑛𝐼 Where, n = No. of turns on solenoid I = Current Passing ∴ Magnetic field due to material kept inside solenoid (π΅π‘š) Here, Net Magnetic Field 𝐡 = 𝐡𝑂 + π΅π‘š We know that, π΅π‘š ∝ π‘šπ‘Žπ‘”π‘›π‘’π‘‘π‘–π‘§π‘Žπ‘‘π‘–π‘œπ‘› ∴ π΅π‘š = πœ‡π‘œπ‘€ Where, πœ‡π‘œ β†’ π‘ƒπ‘’π‘Ÿπ‘šπ‘’π‘Žπ‘π‘–π‘™π‘–π‘‘π‘¦ π‘œπ‘“ π‘“π‘Ÿπ‘’π‘’ π‘ π‘π‘Žπ‘π‘’ ∴ 𝐡 = πœ‡π‘‚π‘›πΌ + πœ‡π‘‚π‘€ Here, new quantity called as magnetic field intensity β€˜H’ ∴ 𝐻 = 𝑛 𝐼 Does not depend upon on material rod.
Magnetization Hence, 𝐡 = πœ‡π‘‚π» + πœ‡π‘‚π‘€ 𝐡 = πœ‡π‘‚(𝐻 + 𝑀) ………..(1) ∴ 𝐻 + 𝑀 = 𝐡 πœ‡0 ∴ 𝐻 = 𝐡 πœ‡0 βˆ’ 𝑀 Unit of H and M is same – A/m If H is not too strong, So Magnetization induced in material ∝ Magnetic Intensity ∴ 𝑀 ∝ 𝐻 𝑀 = πœ’π» Where, πœ’ β†’ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘†π‘’π‘ π‘π‘’π‘π‘‘π‘Žπ‘π‘–π‘™π‘–π‘‘π‘¦
Magnetization From equation no. (1) 𝐡 = πœ‡π‘‚(𝐻 + 𝑀) ∴ 𝐡 = πœ‡π‘‚ 𝐻 + πœ’π» 𝐡 = πœ‡π‘‚ 1 + πœ’ 𝐻 ∴ 𝐡 = πœ‡0πœ‡π‘Ÿπ» 𝐡 = πœ‡π» Where, πœ‡π‘Ÿ = 1 + πœ’ πœ‡ = πœ‡π‘œπœ‡π‘Ÿ ∴ πœ‡ = πœ‡0(1 + πœ’) Where, πœ‡ β†’ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘ƒπ‘’π‘Ÿπ‘šπ‘’π‘Žπ‘π‘–π‘™π‘–π‘‘π‘¦ πœ‡π‘Ÿ β†’ π‘…π‘’π‘™π‘Žπ‘‘π‘–π‘£π‘’ π‘šπ‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘π‘’π‘Ÿπ‘šπ‘’π‘Žπ‘π‘–π‘™π‘–π‘‘π‘¦ πœ‡π‘œ β†’ π‘ƒπ‘’π‘Ÿπ‘šπ‘’π‘Žπ‘π‘–π‘™π‘–π‘‘π‘¦ π‘œπ‘“ π‘“π‘Ÿπ‘’π‘’ π‘ π‘π‘Žπ‘π‘’
Magnetic Permeability in Different Materials
β€’ Magnetic permeability and susceptibility are quantitative measures of magnetic properties of materials. β€’ The key difference between magnetic permeability and susceptibility is that magnetic permeability describes the ability of a material to support the formation of a magnetic field inside itself whereas susceptibility describes whether a material is attracted to a magnetic field or is repelled from it. β€’ Magnetic susceptibility is a dimensionless measure. Summary – Magnetic Permeability vs Susceptibility β€’ Magnetic permeability is given by the units Henries per meter, and magnetic susceptibility is a dimensionless property of materials. β€’ The key difference between magnetic permeability and susceptibility is that magnetic permeability describes the ability of a material to support the formation of a magnetic field inside itself whereas susceptibility describes whether a material is attracted to a magnetic field or is repelled from it.
Magnetic Permeability vs Susceptibility Magnetic permeability of a material is the ability of a material to support the formation of a magnetic field inside itself. Magnetic susceptibility is the measure of magnetic properties of a material which indicates whether the material is attracted or repelled from an external magnetic field. Units of Measurement Magnetic permeability is measured by the SI unit Henries per meter (H/m or HΒ·mβˆ’1) which is equivalent to Newtons per ampere squared (NΒ·Aβˆ’2). The magnetic susceptibility is a dimensionless property. Value for Diamagnetic Materials The value of magnetic permeability for diamagnetic materials is less than 1. The value of magnetic susceptibility for diamagnetic materials is less than zero. Value for Paramagnetic Materials The value of magnetic permeability for paramagnetic materials is greater than 1. The value of magnetic susceptibility for paramagnetic materials is greater than zero.
Example: The region inside a current carrying toroid winding is filled with Aluminium having susceptibility πœ’ = 2.3 Γ— 10βˆ’5. What is the percentage increase in the magnetic field in the presence of Aluminium over that without it? Solution: The magnetic field inside the solenoid without Aluminium 𝐡𝑂 = πœ‡π‘‚π» The magnetic field inside the solenoid with Aluminium B = Β΅ H π΅βˆ’π΅0 𝐡0 = πœ‡βˆ’πœ‡π‘œ πœ‡π‘œ πœ‡ = πœ‡π‘œ(1 + πœ’) πœ‡ πœ‡π‘œ βˆ’ 1 = πœ’ πœ‡βˆ’πœ‡π‘œ πœ‡π‘œ = πœ’ therefore π΅βˆ’π΅0 𝐡0 = πœ‡βˆ’πœ‡π‘œ πœ‡π‘œ = πœ’ Percentage increase in the magnetic field after inserting Aluminium is π΅βˆ’π΅0 𝐡0 Γ— 100 = 2.3 Γ— 10βˆ’5 Γ— 100 = 0.0023 %
Magnetic susceptibility of some material
Magnetic properties of material β€’ Diamagnetic: Susceptibility is Negative β€’ Paramagnetic: Susceptibility is Positive but small β€’ Ferromagnetic: Susceptibility is Positive but large
Diamagnetism β€’ Repels magnetic line of forces β€’ These material having completely filled electron β€’ Having no net magnetic dipole moment β€’ When these material placed in magnetic field, then they move from stronger to weaker β€’ These material are repelled by a magnet β€’ Eg. – Copper, gold, metal etc
Diamagnetic Substances β€’ Diamagnetic substances are those which are repelled by magnets and when placed in a magnetic field move from the stronger to the weaker part of the field. β€’ Diamagnetic materials examples β€’ Bismuth β€’ Phosphorus β€’ Antimony β€’ Copper β€’ Water β€’ Alcohol β€’ hydrogen
Properties of Diamagnetic materials β€’ When a diamagnetic substance is placed in a magnetic field it sets itself at right angles to the direction of the lines of force. β€’ When diamagnetic material is placed within a magnetic field the lines of force tend to go away from the material.
Paramagnetism β€’ Those substances which are weekly magnetized when placed in an external magnetic field in the same direction as the applied field are called paramagnetic substances. β€’ They tend to move from weaker to the stronger part of the field. β€’ According to Piere Curie (Applied for paramagnetic material) β€’ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘§π‘Žπ‘‘π‘–π‘œπ‘› 𝑀 ∝ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ 𝐹𝑖𝑒𝑙𝑑 ……………….(1) β€’ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘§π‘Žπ‘‘π‘–π‘œπ‘› 𝑀 ∝ 1 π΄π‘π‘ π‘œπ‘™π‘’π‘‘π‘’ π‘‡π‘’π‘šπ‘π‘’π‘Ÿπ‘Žπ‘‘π‘’π‘Ÿπ‘’ … … … … . . 2 β€’ i.e. M ∝ 𝐡 𝑇 ……From eq. (1) and (2) β€’ ∴ 𝑀 = 𝐢 𝐡 𝑇 β€’ Where, 𝐢 β†’ πΆπ‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘ …..(3) We know that, 𝐡 = πœ‡π‘‚π» From equation (3), 𝑀 = πΆπœ‡π‘‚π» 𝑇 ∴ 𝑀 𝐻 = πœ’ = 𝐢 πœ‡0 𝑇 ∴ πœ’ = πœ‡π‘Ÿ βˆ’ 1 = 𝐢 πœ‡0 𝑇 (a) No (b) Weak (c) Strong External Magnetic Field
Paramagnetism Paramagnetic substances are those which are attracted by magnets and when placed in a magnetic field move from weaker to stronger parts of the field. Paramagnetic materials examples Aluminum Manganese platinum, crown glass the solution of salts of iron and oxygen Properties of paramagnetic materials If a bar of paramagnetic material is suspended in between the pole pieces of an electromagnet, it sets itself parallel to the lines of force. When a bar of paramagnetic material is placed in a magnetic field the lines of force tend to accumulate in it.
Ferromagnetism Ferromagnetic materials are those materials which exhibit a spontaneous net magnetization at the atomic level, even in the absence of an external magnetic field. When placed in an external magnetic field, ferromagnetic materials are strongly magnetized in he direction of the field. Having strong magnetic property, they become permanent magnet. Domain Theory: In ferromagnetic material There is strong exchange of magnetic dipole moment Due to this exchange, small area formed in which all atoms are present. Small area (domain) Line which separate it called as domain axis. (a) Unmagnetised and (b) Magnetised Ferromagnetic material with domain
Ferromagnetic Substances Ferromagnetic substances are those which are attracted by the magnets and can also be magnetized. Ferromagnetic materials examples β€’ Iron β€’ Nickel β€’ cobalt and their alloys Properties of Ferromagnetic Substances The ferromagnetic substance shows the properties of the paramagnetic substance to a much greater degree. The susceptibility has a positive value and the permeability is also very large. The intensity of magnetization I is proportional to the magnetizing field H for a small value.
Example: A domain in ferromagnetic iron is in the form of cube of side 1 Β΅m. Estimate the number of iron atoms in the domain, maximum possible dipole moment and magnetisation of the domain. The molecular mass of iron is 55 g/mole and density is 7.9 𝑔/π‘π‘š3. Assume that each iron atom has a dipole moment of 9.27 Γ— 10βˆ’24 π΄π‘š2 . Solution: The volume of the cubic domain (10βˆ’6)3 = 10βˆ’18 π‘š3 = 10βˆ’12π‘π‘š3 mass = volume Γ— density = 7.9 Γ— 10βˆ’12 𝑔 An Avogadro number (6.023 x 1023) of iron atoms has mass 55 g. The number of atoms in the domain N = 7.9 Γ—10βˆ’12 Γ— 6.023 x 1023 55 = 8.56 Γ— 1010 The maximum possible dipole moment π‘šπ‘šπ‘Žπ‘₯ is achieved for the case when all the atomic moments are perfectly aligned (though this will not be possible in reality). π‘šπ‘šπ‘Žπ‘₯ = 8.65 Γ— 1010 Γ— 9.27 Γ— 10βˆ’24 = 8 Γ— 10βˆ’13 π΄π‘š2 Magnetisation M = π‘šπ‘šπ‘Žπ‘₯ domain volume = 8 Γ— 105 𝐴/π‘š
Effect of Temperature β€’ Ferromagnetic material depends upon temperature. β€’ Temperature β†’ Increased β†’ Domain Distorted β†’ Dipole moment weaker β†’ It becomes paramagnetic material β€’ The temperature at which a ferromagnetic material transforms into a paramagnetic substance is called Curie temperature (𝑇𝐢) of that material. β€’ Curie Temperature β†’ Temperature at which ferromagnetic material β†’ paramagnetic material β€’ Magnetic Susceptibility, πœ’ = 𝐢 𝑇 βˆ’ 𝑇𝐢 for 𝑇 > 𝑇𝐢 β€’ Where, C is a constant Fig.: Curie Temperature of some Ferromagnetic material. Curie Temperature of some materials
Hysteresis β€’ The behaviour of ferromagnetic material when placed in external magnetic field is quite interesting and informative. β€’ It is nonlinear and provides information of magnetic history of the sample. β€’ Consider an unmagnetized ferromagnetic material in the form of a rod placed inside a solenoid. β€’ On passing the current through solenoid, magnetic field is generated which magnetises the rod. β€’ Knowing the value of Ο‡ of the material of the rod, M (magnetization) = Ο‡ H. From Eq. (1) β€’ 𝐻 = 𝐡 πœ‡0 βˆ’ 𝑀 Fig.: Hysteresis cycle (loop)
Hysteresis β€’ Knowing the value of H (= 𝑛𝑙) and M, one can calculate the corresponding magnetic field B. β€’ Figure shows the behaviour of the material as we take it through one cycle of magnetisation. β€’ At point O in the graph the material is in nonmagnetised state. Fig.: Hysteresis cycle (loop) β€’ As the strength of external magnetic intensity H is increased, B also increases. β€’ But the increase is non linear. β€’ Near point a, the magnetic field is at its maximum value which is the saturation magnetization condition of the rod. β€’ This represents the complete alignment and merger of domains.
Hysteresis β€’ If H is increased, (by increasing the current flowing through the solenoid) there is no increase in B. This process is not reversible. β€’ At this stage if the current in the solenoid is reduced, the earlier path of the graph is not retraced. (Earlier domain structure is not recovered). β€’ When H = 0 (current through the solenoid is made zero, point b in the figure) we do not get B = 0. Fig.: Hysteresis cycle (loop) β€’ The value of B when H = 0 is called retentivity or remanence. β€’ This means some domain alignment is still retained even when H = 0. β€’ Next, when the current in the solenoid is increased in the reverse direction, point c in the graph is reached, where B = 0 at a certain value of H. β€’ This value of H is called coercivity.
Hysteresis β€’ At this point the domain axes are randomly oriented with respect to each other. β€’ If the current is further increased, in the reverse direction, B increases and again reaches a saturation state (point d). β€’ Here if H is increase further, B does not increase. β€’ From this point d onwards, when H is reduced, B also reduces along the path de. Fig.: Hysteresis cycle (loop) β€’ At this point e, again H = 0 but B is not zero. β€’ It means domain structure is present but the direction of magnetisation is reversed. β€’ Further increase in the current, gives the curve efa. β€’ On reaching point a, one loop is complete. β€’ This loop is called hysteresis loop and the process of taking magnetic material through the loop once is called hysteresis cycle.
Permanent Magnet and Electromagnet: β€’ Soft iron having large permeability (>1000) and small amount of retaining magnetization, is used to make electromagnets. β€’ For this purpose, a soft iron rod (or that of a soft ferromagnetic material) is placed in a solenoid core. β€’ On passing current through the solenoid, the magnetic field associated with solenoid increases thousand folds. β€’ When the current through the solenoid is switched off, the associated magnetic field effectively becomes zero. β€’ These electromagnets are used in electric bells, loud speakers, circuit breakers, and also in research laboratories.
Permanent Magnet and Electromagnet: β€’ Giant electromagnets are used in cranes to lift heavy loads made of iron. β€’ Superconducting magnets are used to prepare very high magnetic fields of the order of a few tesla. β€’ Such magnets are used in NMR (Nuclear Magnetic Resonance) spectroscopy. β€’ Permanent magnets are prepared by using a hard ferromagnetic rod instead of soft used in earlier case. β€’ When the current is switched on, magnetic field of solenoid magnetises the rod. β€’ As the hard ferromagnetic material has a property to retain the magnetization to larger extent, the material remains magnetised even after switching off the current through the solenoid.
Do you know? β€’ Soft ferromagntic materials can be easily magnetized and demagnetized. β€’ Hysteresis loop for hard and soft ferramagnetic materials
Magnetic Shielding: Fig. Magnetic Shielding. β€’ When a soft ferromagnetic material is kept in a uniform magnetic field, large number of magnetic lines crowd up inside the material leaving a few outside. β€’ If we have a closed structure of this material, say a spherical shell of iron kept in magnetic field, very few lines of force pass through the enclosed space. β€’ Most of the lines will be crowded into the iron shell. This effect is known as magnetic shielding. β€’ The instrument which need to be protected from magnetic field is completely surrounded by a soft ferromagnetic substance. β€’ This technique is being used in space ships. β€’ Some scientific experiments require the experiment to be protected from magnetic field in the laboratory. β€’ There, high magnetic fields of magnets need to be shielded by providing a case made up of soft ferromagnetic material.
Do you know? β€’ There are different types of shielding available like electrical and accoustic shielding apart from magnetic shielding. β€’ Electrical insulator functions as an electrical barrier or shield and comes in a wide array of materials. β€’ Normally the electrical wires used in our households are also shielded. β€’ In case of audio recording it is necessary to reduce other stray sound which may interfere with the sound to be recorded. β€’ So the recording studios are sound insulated using acoustic material.
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Chap 11 - Magnetic Materials.pptx

  • 2. Can You Recall? 1. What are magnetic lines of force? Magnetic Lines of Force is a an imaginary line representing the direction of magnetic field such that the tangent at any point is the direction of the field vector at that point. 2. Why magnetic monopoles do not exist? A magnetic monopole does not exist . Just as the two faces of a current loop cannot be physically separated, magnetic North pole and the South pole can never be separated even on breaking a magnet to its atomic size. 3. Which materials are used in making magnetic compass needle? The needle of magnetic compass is made of steel. This material can be magnetised for an extended period. On the other hand, plastic, wood and paper are non-magnetic substances and hence, can not be magnetised in order to indicate directions.
  • 3. β€’ Toque on a bar magnet in a magnetic field If a bar magnet placed in uniform magnetic field 𝜏 = π‘šπ΅ sin πœƒ Bar magnet will perform rotational motion Due to any displacement Work will be done (Work – Stored in the form of P.E.) We say magnetic Potential Energy. π‘ˆπ‘š = 0 πœƒ 𝜏 π‘‘πœƒ π‘ˆπ‘š = 0 πœƒ π‘šπ΅π‘ π‘–π‘› πœƒ π‘‘πœƒ = βˆ’π‘šπ΅ sin πœƒ
  • 4. β€’ Toque on a bar magnet in a magnetic field Case I: At πœƒ = 00 π‘ˆπ‘š = βˆ’π‘š 𝐡 Case II: At πœƒ = 1800 π‘ˆπ‘š = π‘š 𝐡 Case III: At πœƒ = 900 π‘ˆπ‘š = 0 Where, m – Magnetic Moment B – Magnetic Field πœƒ βˆ’ 𝐴𝑛𝑔𝑙𝑒 β€’ Two magnet suspended Freely – Mutual Perpendicular to each other
  • 5. β€’ Two magnet suspended Freely – Mutual Perpendicular to each other At equilibrium: 𝜏 = 𝐼 𝛼 𝜏 = 𝐼 𝑑2πœƒ 𝑑𝑑2 __________ (i) 𝛼 = π‘‘πœ” 𝑑𝑑 = 𝑑 𝑑𝑑 π‘‘πœƒ 𝑑𝑑 𝐼 β†’ π‘€π‘œπ‘šπ‘’π‘›π‘‘ π‘œπ‘“ π‘–π‘›π‘’π‘Ÿπ‘‘π‘–π‘Ž 𝛼 β†’ π΄π‘›π‘”π‘’π‘™π‘Žπ‘Ÿ π‘Žπ‘π‘π‘’π‘™π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› πœƒ β†’ π΄π‘›π‘”π‘’π‘™π‘Žπ‘Ÿ π·π‘–π‘ π‘π‘™π‘Žπ‘π‘’π‘šπ‘’π‘›π‘‘ πœ” β†’ π΄π‘›π‘”π‘’π‘™π‘Žπ‘Ÿ π‘‰π‘’π‘™π‘œπ‘π‘–π‘‘π‘¦ If we rotate magnet in opposite direction: Torque will be opposite 𝜏 = βˆ’π‘šπ΅ sin πœƒ ______________(ii) (-ve sign: Bar magnet is rotating in opposite direction) From equation (i) and (ii) ∴ 𝐼 𝑑2πœƒ 𝑑𝑑2 = βˆ’π‘šπ΅ sin πœƒ
  • 6. If πœƒ β†’ π‘‰π‘’π‘Ÿπ‘¦ π‘ π‘šπ‘Žπ‘™π‘™ π‘‘β„Žπ‘’π‘› sin πœƒ β‰ˆ πœƒ ∴ 𝐼 𝑑2πœƒ 𝑑𝑑2 = βˆ’π‘šπ΅ πœƒ 𝑑2πœƒ 𝑑𝑑2 = βˆ’ π‘šπ΅ 𝐼 πœƒ Here, π‘šπ΅ 𝐼 β†’ πΆπ‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘ 𝐼 β†’ π‘€π‘œπ‘šπ‘’π‘›π‘‘ π‘œπ‘“ πΌπ‘›π‘’π‘Ÿπ‘‘π‘–π‘Ž 𝐡 β†’ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ 𝐹𝑖𝑒𝑙𝑑 π‘š β†’ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘šπ‘œπ‘šπ‘’π‘›π‘‘ As we studied in Simple Harmonic Motion (S.H.M) 𝑑2π‘₯ 𝑑𝑑2 = βˆ’πœ”2π‘₯ Where, π‘₯ β†’ π·π‘–π‘ π‘π‘™π‘Žπ‘π‘’π‘šπ‘’π‘›π‘‘ 𝑑2π‘₯ 𝑑𝑑2 β†’ π΄π‘π‘π‘’π‘™π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› On comparing, πœ”2 = π‘šπ΅ 𝐼
  • 7. ∴ πœ” = π‘šπ΅ 𝐼 Time period for Bar Magnet, ∴ 𝑇 = 2πœ‹ πœ” ∴ 𝑇 = 2πœ‹ π‘šπ΅ 𝐼 = 2πœ‹ Γ— 𝐼 π‘šπ΅ ∴ 𝑇 = 2πœ‹ 𝐼 π‘šπ΅ Examples A bar magnet of moment of inertia of 500 𝑔 π‘π‘š2 makes 10 oscillations per minute in a horizontal plane. What is its magnetic moment, if the horizontal component of earth's magnetic field is 0.36 gauss? Ans: 𝑇 = 2πœ‹ 𝐼 π‘šπ΅
  • 8. Examples A bar magnet of moment of inertia of 500 𝑔 π‘π‘š2 makes 10 oscillations per minute in a horizontal plane. What is its magnetic moment, if the horizontal component of earth's magnetic field is 0.36 gauss? Given: Moment of Inertia I = 500 𝑔 π‘π‘š2 Frequency n = 10 oscillation per minute = 10/60 oscillations per second Time period T = 6 sec 𝐡𝐻 = 0.36 gauss 𝑇 = 2πœ‹ 𝐼 π‘šπ΅ π‘š = 4πœ‹2𝐼 𝑇2𝐡 = 4 Γ— (3.14)2 Γ—500 Γ—10βˆ’7 36 Γ— 0.36 Γ— 10βˆ’4 m = 1.524 𝐴 π‘š2
  • 9. π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘š β†’ π΄π‘‘π‘œπ‘šπ‘–π‘ π‘ π‘‘π‘Ÿπ‘’π‘π‘‘π‘’π‘Ÿπ‘’ β†’ 𝐷𝑒𝑝𝑒𝑛𝑑 Origin of Magnetism in Materials: Electron Revolving around the nucleus ↓ Magnetic Dipole Moment (m = IA) Where, I β†’ Moment of Inertia π‘š β†’ π‘šπ‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘‘π‘–π‘π‘œπ‘™π‘’ π‘šπ‘œπ‘šπ‘’π‘›π‘‘ A β†’ π΄π‘Ÿπ‘’π‘Ž π‘…π‘œπ‘‘π‘Žπ‘‘π‘’π‘‘ 𝑏𝑦 π‘’βˆ’ β€’ Magnetism depends upon atom.
  • 10. Magnetic Moment of an Electron Revolving Around the Nucleus of an Atom: Intrinsic Angular Momentum Magnetic dipole moment due to current loop is, m = I A Where, m β†’ magnetic Dipole (Orbital Magnetic Moment) I β†’ Current A β†’ Area enclosed by loop Consider, An electron moving in an orbit with constant velocity (v), Having radius r about nucleus Electron covers distance of circumference i.e. 2πœ‹π‘Ÿ in time 𝑆𝑝𝑒𝑒𝑑 = π·π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’ π‘‡π‘–π‘šπ‘’ = 2πœ‹π‘Ÿ 𝑇
  • 11. Magnetic Moment of an Electron Revolving Around the Nucleus of an Atom: Intrinsic Angular Momentum Current associated with charge π‘’βˆ’ is, 𝐼 = 𝑒 𝑇 _______(i) ∴ πΉπ‘œπ‘Ÿ π‘Žπ‘›π‘”π‘’π‘™π‘Žπ‘Ÿ 𝑠𝑝𝑒𝑒𝑑, 𝑇 = 2πœ‹ πœ” We get from (i), 𝐼 = 𝑒 2πœ‹ πœ” = π‘’πœ” 2πœ‹ 𝐼 = π‘’πœ” 2πœ‹ As 𝑣 = πœ” π‘Ÿ i.e. πœ” = 𝑣 π‘Ÿ ∴ 𝐼 = 𝑒𝑣 2πœ‹π‘Ÿ Now, For orbital magnetic moment: π‘šπ‘œπ‘Ÿπ‘ = 𝐼𝐴 π‘šπ‘œπ‘Ÿπ‘ = 𝑒𝑣 2πœ‹π‘Ÿ πœ‹π‘Ÿ2 = 1 2 evr ________ (ii)
  • 12. Magnetic Moment of an Electron Revolving Around the Nucleus of an Atom: Intrinsic Angular Momentum For some electron, orbital angular momentum: 𝐿 = π‘šπ‘’π‘£π‘Ÿ Where, π‘šπ‘’ β†’ π‘šπ‘Žπ‘ π‘  π‘œπ‘“ π‘’βˆ’ From equation (ii), π‘šπ‘œπ‘Ÿπ‘ = 1 2 π‘’π‘£π‘Ÿ π‘šπ‘œπ‘Ÿπ‘ = 1 2 π‘’π‘£π‘Ÿ Γ— π‘šπ‘’ π‘šπ‘’ = 𝑒 2π‘šπ‘’ Γ— (π‘šπ‘’π‘£π‘Ÿ) π‘šπ‘œπ‘Ÿπ‘ = 𝑒 2π‘šπ‘’ Γ— 𝐿 Where, π‘šπ‘œπ‘Ÿπ‘ β†’ π‘‚π‘Ÿπ‘π‘–π‘‘π‘Žπ‘™ π‘šπ‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘šπ‘œπ‘šπ‘’π‘›π‘‘ Conclusion: π‘‚π‘Ÿπ‘π‘–π‘‘π‘Žπ‘™ π‘šπ‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘šπ‘œπ‘šπ‘’π‘›π‘‘ ∝ π΄π‘›π‘”π‘’π‘™π‘Žπ‘Ÿ π‘šπ‘œπ‘šπ‘’π‘›π‘‘π‘’π‘š 𝑖. 𝑒. π‘šπ‘œπ‘Ÿπ‘ ∝ 𝐿 Where, 𝑒 2π‘šπ‘’ β†’ πΆπ‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘ πΆπ‘Žπ‘™π‘™π‘’π‘‘ π‘Žπ‘  πΊπ‘¦π‘Ÿπ‘œπ‘šπ‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ πΆπ‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘
  • 14. Similarly, From Quantum Mechanics: From 2𝑛𝑑 postulates of Bohr’s theory: Angular momentum of electron is n multiple of β„Ž 2πœ‹ i.e. 𝐿 = π‘šπ‘’π‘£π‘Ÿ = 𝑛 β„Ž 2πœ‹ We know that, π‘šπ‘œπ‘Ÿπ‘ = 𝑒 2π‘šπ‘’ 𝐿 ∴ π‘šπ‘œπ‘Ÿπ‘ = 𝑒 2π‘šπ‘’ . π‘›β„Ž 2πœ‹ = π‘’π‘›β„Ž 4πœ‹π‘šπ‘’ For 1𝑠𝑑 orbit, n = 1 ∴ π‘šπ‘œπ‘Ÿπ‘ = π‘’β„Ž 4πœ‹π‘šπ‘’ The Value π‘’β„Ž 4πœ‹π‘šπ‘’ β†’ π΅β„Žπ‘œπ‘Ÿ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘œπ‘› β†’ 9.274 Γ— 10βˆ’24 𝐴/π‘š2 Example Calculate the gyromagnetic ratio of electron (given 𝑒 = 1.6 Γ— 10βˆ’19 𝐢, π‘šπ‘’ = 9.1 Γ— 10βˆ’31 π‘˜π‘”)
  • 15. Example Calculate the gyromagnetic ratio of electron (given 𝑒 = 1.6 Γ— 10βˆ’19 𝐢, π‘šπ‘’ = 9.1 Γ— 10βˆ’31 π‘˜π‘”) Ans: Gyromagnetic Ratio = 𝑒 2 π‘šπ‘’ Gyromagnetic Ratio = 1.6 Γ— 10βˆ’19 2 Γ— 9.1 Γ— 10βˆ’31 πΊπ‘¦π‘Ÿπ‘œπ‘šπ‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘Ÿπ‘Žπ‘‘π‘–π‘œ = 8.8 Γ— 1010 𝐢/π‘˜π‘”
  • 16. Magnetization β€’ Unpaired electron having magnetic dipole moment β€’ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘§π‘Žπ‘‘π‘–π‘œπ‘› = π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘€π‘œπ‘šπ‘’π‘›π‘‘ π‘‰π‘œπ‘™π‘’π‘šπ‘’ π‘œπ‘“ π‘šπ‘Žπ‘‘π‘’π‘Ÿπ‘–π‘Žπ‘™ β€’ 𝑀 = 𝑀𝑛𝑒𝑑 π‘‰π‘œπ‘™π‘’π‘šπ‘’ β€’ M is vector quantity β€’ Unit - 𝐴 π‘š β€’ Dimension - [πΏβˆ’1𝐴]
  • 17. Magnetization Consider, a rod placed in solenoid ∴ Magnetic field inside solenoid 𝐡𝑂 = πœ‡0𝑛𝐼 Where, n = No. of turns on solenoid I = Current Passing ∴ Magnetic field due to material kept inside solenoid (π΅π‘š) Here, Net Magnetic Field 𝐡 = 𝐡𝑂 + π΅π‘š We know that, π΅π‘š ∝ π‘šπ‘Žπ‘”π‘›π‘’π‘‘π‘–π‘§π‘Žπ‘‘π‘–π‘œπ‘› ∴ π΅π‘š = πœ‡π‘œπ‘€ Where, πœ‡π‘œ β†’ π‘ƒπ‘’π‘Ÿπ‘šπ‘’π‘Žπ‘π‘–π‘™π‘–π‘‘π‘¦ π‘œπ‘“ π‘“π‘Ÿπ‘’π‘’ π‘ π‘π‘Žπ‘π‘’ ∴ 𝐡 = πœ‡π‘‚π‘›πΌ + πœ‡π‘‚π‘€ Here, new quantity called as magnetic field intensity β€˜H’ ∴ 𝐻 = 𝑛 𝐼 Does not depend upon on material rod.
  • 18. Magnetization Hence, 𝐡 = πœ‡π‘‚π» + πœ‡π‘‚π‘€ 𝐡 = πœ‡π‘‚(𝐻 + 𝑀) ………..(1) ∴ 𝐻 + 𝑀 = 𝐡 πœ‡0 ∴ 𝐻 = 𝐡 πœ‡0 βˆ’ 𝑀 Unit of H and M is same – A/m If H is not too strong, So Magnetization induced in material ∝ Magnetic Intensity ∴ 𝑀 ∝ 𝐻 𝑀 = πœ’π» Where, πœ’ β†’ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘†π‘’π‘ π‘π‘’π‘π‘‘π‘Žπ‘π‘–π‘™π‘–π‘‘π‘¦
  • 19. Magnetization From equation no. (1) 𝐡 = πœ‡π‘‚(𝐻 + 𝑀) ∴ 𝐡 = πœ‡π‘‚ 𝐻 + πœ’π» 𝐡 = πœ‡π‘‚ 1 + πœ’ 𝐻 ∴ 𝐡 = πœ‡0πœ‡π‘Ÿπ» 𝐡 = πœ‡π» Where, πœ‡π‘Ÿ = 1 + πœ’ πœ‡ = πœ‡π‘œπœ‡π‘Ÿ ∴ πœ‡ = πœ‡0(1 + πœ’) Where, πœ‡ β†’ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘ƒπ‘’π‘Ÿπ‘šπ‘’π‘Žπ‘π‘–π‘™π‘–π‘‘π‘¦ πœ‡π‘Ÿ β†’ π‘…π‘’π‘™π‘Žπ‘‘π‘–π‘£π‘’ π‘šπ‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ π‘π‘’π‘Ÿπ‘šπ‘’π‘Žπ‘π‘–π‘™π‘–π‘‘π‘¦ πœ‡π‘œ β†’ π‘ƒπ‘’π‘Ÿπ‘šπ‘’π‘Žπ‘π‘–π‘™π‘–π‘‘π‘¦ π‘œπ‘“ π‘“π‘Ÿπ‘’π‘’ π‘ π‘π‘Žπ‘π‘’
  • 20. Magnetic Permeability in Different Materials
  • 21. β€’ Magnetic permeability and susceptibility are quantitative measures of magnetic properties of materials. β€’ The key difference between magnetic permeability and susceptibility is that magnetic permeability describes the ability of a material to support the formation of a magnetic field inside itself whereas susceptibility describes whether a material is attracted to a magnetic field or is repelled from it. β€’ Magnetic susceptibility is a dimensionless measure. Summary – Magnetic Permeability vs Susceptibility β€’ Magnetic permeability is given by the units Henries per meter, and magnetic susceptibility is a dimensionless property of materials. β€’ The key difference between magnetic permeability and susceptibility is that magnetic permeability describes the ability of a material to support the formation of a magnetic field inside itself whereas susceptibility describes whether a material is attracted to a magnetic field or is repelled from it.
  • 22. Magnetic Permeability vs Susceptibility Magnetic permeability of a material is the ability of a material to support the formation of a magnetic field inside itself. Magnetic susceptibility is the measure of magnetic properties of a material which indicates whether the material is attracted or repelled from an external magnetic field. Units of Measurement Magnetic permeability is measured by the SI unit Henries per meter (H/m or HΒ·mβˆ’1) which is equivalent to Newtons per ampere squared (NΒ·Aβˆ’2). The magnetic susceptibility is a dimensionless property. Value for Diamagnetic Materials The value of magnetic permeability for diamagnetic materials is less than 1. The value of magnetic susceptibility for diamagnetic materials is less than zero. Value for Paramagnetic Materials The value of magnetic permeability for paramagnetic materials is greater than 1. The value of magnetic susceptibility for paramagnetic materials is greater than zero.
  • 23. Example: The region inside a current carrying toroid winding is filled with Aluminium having susceptibility πœ’ = 2.3 Γ— 10βˆ’5. What is the percentage increase in the magnetic field in the presence of Aluminium over that without it? Solution: The magnetic field inside the solenoid without Aluminium 𝐡𝑂 = πœ‡π‘‚π» The magnetic field inside the solenoid with Aluminium B = Β΅ H π΅βˆ’π΅0 𝐡0 = πœ‡βˆ’πœ‡π‘œ πœ‡π‘œ πœ‡ = πœ‡π‘œ(1 + πœ’) πœ‡ πœ‡π‘œ βˆ’ 1 = πœ’ πœ‡βˆ’πœ‡π‘œ πœ‡π‘œ = πœ’ therefore π΅βˆ’π΅0 𝐡0 = πœ‡βˆ’πœ‡π‘œ πœ‡π‘œ = πœ’ Percentage increase in the magnetic field after inserting Aluminium is π΅βˆ’π΅0 𝐡0 Γ— 100 = 2.3 Γ— 10βˆ’5 Γ— 100 = 0.0023 %
  • 24. Magnetic susceptibility of some material
  • 25. Magnetic properties of material β€’ Diamagnetic: Susceptibility is Negative β€’ Paramagnetic: Susceptibility is Positive but small β€’ Ferromagnetic: Susceptibility is Positive but large
  • 26. Diamagnetism β€’ Repels magnetic line of forces β€’ These material having completely filled electron β€’ Having no net magnetic dipole moment β€’ When these material placed in magnetic field, then they move from stronger to weaker β€’ These material are repelled by a magnet β€’ Eg. – Copper, gold, metal etc
  • 27. Diamagnetic Substances β€’ Diamagnetic substances are those which are repelled by magnets and when placed in a magnetic field move from the stronger to the weaker part of the field. β€’ Diamagnetic materials examples β€’ Bismuth β€’ Phosphorus β€’ Antimony β€’ Copper β€’ Water β€’ Alcohol β€’ hydrogen
  • 28. Properties of Diamagnetic materials β€’ When a diamagnetic substance is placed in a magnetic field it sets itself at right angles to the direction of the lines of force. β€’ When diamagnetic material is placed within a magnetic field the lines of force tend to go away from the material.
  • 29. Paramagnetism β€’ Those substances which are weekly magnetized when placed in an external magnetic field in the same direction as the applied field are called paramagnetic substances. β€’ They tend to move from weaker to the stronger part of the field. β€’ According to Piere Curie (Applied for paramagnetic material) β€’ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘§π‘Žπ‘‘π‘–π‘œπ‘› 𝑀 ∝ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘ 𝐹𝑖𝑒𝑙𝑑 ……………….(1) β€’ π‘€π‘Žπ‘”π‘›π‘’π‘‘π‘–π‘§π‘Žπ‘‘π‘–π‘œπ‘› 𝑀 ∝ 1 π΄π‘π‘ π‘œπ‘™π‘’π‘‘π‘’ π‘‡π‘’π‘šπ‘π‘’π‘Ÿπ‘Žπ‘‘π‘’π‘Ÿπ‘’ … … … … . . 2 β€’ i.e. M ∝ 𝐡 𝑇 ……From eq. (1) and (2) β€’ ∴ 𝑀 = 𝐢 𝐡 𝑇 β€’ Where, 𝐢 β†’ πΆπ‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘ …..(3) We know that, 𝐡 = πœ‡π‘‚π» From equation (3), 𝑀 = πΆπœ‡π‘‚π» 𝑇 ∴ 𝑀 𝐻 = πœ’ = 𝐢 πœ‡0 𝑇 ∴ πœ’ = πœ‡π‘Ÿ βˆ’ 1 = 𝐢 πœ‡0 𝑇 (a) No (b) Weak (c) Strong External Magnetic Field
  • 30. Paramagnetism Paramagnetic substances are those which are attracted by magnets and when placed in a magnetic field move from weaker to stronger parts of the field. Paramagnetic materials examples Aluminum Manganese platinum, crown glass the solution of salts of iron and oxygen Properties of paramagnetic materials If a bar of paramagnetic material is suspended in between the pole pieces of an electromagnet, it sets itself parallel to the lines of force. When a bar of paramagnetic material is placed in a magnetic field the lines of force tend to accumulate in it.
  • 31. Ferromagnetism Ferromagnetic materials are those materials which exhibit a spontaneous net magnetization at the atomic level, even in the absence of an external magnetic field. When placed in an external magnetic field, ferromagnetic materials are strongly magnetized in he direction of the field. Having strong magnetic property, they become permanent magnet. Domain Theory: In ferromagnetic material There is strong exchange of magnetic dipole moment Due to this exchange, small area formed in which all atoms are present. Small area (domain) Line which separate it called as domain axis. (a) Unmagnetised and (b) Magnetised Ferromagnetic material with domain
  • 32. Ferromagnetic Substances Ferromagnetic substances are those which are attracted by the magnets and can also be magnetized. Ferromagnetic materials examples β€’ Iron β€’ Nickel β€’ cobalt and their alloys Properties of Ferromagnetic Substances The ferromagnetic substance shows the properties of the paramagnetic substance to a much greater degree. The susceptibility has a positive value and the permeability is also very large. The intensity of magnetization I is proportional to the magnetizing field H for a small value.
  • 33. Example: A domain in ferromagnetic iron is in the form of cube of side 1 Β΅m. Estimate the number of iron atoms in the domain, maximum possible dipole moment and magnetisation of the domain. The molecular mass of iron is 55 g/mole and density is 7.9 𝑔/π‘π‘š3. Assume that each iron atom has a dipole moment of 9.27 Γ— 10βˆ’24 π΄π‘š2 . Solution: The volume of the cubic domain (10βˆ’6)3 = 10βˆ’18 π‘š3 = 10βˆ’12π‘π‘š3 mass = volume Γ— density = 7.9 Γ— 10βˆ’12 𝑔 An Avogadro number (6.023 x 1023) of iron atoms has mass 55 g. The number of atoms in the domain N = 7.9 Γ—10βˆ’12 Γ— 6.023 x 1023 55 = 8.56 Γ— 1010 The maximum possible dipole moment π‘šπ‘šπ‘Žπ‘₯ is achieved for the case when all the atomic moments are perfectly aligned (though this will not be possible in reality). π‘šπ‘šπ‘Žπ‘₯ = 8.65 Γ— 1010 Γ— 9.27 Γ— 10βˆ’24 = 8 Γ— 10βˆ’13 π΄π‘š2 Magnetisation M = π‘šπ‘šπ‘Žπ‘₯ domain volume = 8 Γ— 105 𝐴/π‘š
  • 34. Effect of Temperature β€’ Ferromagnetic material depends upon temperature. β€’ Temperature β†’ Increased β†’ Domain Distorted β†’ Dipole moment weaker β†’ It becomes paramagnetic material β€’ The temperature at which a ferromagnetic material transforms into a paramagnetic substance is called Curie temperature (𝑇𝐢) of that material. β€’ Curie Temperature β†’ Temperature at which ferromagnetic material β†’ paramagnetic material β€’ Magnetic Susceptibility, πœ’ = 𝐢 𝑇 βˆ’ 𝑇𝐢 for 𝑇 > 𝑇𝐢 β€’ Where, C is a constant Fig.: Curie Temperature of some Ferromagnetic material. Curie Temperature of some materials
  • 35. Hysteresis β€’ The behaviour of ferromagnetic material when placed in external magnetic field is quite interesting and informative. β€’ It is nonlinear and provides information of magnetic history of the sample. β€’ Consider an unmagnetized ferromagnetic material in the form of a rod placed inside a solenoid. β€’ On passing the current through solenoid, magnetic field is generated which magnetises the rod. β€’ Knowing the value of Ο‡ of the material of the rod, M (magnetization) = Ο‡ H. From Eq. (1) β€’ 𝐻 = 𝐡 πœ‡0 βˆ’ 𝑀 Fig.: Hysteresis cycle (loop)
  • 36. Hysteresis β€’ Knowing the value of H (= 𝑛𝑙) and M, one can calculate the corresponding magnetic field B. β€’ Figure shows the behaviour of the material as we take it through one cycle of magnetisation. β€’ At point O in the graph the material is in nonmagnetised state. Fig.: Hysteresis cycle (loop) β€’ As the strength of external magnetic intensity H is increased, B also increases. β€’ But the increase is non linear. β€’ Near point a, the magnetic field is at its maximum value which is the saturation magnetization condition of the rod. β€’ This represents the complete alignment and merger of domains.
  • 37. Hysteresis β€’ If H is increased, (by increasing the current flowing through the solenoid) there is no increase in B. This process is not reversible. β€’ At this stage if the current in the solenoid is reduced, the earlier path of the graph is not retraced. (Earlier domain structure is not recovered). β€’ When H = 0 (current through the solenoid is made zero, point b in the figure) we do not get B = 0. Fig.: Hysteresis cycle (loop) β€’ The value of B when H = 0 is called retentivity or remanence. β€’ This means some domain alignment is still retained even when H = 0. β€’ Next, when the current in the solenoid is increased in the reverse direction, point c in the graph is reached, where B = 0 at a certain value of H. β€’ This value of H is called coercivity.
  • 38. Hysteresis β€’ At this point the domain axes are randomly oriented with respect to each other. β€’ If the current is further increased, in the reverse direction, B increases and again reaches a saturation state (point d). β€’ Here if H is increase further, B does not increase. β€’ From this point d onwards, when H is reduced, B also reduces along the path de. Fig.: Hysteresis cycle (loop) β€’ At this point e, again H = 0 but B is not zero. β€’ It means domain structure is present but the direction of magnetisation is reversed. β€’ Further increase in the current, gives the curve efa. β€’ On reaching point a, one loop is complete. β€’ This loop is called hysteresis loop and the process of taking magnetic material through the loop once is called hysteresis cycle.
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  • 40.
  • 41. Permanent Magnet and Electromagnet: β€’ Soft iron having large permeability (>1000) and small amount of retaining magnetization, is used to make electromagnets. β€’ For this purpose, a soft iron rod (or that of a soft ferromagnetic material) is placed in a solenoid core. β€’ On passing current through the solenoid, the magnetic field associated with solenoid increases thousand folds. β€’ When the current through the solenoid is switched off, the associated magnetic field effectively becomes zero. β€’ These electromagnets are used in electric bells, loud speakers, circuit breakers, and also in research laboratories.
  • 42. Permanent Magnet and Electromagnet: β€’ Giant electromagnets are used in cranes to lift heavy loads made of iron. β€’ Superconducting magnets are used to prepare very high magnetic fields of the order of a few tesla. β€’ Such magnets are used in NMR (Nuclear Magnetic Resonance) spectroscopy. β€’ Permanent magnets are prepared by using a hard ferromagnetic rod instead of soft used in earlier case. β€’ When the current is switched on, magnetic field of solenoid magnetises the rod. β€’ As the hard ferromagnetic material has a property to retain the magnetization to larger extent, the material remains magnetised even after switching off the current through the solenoid.
  • 43. Do you know? β€’ Soft ferromagntic materials can be easily magnetized and demagnetized. β€’ Hysteresis loop for hard and soft ferramagnetic materials
  • 44. Magnetic Shielding: Fig. Magnetic Shielding. β€’ When a soft ferromagnetic material is kept in a uniform magnetic field, large number of magnetic lines crowd up inside the material leaving a few outside. β€’ If we have a closed structure of this material, say a spherical shell of iron kept in magnetic field, very few lines of force pass through the enclosed space. β€’ Most of the lines will be crowded into the iron shell. This effect is known as magnetic shielding. β€’ The instrument which need to be protected from magnetic field is completely surrounded by a soft ferromagnetic substance. β€’ This technique is being used in space ships. β€’ Some scientific experiments require the experiment to be protected from magnetic field in the laboratory. β€’ There, high magnetic fields of magnets need to be shielded by providing a case made up of soft ferromagnetic material.
  • 45. Do you know? β€’ There are different types of shielding available like electrical and accoustic shielding apart from magnetic shielding. β€’ Electrical insulator functions as an electrical barrier or shield and comes in a wide array of materials. β€’ Normally the electrical wires used in our households are also shielded. β€’ In case of audio recording it is necessary to reduce other stray sound which may interfere with the sound to be recorded. β€’ So the recording studios are sound insulated using acoustic material.