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magnetic materials

1. 1 MAGNETIC PROPERTIES Basic Definitions Origin of magnetic momentum Orbital angular momentum Spin Angular momentum

2. 2 INTRODUCTION Magnetic material play an important role in industrial and scientific research fields. Magnetism is a phenomenon by which a material exerts either attractive or repulsive force on another. • Basic source of magnetic force is movement of electrically charged particles. .

3. 3 INTRODUCTION Magnetic dipoles : • Magnetic dipoles are found to exist in magnetic materials, analogous to electric dipoles. A magnetic dipole is a small magnet composed of north and south poles instead of positive and negative charges.

4. 4 Basic Definitions Magnetic dipole moment or Magnetic moment: if ‘m’ is the magnetic pole strength and ‘2 l ’ is the length of the magnet then its magnetic dipole moment is given by µ m = m*2 l . When an electric current of I ampere flows through a circular wire of one turn having an area of cross section A , then the magnetic moment is µ m =I A Units : Am 2 2 l

5. 5 Basic Definitions Magnetic field : The space surrounding the magnet up to which its attracting influence is felt is known as magnetic field. Magnetic induction field strength(or) Magnetic Flux density(B): The magnetic flux density B is defined as the number of magnetic lines of forces passing through a unit area of cross section of magnetic material .if Φ is the number of magnetic lines of forces that passes through ‘A’ area cross section of a material , then B= Φ /A Units : Wb m -2 or Tesla

6. 6 Basic Definitions Magnetic field strength (H) : The magnetic field strength H is the force experienced by a unit north pole placed at given point in a magnetic field . It is expressed as Am -1 . Magnetic Permeability (µ): The magnetic Permeability ‘µ’ is measure of the amount of magnetic lines of forces penetrating through a material . It is defined as the ratio of the magnetic flux density (or) magnetic induction field strength (B) is in the material to the applied magnetic field intensity H. µ=B/H

7. 7 Magnetic Permeability of free space( µ ) The Magnetic Permeability of free space( µ ) is measure of the amount of magnetic lines of force passing through the air medium . It is defined as the ratio of magnetic induction field strength B of free space or air to the applied magnetic field strength H. µ =B /H Where µ =4 π *10 -7 Hm -1 Relative permeability It is defined as the ratio of permeability of a material to the permeability of free space µ r =µ/µ µ=µ µ r

8. 8 Basic Definitions Magnetization or intensity of magnetization (M): The Magnetization M is defined as the magnetic moment per unit volume . It is expressed as Am -1 Magnetic Susceptibility( χ ): This indicates the ease with which a substance is magnetized. It is the ratio between the magnetization produced in a sample to the magnetic field strength χ =M/H

9. 9 Relation between B,H and M B=µH B=µ µ r H Adding and subtracting µ H B=µ µ r H +µ H-µ H B=µ (µ r -1) H+µ H B= µ M+µ H (Since M=(µ r -1)H) B=µ (H+M)

10. 10 Relation between χ and µ r

11. 11 In atoms, the permanent magnetic moment can arise due to the following . i. Due to this motion the electrons in the orbits – Orbital magnetic moment ii. Due to intrinsic spin of the electrons – S pin magnetic moment Origin of Magnetic Moment

12. 12 Orbital Magnetic Moment Consider an electron of mass ‘m’, charge ‘e’ revolving around the nucleus in circular orbit of radius ‘r’ in anti clock wise direction . Let ‘v’ be the linear velocity of electron and ‘ ω ’ is the angular velocity of revolving electron (angular frequency)

13. 13 Orbital Magnetic Moment Then the linear frequency of the revolving electron = ω /2 π Time period of revolutions=2 π / ω The revolving electron in circular orbit estabilishes a current is given by I=charge/timeperiod= -e/T = -e ( ω /2 π ) The orbital magnetic moment of the electron is given by

14. 14 Orbital Magnetic Moment     radius

15. 15 . L . Orbital Magnetic Moment is called Bohr magneton It is a unit to measure the atomic magnetic momentum

16. 16 Spin Magnetic Moment Of Electron   Spin angular momentum of an electron is given by

17. 17 Magnetic Moment Due To Nuclear Spin In addition to electronic contribution ,nuclear spin also contributes to magnetic moment of atoms The nuclear spin magnetic moment is given by µ nuclear spin =eh/4 π M p M p represents the mass of the proton. µ nuclearspin =5.05*10 -27 Am 2