Magnetic properties of materials- I

1. Magnetic properties of materials- I

2. Magnetic properties of materials- I • Magnetic dipoles • Field of a magnetic dipole • Force on a dipole in a non uniform field • Induced magnetic dipole moment

3. B p r z   Circular current loop dB

4. Circular current loop If z >>R

5.  and B are in the same direction. • B is produced by . Where  is = R2 I Known as Magnetic dipole moment

6. In general,  = I A, true for any shape of the loop. • A is a vector area, with direction assign by right hand rule.

7. Magnetic dipole in an external Magnetic field Magnetic dipole experiences a torque

8. z n h y e g x f Torque of a current loop

9. z n h y e g x f Torque on a current loop a b Plane of the loop makes angle  with the field

10. z e  y  b f

11. z h  y  b g

12. z n h y g x f Forces on a current loop  e b a y

13. Forces on a current loop Contribute to torque

14. z e  Fhe  Ffg f  y 

15. Torque on a current loop

16. Torque of a magnetic dipole Torque tends to rotate  so that it lines up with B.

17. Potential energy for the dipole • B makes an angle  with the dipole

18. U has smallest value when  and B are parallel  - B • Largest when anti-parallel  B

19. Find the magnetic dipole moment of the circuit.

20. z Find the magnetic dipole moment of the loop. All sides have equal length and it carries a current I. a a y a Direction is along the line y = z. x

21. Important to note • In general, potential energy (PE) can not be defined for a Magnetic field alone. • Since torque on the dipole depends upon the its position with respect to the field, PE can be defined for magnetic dipole in the field. • This PE corresponds to any change in the rotational configuration.

22. Comparison with electric dipole

23. The field of a magnetic dipole

24. Electric field of an electric dipole

25. Magnetic field lines of a magnetic dipole

26. Bar magnet can also be considered to be a magnetic dipole. Field lines do not start or end but continue through the interior of the magnets, forming close loops.

27. Similarities Electric and magnetic dipole fields vary as r-3 when we are far from the dipoles.

28. Force on a dipole in a nonuniform field In a uniform field total force on the dipole (electric as well as magnetic) is zero. There is only torque but no net motion In a non uniform field net force is not zero. Dipole may move.

29. Net force will be downward on the loop.

31. Force on the loop 2 due to 1 is attractive (downward). If, F21< 0

32. Induced magnetic dipole moments

33. Induced magnetic dipole moments I-Iind • An applied magnetic field can induce dipole moments I+Iind Downward Induced magnetic dipole moment.

34. Important points • In a non uniform magnetic field, permanent dipoles are attracted towards the source of the field • Induced dipoles are repelledfrom the source of the field. • Similar effect is observed in materials that lack permanent magnetic dipole moments.

35. An idea about magnetic moments

36. Atomic and nuclear magnetism • Magnetic properties depend upon magnetic properties of the individual atoms. • Magnetic material is consists of atomic dipoles dipole moment associated with circulation of electron.

37. Calculation • We consider magnetic materials to be composed of a collection of atomic dipoles. • These dipoles might align when an external electric field is applied. • An electron circulating about the nucleus can be considered as a current loop of radius r and speed v.

38. Calculation • Current in the loop = • Bohr’s model • Orbital magnetic dipole moment

39. Bohr’s magneton • This is a basic unit of atomic magnetic dipole moment

40. Nuclear magnetism Nuclear magnetic moments Orbital part Intrinsic part (spin)