Lesson 9 Dipoles and Magnets

1. Lesson 9Dipoles and Magnets

2. Today we will: • learn the definitions of electric and magnetic dipoles. • find the forces, torques, and energies on dipoles in uniform fields. • learn what happens when we put dipoles in nonuniform fields. Class 27

3. Lesson 9Dipoles and Magnets

4. Section 1Force on a Current-carrying Wire

5. Force on a Wire in a Magnetic Field There is a force on charge carriers in a current-carrying wire. This force is transferred to the wire itself. i L

6. Force on a Wire in a Magnetic Field N charge carriers are in length L of the wire. T is the time it takes a charge to go the distance L. The force is: i L

7. Force on a Wire in a Magnetic Field More generally

8. Section 2Force and Torque on Wire Loops

9. Force on a Wire Loop in a Uniform Magnetic Field The net force on a wire loop is zero. i

10. Torque on a Wire Loop in a Uniform Magnetic Field The net torque on a wire loop is not zero. i

11. Torque on a Wire Loop in a Uniform Magnetic Field We define an area vector for the loop, by using the right hand rule. i

12. Right-hand Rule for Current Loops The direction of an area for a current loop is normal to the plane of the loop and In the direction of your thumb if your fingers loop in the direction of the current. i

13. Right-hand Rule for Current Loops Note that the directed area of the loop is the same as the direction of the magnetic field produced by the loop! i

14. Torque on a Wire Loop in a Uniform Magnetic Field Now calculate the torque about an axis through the center of the loop going into the screen. i

15. Torque on a Wire Loop in a Uniform Magnetic Field The magnitude of the torque is the product of the force and the moment arm.

16. Torque on a Wire Loop in a Uniform Magnetic Field The magnitude of the torque is the product of the force and the moment arm.

17. Torque on a Wire Loop in a Uniform Magnetic Field

18. Torque on a Wire Loop in a Uniform Magnetic Field

19. Section 3Magnetic Dipoles

20. Define the Magnetic Dipole Moment Since appears in a number of formulas, we give it a name: the magnetic dipole moment. Note that it is a vector with the direction given by the right-hand rule.

21. In terms of the magnetic dipole moment: Torque on a Wire Loop in a Magnetic Field

22. Direction of the Torque A dipole feels a torque that tends to align the dipole moment with the external field.

23. Potential Energy of a Dipole The maximum potential energy is when the dipole is opposite the field. The minimum potential energy is when the dipole is in the direction of the field.

24. Potential Energy of a Dipole The work done by a force is

25. Potential Energy of a Dipole The work done by a force is Similarly, the work done by a torque is

26. Potential Energy of a Dipole The work done by a force is Similarly, the work done by a torque is Since the change in potential energy is the work it takes to rotate the dipole, we have:

27. Potential Energy of a Dipole We can choose the constant of integration to be anything we want.

28. Potential Energy of a Dipole It’s simplest if we choose it to be zero.

29. Potential Energy of a Dipole Caution!!! U=0 is not the minimum energy. It is the energy when the dipole is perpendicular to the field!

30. Section 4Electric Dipoles

31. The Electric Dipole An electric dipole is a charge +q and a charge -- q held apart a distance apart.

32. The Electric Dipole Moment An electric dipole moment is The direction of goes from the  charge to the + charge.

33. Torque and Potential Energy of an Electric Dipole Electric dipoles work just the same way as magnetic dipoles. In uniform fields, there is no net force on the dipole. Torque: Potential energy:

34. An Electric Dipole in a Nonuniform Field First, the dipole feels a torque that aligns the dipole with the field. ( end toward the source of the field.)

35. An Electric Dipole in a Nonuniform Field Then, the dipole feels a net force in the direction of the stronger field.

36. I A Magnetic Dipole in a Nonuniform Field Magnetic dipoles behave in much the same way. They first experience a torque that aligns them with external field.

37. I A Magnetic Dipole in a Nonuniform Field Then, they experience a net force that pulls them in the direction of the stronger field.

38. S N Permanent Magnets Permanent magnets have magnetic dipole moments much as current loops.

39. N S S N Permanent Magnets In a nonuniform external field, permanent magnets experience a torque…

40. S N S N Permanent Magnets …then a net force in the direction of stronger magnetic field.

41. S N S N Permanent Magnets …then a net force in the direction of stronger magnetic field.

42. Today we will: • define magnetization and magnetic susceptiblity • learn about paramagnetic, diamagnetic, and ferromagnetic materials • learn about the opposing effects of domain alignment and thermal disalignment • learn how to understand hysteresis curves • characterize ferromagnetic materials in terms of residual magnetization and coercive force Class 28

43. Section 5Paramagnetism and Diamagnetism

44. Permanent Magnets Magnetite or loadstone was known from antiquity.

45. "Magnetism" comes from the region called Magnesia, where loadstone (magnetite) was found. Permanent Magnets

46. Permanent Magnets Magnetite or loadstone was known from antiquity. Loadstone floating on wood rotates so one end always points north.

47. Permanent Magnets Magnetite or loadstone was known from antiquity. Loadstone floating on wood rotates so one end always points north. This is the north pole.

48. Permanent Magnets Magnetite or loadstone was known from antiquity. Loadstone floating on wood rotates so one end always points north. This is the north pole. If two magnets are placed near other, like poles attract and unlike poles repel.

49. Permanent Magnets William Gilbert in 1600 publushed De Magnete – where he described magnetism as the “soul of the earth.”

50. N S Permanent Magnets Gilbert: A perfectly spherical magnet spins without stopping – because the earth is a perfect sphere and it’s a magnet and it spins without stopping.