1. Measuring the strength of a Magnetic Field © David Hoult 2009

2. When current flows through a conductor which is in a magnetic field, it experiences a force, except when the conductor is © David Hoult 2009

3. When current flows through a conductor which is in a magnetic field, it experiences a force, except when the conductor is parallel to the flux lines © David Hoult 2009

4. When current flows through a conductor which is in a magnetic field, it experiences a force, except when the conductor is parallel to the flux lines The direction of the force is at 90° to both the current and the flux lines © David Hoult 2009

5. When current flows through a conductor which is in a magnetic field, it experiences a force, except when the conductor is parallel to the flux lines The direction of the force is at 90° to both the current and the flux lines Fleming’s left hand rule helps to remember the relation between the three directions… © David Hoult 2009

8. Thumb First finger Second finger © David Hoult 2009

9. Motion ThuMb First finger Second finger © David Hoult 2009

10. Motion ThuMb Second finger Field First finger © David Hoult 2009

11. Motion ThuMb Field Current First finger SeCond finger © David Hoult 2009

16. Factors affecting the Magnitude of the Force The force depends on © David Hoult 2009

17. The force depends on - the current flowing through the conductor, I © David Hoult 2009

18. The force depends on - the current flowing through the conductor - the length of conductor in the field © David Hoult 2009

19. The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that © David Hoult 2009

20. The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that F  current, I © David Hoult 2009

21. The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that F  current, I F  length of conductor, L © David Hoult 2009

22. The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that F  current, I F  length of conductor, L F = I L × a constant © David Hoult 2009

23. The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that F  current, I F  length of conductor, L F = I L × a constant magnetic field strength or © David Hoult 2009

24. The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that F  current, I F  length of conductor, L F = I L × a constant magnetic field strength or magnetic flux density © David Hoult 2009

25. F = I L B © David Hoult 2009

26. F = I L B units of B Newtons per Amp per meter, NA -1 m -1 © David Hoult 2009

27. F = I L B units of B Newtons per Amp per meter, NA -1 m -1 1 NA -1 m -1 is called 1 Tesla (1 T) © David Hoult 2009

28. F = I L B units of B Newtons per Amp per meter NA -1 m -1 The flux density of a magnetic field is 1 NA -1 m -1 is called 1 Tesla (1 T) © David Hoult 2009

29. F = I L B units of B Newtons per Amp per meter NA -1 m -1 The flux density of a magnetic field is the force per unit current per unit length acting on a conductor placed at 90° to the field 1 NA -1 m -1 is called 1 Tesla (1 T) © David Hoult 2009

30. F = I L B units of B Newtons per Amp per meter NA -1 m -1 The flux density of a magnetic field is the force per unit current per unit length acting on a conductor placed at 90° to the field F = I L B sin  1 NA -1 m -1 is called 1 Tesla (1 T) © David Hoult 2009

31. Force acting on a charged particle moving through a magnetic field © David Hoult 2009

33. Consider a conductor of length L, having n free electrons per unit volume. A current, I, is flowing through it © David Hoult 2009

34. Consider a conductor of length L, having n free electrons per unit volume. A current, I, is flowing through it © David Hoult 2009

35. In this piece of conductor there are © David Hoult 2009

36. In this piece of conductor there are NAL free electrons © David Hoult 2009

37. If all these electrons pass through end x in time t then the current, I is given by In this piece of conductor there are NAL free electrons © David Hoult 2009

38. n A L en A L e t If all these electrons pass through end x in time t then the current, I is given by In this piece of conductor there are NAL free electrons © David Hoult 2009

39. If there is a magnetic field of flux density B at 90° to the current, the conductor will experience a force of magnitude © David Hoult 2009

40. If there is a magnetic field of flux density B at 90° to the current, the conductor will experience a force of magnitude I L B © David Hoult 2009

41. If there is a magnetic field of flux density B at 90° to the current, the conductor will experience a force of magnitude I L B This is the sum of the forces on all the electrons, so the force F acting on each electron is given by © David Hoult 2009

42. I L BI L B If there is a magnetic field of flux density B at 90° to the current, the conductor will experience a force of magnitude I L B This is the sum of the forces on all the electrons, so the force F acting on each electron is given by n A Ln A L F == I BI B n An A © David Hoult 2009

43. Substituting for I gives F = © David Hoult 2009

44. Substituting for I gives n A L e Bn A L e B t n At n A F == © David Hoult 2009

45. Substituting for I gives n A L e Bn A L e B t n At n A F = L e BL e B t = © David Hoult 2009

46. Substituting for I gives n A L e Bn A L e B t n At n A F = L e BL e B t = © David Hoult 2009

47. but L/t is © David Hoult 2009

48. but L/t is the (drift) velocity of the electrons © David Hoult 2009

49. but L/t is the (drift) velocity of the electrons therefore © David Hoult 2009

50. but L/t is the (drift) velocity of the electrons therefore F = e v B © David Hoult 2009

51. F = q v B In general the magnitude of the force acting on a charged particle moving with velocity v, at 90° to a magnetic field of flux density B, is given by where q is the charge on the particle © David Hoult 2009

52. If the particle moves at angle  to the field © David Hoult 2009

53. If the particle moves at angle  to the field the magnitude of the component of its velocity at 90° to the field is © David Hoult 2009

54. If the particle moves at angle  to the field the magnitude of the component of its velocity at 90° to the field is v cos  © David Hoult 2009

55. If the particle moves at angle  to the field the magnitude of the component of its velocity at 90° to the field is v cos  = v sin  Therefore, in general F = © David Hoult 2009

56. Therefore, in general F = q v B sin  If the particle moves at angle  to the field the magnitude of the component of its velocity at 90° to the field is v cos  = v sin  © David Hoult 2009

57. The Motion of Charged Particles in Magnetic Fields © David Hoult 2009

58. A charged particle moving parallel to the flux lines © David Hoult 2009

59. A charged particle moving parallel to the flux lines experiences no force © David Hoult 2009

60. A charged particle moving parallel to the flux lines experiences no force There are three possible paths for a charged particle moving through a uniform magnetic field © David Hoult 2009

61. If the angle,  between the field and the direction of motion is zero the path is © David Hoult 2009

62. If the angle,  between the field and the direction of motion is zero the path is a straight line © David Hoult 2009

63. If the angle,  between the field and the direction of motion is 90° the path is © David Hoult 2009

64. field into plane of diagram If the angle,  between the field and the direction of motion is 90° the path is circular © David Hoult 2009

65. field into plane of diagram If the angle,  between the field and the direction of motion is 90° the path is circular © David Hoult 2009

66. field into plane of diagram If the angle,  between the field and the direction of motion is 90° the path is circular © David Hoult 2009

67. If the angle between the field and the direction of motion is 0° <  < 90° the path is © David Hoult 2009

68. If the angle between the field and the direction of motion is 0° <  < 90° the path is © David Hoult 2009

69. If the angle between the field and the direction of motion is 0° <  < 90° the path is © David Hoult 2009

70. If the angle between the field and the direction of motion is 0° <  < 90° the path is a helix © David Hoult 2009