Measuring the strength of a Magnetic Field

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

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8. Thumb First finger Second finger © David Hoult 2009

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

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

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

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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 acurrent, 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 acurrent, I F alength 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 a current, I F a 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 a current, I F a 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 a current, I F a length of conductor, L F = I L × a constant magnetic field strength or magnetic flux density © David Hoult 2009

25. F = ILB © David Hoult 2009

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

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

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

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

30. F = ILB units of B Newtons per Amp per meter NA-1m-1 1NA-1m-1 is called 1 Tesla (1T) 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 = ILBsinq © David Hoult 2009

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

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

38. In this piece of conductor there are NAL free electrons If all these electrons pass through end x in time t then the current, I is given by nALe t © 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 ILB © 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 ILB 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. If there is a magnetic field of flux density B at 90° to the current, the conductor will experience a force of magnitude ILB This is the sum of the forces on all the electrons, so the force F acting on each electron is given by ILB IB F = = nA nAL © David Hoult 2009

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

44. Substituting for I gives nALeB F = = tnA © David Hoult 2009

45. Substituting for I gives nALeB LeB F = = tnA t © David Hoult 2009

46. Substituting for I gives nALeB LeB F = = tnA 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