1. Electro-Magnetic Induction © David Hoult 2009

2. Magnetic flux © David Hoult 2009

6. If the magnitude of the flux density is B then the magnitude of the magnetic flux (  ) linked with the area A is defined to be © David Hoult 2009

7. If the magnitude of the flux density is B then the magnitude of the magnetic flux (  ) linked with the area A is defined to be   = A B © David Hoult 2009

8. units of flux   = A B © David Hoult 2009

9.   = A B units of flux T m 2 © David Hoult 2009

10.   = A B units of flux T m 2 1 T m 2 = 1 Weber (Wb) © David Hoult 2009

12. Now, the magnitude of the component of the flux density perpendicular to the area is B cos  © David Hoult 2009

13. Now, the magnitude of the component of the flux density perpendicular to the area is B cos    = A B cos  so the magnetic flux (  ) linked with the area is now alternatively © David Hoult 2009

14. In practice, the area in question is usually surrounded by a conductor, often a coil of wire. © David Hoult 2009

15. In practice, the area in question is usually surrounded by a conductor, often a coil of wire. If the coil of wire has N turns, we define the flux linkage as follows © David Hoult 2009

16. Flux linkage = N  In practice, the area in question is usually surrounded by a conductor, often a coil of wire. If the coil of wire has N turns, we define the flux linkage as follows © David Hoult 2009

17. EMF induced in a conductor moving through a uniform magnetic field © David Hoult 2009

23. The wire moves distance  s in time  t. In this time, a charge  q moves past any point in the wire. © David Hoult 2009

24. work done = F  s The wire moves distance  s in time  t. In this time, a charge  q moves past any point in the wire. © David Hoult 2009

25. work done = F  s The wire moves distance  s in time  t. In this time, a charge  q moves past any point in the wire. work done per unit charge = F sF s qq © David Hoult 2009

26. work done = F  s The wire moves distance  s in time  t. In this time, a charge  q moves past any point in the wire. work done per unit charge = F sF s qq work done per unit charge is the induced emf © David Hoult 2009

27. If the wire moves at constant speed, the force F must be © David Hoult 2009

28. If the wire moves at constant speed, the force F must be equal but opposite to the force acting on it due to the current I, induced in it © David Hoult 2009

29. If the wire moves at constant speed, the force F must be equal but opposite to the force acting on it due to the current I, induced in it F = - I L B © David Hoult 2009

30. If the wire moves at constant speed, the force F must be equal but opposite to the force acting on it due to the current I, induced in it F = - I L B F sF s qq E = © David Hoult 2009

31. If the wire moves at constant speed, the force F must be equal but opposite to the force acting on it due to the current I, induced in it F = - I L B F sF s qq E = - I LB  s qq E = © David Hoult 2009

32. I =I =

33. I =I = qq tt

34. I =I = qq tt - (  q/  t) L B  s qq E = and © David Hoult 2009

35. I =I = qq tt - (  q/  t) L B  s qq E = and ss tt = © David Hoult 2009

36. I =I = qq tt - (  q/  t) L B  s qq E = and ss tt = v © David Hoult 2009

37. I =I = qq tt - (  q/  t) L B  s qq E = and ss tt = v E = - B L v © David Hoult 2009

38. The Laws of Electro-magnetic Induction © David Hoult 2009

39. When e.m.i. occurs, any induced current will flow in such a direction as to Lenz’s Law © David Hoult 2009

40. When e.m.i. occurs, any induced current will flow in such a direction as to oppose the change producing it Lenz’s Law © David Hoult 2009

41. When e.m.i. occurs, any induced current will flow in such a direction as to oppose the change producing it Lenz’s Law It should be clear that Lenz’s law is an “electro- magnetic version” of © David Hoult 2009

42. When e.m.i. occurs, any induced current will flow in such a direction as to oppose the change producing it Lenz’s Law It should be clear that Lenz’s law is an “electro- magnetic version” of the law of conservation of energy © David Hoult 2009

43. When e.m.i. occurs, any induced current will flow in such a direction as to oppose the change producing it Lenz’s Law Faraday’s Law The induced emf is directly proportional to the © David Hoult 2009

44. When e.m.i. occurs, any induced current will flow in such a direction as to oppose the change producing it Lenz’s Law Faraday’s Law The induced emf is directly proportional to the rate of change of flux linking the conductor © David Hoult 2009

45. The sense of the induced current can be predicted using Fleming’s RIGHT hand rule © David Hoult 2009

46. The sense of the induced current can be predicted using Fleming’s RIGHT hand rule which is pretty much like Fleming’s left hand rule © David Hoult 2009

47. The sense of the induced current can be predicted using Fleming’s RIGHT hand rule which is pretty much like Fleming’s left hand rule except, guess what... © David Hoult 2009

48. The sense of the induced current can be predicted using Fleming’s RIGHT hand rule which is pretty much like Fleming’s left hand rule except, guess what... using the right hand instead of the left hand ! © David Hoult 2009

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

50. Both the laws of e.m.i. can be combined in a single mathematical statement © David Hoult 2009

51. Faraday Both the laws of e.m.i. can be combined in a single mathematical statement © David Hoult 2009

52. E   tt Faraday Both the laws of e.m.i. can be combined in a single mathematical statement © David Hoult 2009

53. E   tt Faraday Faraday + Lenz Both the laws of e.m.i. can be combined in a single mathematical statement © David Hoult 2009

54. E   tt Faraday E  -  tt Faraday + Lenz Both the laws of e.m.i. can be combined in a single mathematical statement © David Hoult 2009

55. Using the S.I. system of units the constant of proportionality is 1 so, if (as is often the case) the conductor is a coil of wire having N turns, we have © David Hoult 2009

56. E = -N  tt Using the S.I. system of units the constant of proportionality is 1 so, if (as is often the case) the conductor is a coil of wire having N turns, we have © David Hoult 2009

57. E = -N  tt Using the S.I. system of units the constant of proportionality is 1 so, if (as is often the case) the conductor is a coil of wire having N turns, we have This equation is often referred to as Neumann’s Law © David Hoult 2009

58. For a wire moving at 90° to a field with speed v, the induced emf is given by © David Hoult 2009

59. For a wire moving at 90° to a field with speed v, the induced emf is given by E = - B L v © David Hoult 2009

60. E = - B L v © David Hoult 2009

61. E = - B L v = - B L ss tt © David Hoult 2009

62. E = - B L v = - B L ss tt = - B AA tt © David Hoult 2009

63. E = - B L v = - B L  tt ss tt = - B AA tt = - © David Hoult 2009

64. E = - B L v = - B L  tt ss tt = - B AA tt = - This suggests that change of flux linking a conductor and flux cutting by a conductor are equivalent actions © David Hoult 2009

65. Simple a.c. generator © David Hoult 2009

66. Simple a.c. generator © David Hoult 2009

67. Simple a.c. generator © David Hoult 2009

68. Simple a.c. generator © David Hoult 2009

69. Simple a.c. generator © David Hoult 2009

70. Simple a.c. generator © David Hoult 2009

71. Simple a.c. generator Fleming’s right hand rule gives the sense of the current to be... © David Hoult 2009

72. Simple a.c. generator © David Hoult 2009

73. Simple a.c. generator Fleming’s right hand rule gives the sense of the current to be... which means that, at the instant shown in the diagram, terminal Q is the positive terminal of the generator © David Hoult 2009

74. Simple a.c. generator Fleming’s right hand rule gives the sense of the current to be which means that, at the instant shown in the diagram, terminal Q is the positive terminal of the generator When the coil has turned through 180°, P will be the positive terminal so the generator gives us alternating current © David Hoult 2009

75. The Transformer © David Hoult 2009

81. weak induced alternating emf © David Hoult 2009

82. iron core © David Hoult 2009

85. The Ideal Transformer If a transformer is described as ideal we mean it is 100% efficient © David Hoult 2009

86. The Ideal Transformer If a transformer is described as ideal we mean it is 100% efficient In other words, power output (at secondary coil) equals power input (to primary coil) © David Hoult 2009

87. The Ideal Transformer Therefore, in an ideal transformer: © David Hoult 2009

88. The Ideal Transformer Therefore, in an ideal transformer: i) the coils have zero resistance © David Hoult 2009

89. The Ideal Transformer Therefore, in an ideal transformer: i) the coils have zero resistance ii) all the magnetic flux  produced by the primary current I p is linked with the secondary coil © David Hoult 2009

90. The Ideal Transformer Therefore, in an ideal transformer: i) the coils have zero resistance ii) all the magnetic flux  produced by the primary current I p is linked with the secondary coil iii) no current flows in the iron core © David Hoult 2009

91. The Ideal Transformer © David Hoult 2009

92. The Ideal Transformer When I p changes,  changes. © David Hoult 2009

93. The Ideal Transformer When I p changes,  changes. When  changes, an emf is induced in both coils. © David Hoult 2009

94. At the primary coil, the magnitude of the induced emf is given by © David Hoult 2009

95. At the primary coil, the magnitude of the induced emf is given by E p = - N p  tt © David Hoult 2009

96. At the primary coil, the magnitude of the induced emf is given by E p = - N p  tt as we are assuming zero resistance coils, the supply voltage must also have this magnitude in order to maintain the flow of current © David Hoult 2009

97. At the primary coil, the induced emf is given by as we are assuming zero resistance coils, the supply voltage must also have this magnitude in order to maintain the flow of current At the secondary coil, the magnitude of the induced emf is given by E s = - N s  tt E p = - N p  tt © David Hoult 2009

98. EsEs EpEp = NpNp NsNs

99. EsEs EpEp = NpNp NsNs here we are assuming that  is the same for both coils © David Hoult 2009

100. The power input to the primary coil is given by power in = © David Hoult 2009

101. The power input to the primary coil is given by power in = E p I p © David Hoult 2009

102. The power input to the primary coil is given by power in = E p I p The power output from the secondary coil is given by power out = © David Hoult 2009

103. The power input to the primary coil is given by power in = E p I p The power output from the secondary coil is given by power out = E s I s © David Hoult 2009

104. The power input to the primary coil is given by power in = E p I p The power output from the secondary coil is given by power out = E s I s as we are considering an ideal transformer © David Hoult 2009

105. The power input to the primary coil is given by power in = E p I p The power output from the secondary coil is given by power out = E s I s as we are considering an ideal transformer E p I p = E s I s © David Hoult 2009

106. E p I p = E s I s Therefore, with an ideal transformer, when the secondary coil is open circuit (not connected to anything), there is no net energy taken from the supply. © David Hoult 2009

107. E p I p = E s I s Therefore, with an ideal transformer, when the secondary coil is open circuit (not connected to anything), there is no net energy taken from the supply. Energy is stored in the magnetic field during the time the current is increasing but is recovered from the field when it “collapses”. © David Hoult 2009

108. Transmission of Electrical Energy © David Hoult 2009

110. If the voltage across the bulb is 6V the current will be © David Hoult 2009

111. If the voltage across the bulb is 6V the current will be 1A © David Hoult 2009

112. If the voltage across the bulb is 6V the current will be 1A Power wasted in R = R I 2 = R © David Hoult 2009

116. If the voltage across the bulb is still 6V the current flowing through the bulb is still 1A © David Hoult 2009

117. If the step down transformer is 100% efficient the current flowing through R is © David Hoult 2009

118. If the step down transformer is 100% efficient the current flowing through R is 1/8 A © David Hoult 2009

119. If the step down transformer is 100% efficient the current flowing through R is 1/8 A Power wasted in R = R I 2 = © David Hoult 2009

120. If the step down transformer is 100% efficient the current flowing through R is 1/8 A Power wasted in R = R I 2 = R 64 © David Hoult 2009

121. 64 times less energy wasted ! © David Hoult 2009