1. Electromagnetic Induction
Chapter 29
Electromagnetic Induction

2. Goals for Chapter 29
To examine experimental evidence that a changing magnetic field induces an emf
To learn how Faraday’s law relates the induced emf to the change in magnetic flux
To determine the direction of an induced emf

3. Goals for Chapter 29
To calculate the emf induced by a moving conductor
To learn how a changing magnetic flux generates an electric field
To study Maxwell’s Equations – the four fundamental equations that describe electricity and magnetism

4. Introduction How is a credit card reader related to magnetism?
Energy conversion makes use of electromagnetic induction.

5. Magnetic flux from Chapter 27

6. Induced current
A changing magnetic flux causes an induced current. No change => NO induced current!

7. Induced current
A changing magnetic flux causes an induced current. The induced emf is the corresponding emf causing the current.

8. Whether the source is a magnet or electromagnet doesn’t matter!
Induced current
A changing magnetic flux causes an induced current. The induced emf is the corresponding emf causing the current.
Whether the source is a magnet or electromagnet doesn’t matter!

9. Whether the source is moving or its current changes doesn’t matter
Induced current
A changing magnetic flux causes an induced current. The induced emf is the corresponding emf causing the current.
Whether the source is moving or its current changes doesn’t matter

10. Induced current
A changing magnetic flux causes an induced current. The induced emf is the corresponding emf causing the current.
Change B flux 
Create EMF 
Create Current!

11. Magnetic flux through an area element

12. Flux revisited
Flux depends on orientation of surface with respect to B field.

13. Flux revisited
Flux depends on orientation of surface with respect to B field.

14. Flux revisited
Flux depends on orientation of surface with respect to B field.

15. Faraday’s law
Induced emf in a closed loop equals negative of time rate of change of magnetic flux through the loop  = –dB/dt
= VOLTS (Electromotive Force)
dB/dt = Rate of Change of B field FLUX through surface
– sign means EMF opposes change

16. Faraday’s law
Induced emf in a closed loop equals negative of time rate of change of magnetic flux through the loop  = –dB/dt
In this case, if the flux changed from maximum to minimum in some time t, and loop was conducting, an EMF would be generated!

17. Faraday’s law
Induced emf in a closed loop equals negative of time rate of change of magnetic flux through the loop  = –dB/dt
[B ]= Tesla-m2
[d B/ dt] = Tesla-m2/sec
and from F = qv x B Teslas = Newtons-sec/Coulomb-meters [N/C][sec/meters]
[d B/ dt] = [N/C][sec/meter][m2/sec] = Nm/C
= Joule/C
= VOLT!

18. Emf and the current induced in a loop
Example 29.1: What is induced EMF & Current?

19. Emf and the current induced in a loop
Example 29.1: What is induced EMF & Current?
df/dt = d(BA)/dt = (dB/dt) A = T/s x m2
= 0.24 mV
I = E/R = mV/5.0W = mA

20. What are fundamental differences between
Goal
What are fundamental differences between
Generators
Motors
Alternators

21. How do you solve HW problem like 29.30?
Goal
What are fundamental differences between generators, motors, & alternators?
How do you solve HW problem like 29.30?
A m-long metal bar is pulled to the right at a steady 6.0 m/s perpendicular to a uniform, 0.850-T magnetic field. The bar rides on parallel metal rails connected through a 25-Ohm, resistor  so the apparatus makes a complete circuit. Ignore the resistance of the bar and the rails.
Calculate the magnitude & direction of the emf induced in the circuit, and the current.

22. Direction of the induced emf
Direction of induced current from EMF creates B field to KEEP original flux constant!
Increasing FLUX N v

23. Direction of the induced emf
Direction of induced current from EMF creates B field to KEEP original flux constant!
Induced current generates B field flux opposing change

24. Direction of the induced emf
Direction of induced current from EMF creates B field to KEEP original flux constant!

25. Direction of the induced emf
Direction of induced current from EMF creates B field to KEEP original flux constant!
Induced current generates B field flux opposing change

26. Direction of the induced emf
Direction of induced current from EMF creates B field to KEEP original flux constant!

27. Direction of the induced emf
Direction of induced current from EMF creates B field to KEEP original flux constant!
Induced current generates B field flux opposing change

28. Direction of the induced emf
Direction of induced current from EMF creates B field to KEEP original flux constant!

29. Direction of the induced emf
Direction of induced current from EMF creates B field to KEEP original flux constant!
Induced current generates B field flux opposing change

30. Lenz’s law
Lenz’s law: The direction of any magnetic induction effect is such as to oppose the cause of the effect.

31. Lenz’s law
Lenz’s law: The direction of any magnetic induction effect is such as to oppose the cause of the effect.
WHY???

32. Suppose induced current went this way!
Why Lenz’s Law?
Suppose the opposite was true – increasing flux generated supportive current…
Suppose induced current went this way! N v

33. Why Lenz’s Law?
Suppose the opposite was true – increasing flux generated supportive current…
Induced current creates B field! N S N v
Remember – this isn’t the case!

34. Why Lenz’s Law?
Suppose the opposite was true – increasing flux generated supportive current…
B field would ATTRACT incoming magnet! N S N v
Force
Remember – this isn’t the case!

35. Why Lenz’s Law?
Suppose the opposite was true – increasing flux generated supportive current…
Magnet would accelerate! N S N
V + at
Remember – this isn’t the case!

36. Why Lenz’s Law?
Suppose the opposite was true – increasing flux generated supportive current…
KE increases with no work done! N S N
V + at
Remember – this isn’t the case!

37. Lenz’s Law is like a conservation of energy relation!
Direction of induced current from EMF creates B field to KEEP original flux constant!
Induced B field opposes increase in flux! N v

38. Magnitude and direction of an induced emf
500 loop circular coil with radius 4.00 cm between poles of electromagnet. B field decreases at T/second. What are magnitude and direction of induced EMF?

39. Magnitude and direction of an induced emf
500 loop circular coil with radius 4.00 cm between poles of electromagnet. B field decreases at T/second. What are magnitude and direction of induced EMF?
Careful with flux ANGLE! f between A and B!
 = –N dB/dt = [NdB/dt] x [A cos f]
Direction? Since B decreases, EMF resists change…

40. A simple alternator – Example 29.3
An alternator creates alternating positive and negative currents (AC) as a loop is rotated by an external torque while in a fixed magnetic field (or vice-versa!)
Note – w comes from an external rotating force!
Water turning a turbine (hydroelectric)
Gasoline Motor turning a shaft (AC generator)

41. A simple alternator – Example 29.3
An alternator creates alternating positive and negative currents (AC) as a loop rotates in a fixed magnetic field (or vice-versa!)
Note – NO commutator to reverse current direction in the loop – so you will get ALTERNATING current
Recall DC motors! DIFFERENT!

42. A simple alternator – Example 29.3
An alternator creates alternating positive and negative currents (AC) as a loop rotates in a fixed magnetic field (or vice-versa!)
For simple alternator rotating at angular rate of w, what is the induced EMF?

43. A simple alternator
Example 29.3: For simple alternator rotating at angular rate of w, what is induced EMF?
B is constant; A is constant
Flux B is NOT constant!
B = BAcos f
Angle f varies in time: f = wt
EMF = - d [B ]/dt = -d/dt [BAcos(wt)]
So EMF = wBAsin(wt)

44. A simple alternator
EMF = wBAsin(wt)

45. A simple alternator (check out video!)
EMF = wBAsin(wt)

46. AC Alternators vs. DC Generators
An AC generator “Alternator” has continuous slip rings so current always “sloshes” back and forth
Slip rings
DC generator

47. AC Alternators vs. DC Generators
An AC Alternator has continuous slip rings so current always “sloshes” back and forth
Slip rings
DC generator
AC alternator

48. AC Alternators vs. DC Generators
A DC generator creates ONLY one-directional (positive) current flow with EMF always the same “sign.”
Commutator
AC alternator
DC generator

49. DC generator and back emf in a motor
Commutator results in ONLY unidirectional (“direct”) current flow:
EMF(DC gen) = | wBAsin(wt) |

50. DC generator and back emf in a motor
A DC generator creates ONLY one-directional (positive) current flow with EMF always the same “sign.”
“Back EMF”
Generated from changing flux through the loop
DC generator

51. DC generator and back emf in a motor
Average EMF generated = AVG( | wBAsin(wt) | ) over Period T where T = 1/f = 2p/w

52. DC generator and back emf in a motor

53. DC generator and back emf in a motor
Example 29.4: 500 turn coil, with sides 10 cm long, rotating in B field of T generates 112 V. What is w?

54. Lenz’s law
Lenz’s law:

55. Lenz’s law and the direction of induced current

56. Lenz’s law and the direction of induced current

57. Slidewire generator – Example 29.5
What is magnitude and direction of induced emf?
Area A vector chosen to be into page

58. Slidewire generator – Example 29.5
B is constant; A is INCREASING => flux increases!

59. Slidewire generator – Example 29.5
Area A = Lx so dA/dt = L dx/dt = Lv
Width x

60. EMF = - d [B ]/dt = -BdA/dt = -BLv
Slidewire generator
EMF = - d [B ]/dt = -BdA/dt = -BLv
Induced current creates B OUT of page

61. Work and power in the slidewire generator
Let resistance of wires be “R”
What is rate of energy dissipation in circuit and rate of work done to move the bar?

62. Work and power in the slidewire generator
EMF = -BLv
I = EMF/R = -BLv/R
Power = I2R = B2L2v2/R

63. Work and power in the slidewire generator
Work done = Force x Distance
Power applied = Work/Time = Force x velocity
Power = Fv = iLBv and I = EMF/R
Power = (BLv/R)LBv = B2L2v2/R

64. Motional electromotive force
The motional electromotive force (VOLTAGE!) across the ends of a rod moving perpendicular to a magnetic field is  = vBL.

65. Motional electromotive force
The motional electromotive force across the ends of a rod moving perpendicular to a magnetic field is  = vBL.
Without any other forces present FE = FB
=> No net acceleration

66. Motional electromotive force
Make a complete circuit by adding stationary conducting loop
Across entire (stationary) conductor, E field from moving bar will push current

67. Induced motional electromotive force

68. Motional electromotive force
So what happens?
Force on Bar = ILB is to LEFT
Bar slows down…

69. Motional electromotive force
So what happens?
Force on Bar = ILB is to LEFT
Bar slows down…
Or… equally!
B field flux (into page) increases in loop
Generate EMF opposing increase from Faraday’s Law

70. Motional electromotive force
Are these saying the same thing??

71. Motional electromotive force

72. How can we use Induced EMF?B +V
current
Push a large current across the bar – it accelerates!

73. Rail Guns
Use induced forces to accelerate particles to amazing speeds!
Not science fiction…

74. Induced electric fields
Wire loop around a solenoid that experiences a changing current.
See a NEW current flow in surrounding loop!
WHY??
There must be an EMF…

75. Induced electric fields
Vary current in solenoid => vary B field through cylinder
Vary flux through loop!
Faraday’s Law applies!
EMF created! A current will flow…
But wait a minute!!
© 2016 Pearson Education Inc.

76. Induced electric fields
Solenoid doesn’t HAVE a B field outside!!
Wire loop itself is NOT in a B field
No “qv x B” applies to make charges in wire loop move!!
AHA! Changing magnetic flux causes an induced electric field.

77. Induced electric fields
AHA! Changing magnetic flux causes an induced electric field.

78. Induced electric fields
Key – the integral path must be stationary
And…
The E field created is NOT conservative!

79. Induced electric fields
Electric field in loop must drive the current
When solenoid current I changes with time, B field flux also changes, & induced EMF can be written in terms of induced electric field:
© 2016 Pearson Education Inc.

80. Displacement current
Ampere’s law works fine for wires carrying current. But…. It is incomplete! Consider charging a capacitor – with no wires between the plates! Ampere’s Law: Take line integral around wire: i

81. Displacement current
For the plane circular area bounded by the circle, Iencl is the current iC in the left conductor. But surface that bulges out to right is bounded by the same circle, and the current through that surface is zero. This leads to a contradiction.

82. Displacement current
When capacitor is charging, E field is increasing between the plates. Define “fictitious” displacement current iD in region between the plates. Regard this as source of magnetic field between plates.

83. Eddy currents
When a piece of metal moves through a magnetic field or is located in a changing magnetic field, eddy currents of electric current are induced. The metal detectors used at airport security checkpoints operate by detecting eddy currents induced in metallic objects.

84. Magnetic Braking!
Slowing a falling magnet! Slow a saw blade… Magnetic Braking… Magnetic Trains! Eddy Currents

85. Eddy Currents – what are they good for?
Stop a saw blade!

86. Faraday disk dynamo
Spinning conducting disc in uniform magnetic field.
Generates current in connecting wires!

87. Faraday disk dynamo
Current increases with B, with Area, and with rotation rate w
What is the EMF in terms of these variables?

88. Faraday disk dynamo – does this violate Faraday’s Law?
NO change in B field!
NO change in Area!
No change in flux?!!
There should NOT be an induced EMF??!
But there IS!
But if you rotate the *magnet* instead, there is NOT an EMF
Shouldn’t it be relative? !$%##

89. Faraday disk dynamo – does this violate Faraday’s Law?

90. What are fundamental differences between
Goal
What are fundamental differences between
Generators
Motors
Alternators