1. Electromagnetic Induction and Faraday’s Law
Chapter 27
Electromagnetic Induction and Faraday’s Law

2. Faraday’s experiments (1820-1821)
Induced EMF (1)
Electric current
magnetic field
Faraday’s experiments ( )
Changing magnetic field can produce a current 2

3. Phenomenon of electromagnetic induction
Induced EMF (2)
Phenomenon of electromagnetic induction
An induced EMF (electromotive force in P566) is produced by a changing magnetic field. 3

4. Faraday’s law of induction
The EMF induced in a circuit is equal to the changing rate of magnetic flux through the circuit.
Faraday’s law of induction
1) EMF is produced even if no current can flow (as when the circuit is not complete)
2) N loops coil:
3) Induction current in circuit: 4

5. This is known as Lenz’s law
An induced EMF is always in a direction that opposes the original change in flux that caused it.
This is known as Lenz’s law
1) Conservation of energy
2) Three ways to create EMF 5

6. Solution: The magnetic flux:
Rotating coil
Example1: A circular coil is rotating in uniform magnetic field. Determine the EMF.
Solution: The magnetic flux:
If the magnetic field is changing: 6

7. Induced charges
Thinking: A small coil moves far away from the position in figure. How to determine the total induced charge going through the coil? 7

8. EMF induced in moving conductor
Conductor moves in B → motional EMF
Caused by Lorentz force:
+ +
- - -
: non-electrostatic field
Motional EMF:
All ⊥ case:
Direction? 8

9. Derived by Faraday’ law
The result can also be derived by Faraday’ law
moves with velocity
It sweeps out an area dS
Magnetic flux:
EMF: 9

10. Motion in uniform field
Example2: Determine the EMF induced in the conductor in a uniform magnetic field.
(a)
(b) v l v B
EMF:
→ straight wire:
Force:
Power: 10

11. Rotates in uniform field
Example3: A conductor rod rotates about axis o. Determine the induced EMF. (B, L, ω)
Solution: For an infinitesimal:
Total EMF in the conductor:
Faraday’s law: 11

12. Rotates in nonuniform field
Question: A conductor rod rotates about axis o. Determine the induced EMF when the two wires are perpendicular to each other. I L o 12

13. Motion on rails
Example4: Conducting rod rests on frictionless parallel rails with an EMF source. Determine the speed of rod if the source puts out (a) constant I; (b) constant EMF. (c) What is the terminal speed?
Solution: (a)
m, R 13

14. (b) source puts out constant EMF:
m, R
(c) Terminal speed 14

15. Conductor stays at rest, magnetic field changes
Changing B produces E
Conductor stays at rest, magnetic field changes
→ Induced EMF
→ induced current
Forces on static charges?
Maxwell: It’s caused by electric field
Induced (vortex) electric field: produced by changing magnetic field, and acts on electric charges. 15

16. General form of Faraday’s law
Faraday’s law → general form
Generalize the definition of V :
For induced EMF in a closed circuit:
where is the induced electric field
General form of Faraday’s law 16

17. Induced electric field
1) Ei is produced by changing B, not by charges
2) Even if there is no conductor, Ei still exists
3) Induced electric field is nonconservative
4) Minus sign shows the direction of Ei 17

18. Electrostatic / induced electric / magnetic field
Comparison of fields
Electrostatic / induced electric / magnetic field
Field lines:
vortex I 18

19. Solution: Analyze the symmetry
Vortex electric field
Example5: Uniform magnetic field in cylindrical space changes as dB/dt = C > 0. Determine the induced electric field. R
Solution: Analyze the symmetry 19

20. Solution: Induced electric field:
EMF in a wire
Example6: Magnetic field in a solenoid changes as dB/dt = C > 0. A straight wire lies tangent to the solenoid at its center. What is the EMF in wire?
Solution: Induced electric field: R 2R 20

21. Imagine a closed circuit
Another Solution: R 2R 1 2
Imagine a closed circuit
Discussion: a b 21

22. Self inductance
Thinking: If a solenoid with current I is cut off from the battery, will I drop abruptly to 0? How does I change over time? 22

23. *Applications of induction
Sound systems / microphones:
Transformers:
Recording tape / computer memory 23

24. Vortex electric field → vortex current
Heating effect → induction cooker
Electromagnetic damping 24