1. Faraday’s Law
Michael Faraday
( )
Faraday’s law cannot be derived from the other fundamental principles we have studied
Formal version of Faraday’s law:
Unlike motional emf – Faraday cannot be derived
. A British physicist and chemist, he is best known for his discoveries of electro-magnetic rotation, electro-magnetic induction and the dynamo.
Faraday's ideas about conservation of energy led him to believe that since an electric current could cause a magnetic field, a magnetic field should be able to produce an electric current. He demonstrated this principle of induction in Faraday expressed the electric current induced in the wire in terms of the number of lines of force that are cut by the wire. The principle of induction was a landmark in applied science, for it made possible the dynamo, or generator, which produces electricity by mechanical means
Sign: given by right hand rule
“Current opposes change in B”

2. Various ways of making changing magnetic field
Change current through the solenoid
Time varying B can be
produced by moving coil:
by moving magnet:
move coil – get changing B and curly E
How to create a time-varying magnetic field?
by rotating magnet:
(or coil)

3. Clicker
Solenoid has circumference 10 cm. The current I1 is increasing causing increasing B1 as in the figure.
Solenoid is surrounded by a wire with finite resistance.
When length of the wire is changed from 30 to 20 cm what will happen to detected current?
It will decrease
Increase
Does not change
ammeter + - B

4. A Circuit Surrounding a Solenoid
Example:
B1 changes from 0.1 to 0.7 T in 0.2 seconds; area=3 cm2.
Application of Faraday’s law
Circuit acts as battery.
What is the ammeter reading? (resistance of ammeter+wire is 0.5)

5. Clicker: A Circuit Not Surrounding a Solenoid
If we increase current through solenoid what will be ammeter reading?
positive current
negative current
zero
zero

6. Voltmeter Reading
Voltmeter will read emf. Be careful using voltmeter when AC currents are present.
Problem – when measuring dV keep wires which go to Voltmeter so that they do not encircle area with changing B
Voltmeter = ammeter with large resistance

7. The EMF for a Coil With Multiple Loops
Each loop is subject to similar
magnetic field  emf of loops
in series:
Series connection of many loops with the same emf

8. Exercise
1. A bar magnet is moved toward a coil. What is the ammeter reading (+/-)?
2. The bar magnet is moved away from the coil.
What will ammeter read?
S side in = B –field increasing and points to the left, to opposes the change current should run CW – positive current into (+) side of voltmeter
move coil – get changing B and curly E
Positive
Negative

9. Clicker 2

10. Faraday’s Law and Motional EMF
‘Magnetic force’ approach: I
Use Faraday law:
When a wire moves through magnetic field -> magnetic forces drive current through wire I

11. Faraday’s Law and GeneratorI
Old problem

12. Exercise A uniform time-independent magnetic field B=3 T points 30o to
the normal of the rectangular loop.
The loop moves at constant speed v
1. What is the emf?
2. In 0.1 s the loop is stretched to be 0.12 m by 0.22 m. What is average emf during this time?
Old problem

13. Two Ways to Produce Changing 
Two ways to produce curly electric field:
1. Changing B
2. Changing A
Changing B field or area (shape, orientation)

14. Inductance Constant voltage – constant I, no curly electric field.
Increase voltage: dB/dt is not
zero  emf
For long solenoid:
Change current at rate dI/dt:
One factor of N from B field of solenoid, other factor due to changing flux through the N loops.
(one loop)
emfbat R
emfcoil

15. Inductance ENC emfbat R emfcoil EC Increasing I  increasing B emfbat
emfind
L – inductance, or self-inductance

16. Inductance ENC R L emfbat EC emfind Unit of inductance L:
American physicist Joseph Henry, in 1831 discovered the effect of time-varying magnetic field simultaneously with Michael Faraday.
Unit of inductance L:
Henry = Volt.second/Ampere
Increasing the current causes ENC to oppose this increase

17. Inductance: Decrease Current
ENC EC
emfbat R
emfind L
Conclusion: Inductance resists changes in current
Orientation of emfind depends on sign of dI/dt

18. Current in RL Circuit
Last shown.
If t is very long:

19. Current in RL Circuit
If t is zero:
Current in RL circuit:

20. Time Constant of an RL Circuit
Current in RL circuit:
Time constant: time in which exponential factor drops e times