1. Chapter 23
Faraday’s Law

2. 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”

3. Clicker 2

4. 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

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

6. 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

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

8. Transformer
Magnetic core conducts magnetic flux.
Energy conservation:

9. Magnetic Field Energy Density
Is there energy stored in magnetic field?
Did it for capacitor. Now can show that there is an energy density associated with magnetic field by expressing the energy in an inductor in terms of the magnetic field.

10. Field Energy Density
Electric and magnetic field energy density:

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

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

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

14. Classical Theory of Electromagnetic Radiation
Chapter 24
Classical Theory of Electromagnetic Radiation

15. Maxwell’s Equations Four equations: Gauss’s law for electricity
Gauss’s law for magnetism
Faraday’s law
Ampere’s law for magnetism
(incomplete)
Provide a complete description of possible spatial patterns of electric
and magnetic field in space.

16. Ampere’s Law Charging a capacitor: Current inside No current inside
Lets work with the last one… Grey area soap film is stretched flat over the circular Ampere’s path.

17. Maxwell’s Approach
Time varying magnetic field leads to curly electric field.
Time varying electric field leads to curly magnetic field? I
Current in wire I – causes change in E flux, should cause the same effect in curly B
‘equivalent’ current
combine with current in Ampere’s law

18. The Ampere-Maxwell Law
Works!
This law cannot be derived, but all experimental facts prove it, especially phenomena of radio and light-waves

19. Maxwell’s Equations Four equations (integral form) : Gauss’s law
Gauss’s law for magnetism
Faraday’s law
Ampere-Maxwell law
Add Lorentz to complete the list of fundamental equations of electricity and magnetism
Lorentz eq – defines the meaning of electric and magnetic field in terms of their effect on charge
+ Lorentz force