1. Lesson 9 Faraday’s Law  Faraday’s Law of Induction  Motional EMF  Lenz’s Law  Induced EMF’s and Induced Electric Fields  Eddy Currents

2. Torque on Loop Current in loop in a magnetic field produces torque on a loop

3. Induced Current Does torque on loop in a magnetic field produces current in a loop ? YES

4. Picture ¨current depends on the torque ¨thus on rotational frequency I B

5. Change of Flux Picture  Current depends on speed of magnet  Thus rate of change of magnetic Field

6. Change of Flux Picture Equations Common factors, change of area, change of magnetic field

7. Induced Current in Wire I B v FBFB moving wire in field B produces current I if there is a conduction path

8. Induced emf j i k z2)z2) y1y1 (y, z1)z1)

9. Equations I

10. Equations II Work done per unit charge byF B in moving charges fromz 1 toz 2  vBl wherel  z 2  z 1 No work is done in moving charges in other sections of path(ignore Hall effect) Work done per unit charge dW dQ = emf Thus  vBl

11. Equations III Area of loop in magnetic field At   yt   y 1  l Total magnetic flux through loop  t  Rate of change of magnetic flux d  dt  -B dy dt l  Bvl  

12. Faradays Law of Induction for N loops

13. This defines an Induced Electric Field by

14. Faradays Law of Electromagnetic Induction '        The work done per unit charge by magnetic force moving charge fromz 1 toz 2 dW dQ  1 Q F B  d s z 1 z 2   1 Q F B  d s loop   E ind  d s loop  thus   N d  dt  E ind  d s loop 

15.  An induced EMF is a measure of  An induced Electric Field  If charge is in this region and there is a conduction path it will feel a force from the induced Electric Field and flow  An induced EMF is a measure of  An induced Electric Field  If charge is in this region and there is a conduction path it will feel a force from the induced Electric Field and flow Induced Electric Field

16. Equations Remember for a static electric field E stat V ab  E stat  d s a b  and  E stat  d s   0 as E stat is conservative But for an induced electric field E ind E  d s   0 thus E ind is not conservative

17. Magnetic Flux and Induced Electric Field Changing Magnetic Flux produces an Induced Electric Field

18. Mechanical Work to Electrical work I I F appl v l B  B l v Pulling at constant velocity v k j i y

19. Mechanical Work to Electrical work II wire l with current I flowing in it moving in a magnetic field B feels a force given by F  I l  B F  IlB k  i  j This force opposes the applied force F appl and must be equal and opposite if the velocity is to remain constant F  F appl  IlB

20. Mechanical Work to Electrical work III I F appl v l B  B l v F

21. Mechanical Power to Electrical Power I

22. Mechanical Power to Electrical Power II I F appl v l B  B l v Pulling at constant velocity v F

23. Magnetic Field produced by Changing Current Circulating current produces an induced magnetic field I B ind That opposes the external magnetic field B That produces the current

24. Current produced by Changing Magnetic Field (a) Change of External Magnetic Field Produces Current (b) Current Produces Induced Magnetic Field

25. Lenz's Law Lenz’s Law Polarity of  is such that it opposes the change that caused it Direction of E  is such that it opposes the change that caused it Direction of induced current is such that it opposes the change that caused it

26. Conservation of Energy

27. AC Generator

28. AC Potential  t   d  dt  d B  A   d BACos    BA sin  t  if rotational speed is constant  t    BA sin  t    max sin  t   max  BA  d dt   t

29. DC Generator

30. Eddy Currents