Lesson 9

1. Lesson 9 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 loop

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

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

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 moving wire in field B produces current I if there is a conduction path I B v FB

8. Induced emf (y, z1) (y, z2) y1 k j i

9. Equations I

10. Equations II

11. Equations III Area of loop in magnetic field ( ) ( ) ( ) A t = y t - y l 1 Total magnetic flux through loop ( ) ( ) ( ) ( ) F t = BA t = B y t - y l 1 Rate of change of magnetic flux e d F dy = B l = - Bvl = - dt dt

12. Faradays Law of Electromagnetic Induction Faraday ' s Law of Induction for N loops ì ü ò e ï ï F d d = - = - í · ý B A N N d ï ï dt dt î þ loop The work done per unit charge by magnetic force moving charge from z to z 1 2 ò ò ò z 2 dW 1 1 = · = · = · F s F s E s d d d B B ind dQ Q Q z loop loop 1 thus ò e F d = - = · E s N d ind dt loop

13. Induced Electric Field • 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

14. Equations E Remember for a static electric field stat ò b = · E s V d and ab stat a ò = · = E s E d 0 as is conservative stat stat E but for an induced electric field ind ò · ¹ E s d 0 ind thus E is not conservative ind

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

16. Mechanical Work to Electrical work I Pulling at constant velocity v B v l I Fappl Blv k j i

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

18. Mechanical Work to Electrical work III B v F l I Fappl Blv

19. Mechanical Power to Electrical Power I

20. Mechanical Power to Electrical Power II Pulling at constant velocity v B v l I Fappl Blv

21. Magnetic Field produced by Changing Current Circulating current produces an induced magnetic field I Bind That opposes the magnetic field B

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

23. 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

24. Conservation of Energy Conservation of Energy

25. AC Generator AC Generator

26. AC Potential

27. DC Generator DC Generator

28. Eddy Currents