1. Faraday’s Law M&I Chapter 23

2. Maxwell’s Equations (so far…) *Not complete

3. for fields made by charges at rest. Can a distribution of static charges make this field? Electrostatic forces are conservative. The change in potential around a loop must be zero.

4. means: No curly electric fields. BUT: This is only true for “Coulomb” fields (fields caused by stationary charges).

5. There is another way to make electric fields.

6. Solenoid

7. Curly electric field (both inside and outside solenoid)

8. Where there is a time-varying magnetic field, there is also a curly electric field.

9. No curly electric field

10. We call the curly electric fields Non-Coulomb electric fields E NC They are related to magnetic fields that are changing in time:

11. Which direction does the electric field curl?

12. Right thumb along Fingers curl in direction of

19. Which direction does the electric field curl?

23. What if we put a conducting wire around the solenoid? A current is induced in the wire.

24. Solenoid B increasing Metal wire How big is the current I 2 ?

25. EMF (ElectroMotive Force) EMF is actually not a force. It is the energy per unit charge added to a circuit during a single round trip. EMF = Units: Volts

26. Metal wire EMF = Solenoid B increasing

27. Metal wire (Ohm’s Law) 电阻 Solenoid B increasing

28. We can measure E NC by measuring the induced current.

30. Experiments: I 2 is only present when I 1 is changing. EMF

31. Experiments: i 2 is proportional to the area of the solenoid. EMF

32. Faraday’s Law This is the magnetic flux through the loop. EMF

33. Faraday’s Law The EMF around a closed path is equal to the rate of change of the magnetic flux inside the path. EMF

34. Faraday’s Law The EMF around a closed path is equal to the rate of change of the magnetic flux inside the path.

35. Michael Faraday (1791 – 1876)

38. Solenoid Wire Ammeter 电表 The magnetic field in the solenoid increases from 0.1 T to 0.7 T in 0.2 seconds. What current will the ammeter measure? Example

39. Solenoid Wire Ammeter 电表 The magnetic field in the solenoid increases from 0.1 T to 0.7 T in 0.2 seconds. What current will the ammeter measure? Example

40. EMF in a coil with many turns B increasing

41. EMF in a coil with many turns B increasing

42. EMF in a coil with many turns B increasing

43. Solenoid Wire Ammeter 电表 The ammeter measures a current of 10 A. Now, we replace the single wire with a coil containing N = 20 turns. What is the current now? Example

44. Maxwell’s Equations (so far…) *Not complete

45. Maxwell’s Equations (so far…) *Not complete Gauss’ Law for electric fields Gauss’ Law for magnetic fields Faraday’s Law

46. Maxwell’s Equations (so far…) Gauss’ Law for electric fields Gauss’ Law for magnetic fields Faraday’s Law Ampere-Maxwell Law

47. Maxwell’s equations predict travelling waves.

50. Maxwell’s equations predict light.