1. Homework set #3 is posted Due Tuesday by 5PM No late homework accepted Homework set #4 is posted Due Tuesday September 29 th by 5PM Same day as Exam I No late homework accepted Exam I – September 29 th Chapter 33-36 omitting section 36.6

2. Last time Changing flux creates E-fields:

3. K2-42: LENZ'S LAW - MAGNET IN ALUMINUM TUBE K2-44: EDDY CURRENT PENDULUM K2-61: THOMSON'S COIL Last time

4. Back – emf, Inductance: examples: Infinite solenoid (inductor!) Energy in B-fields: Inductor applications: Transformers, LR and LC circuits E-fields and B-fields transform into one another with relative motion!

5. MIT simulation of EM waves G3-01: SHIVE WAVE MACHINE - TRAVELING WAVES M7-04: MALUS' LAW K8-05: ELECTROMAGNETIC PLANE WAVE MODEL K8-42: RADIOWAVES - ENERGY AND DIPOLE PATTERN http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/ 07-EBlight/07-EB_Light_320.html

6. Bill observes an electric field from charged particle AND magnetic field produced by the moving charge Sharon only observes an electric field from charge E or B? Galilean transformation Both observe no net force on particle Only consider constant velocity between reference frames!

7. Both observers agree on the net force on the particle! E or B? Galilean transformation

8. Bill (frame S) sets up B-field, observes charge moving at velocity  Force up: Sharon (frame S’) is moving along with charge so v=0 There MUST be a force observed by Sharon since Bill observes one. There must be an E-field in Sharon’s frame that push’s the charge! Consider a TEST charge (to measure forces).

9. E or B? Galilean transformation Bill (frame S) sets up B-field, observes charge moving at velocity  Force up: Sharon (frame S’) is moving along with charge so v=0 Must have: Lorentz Force:

10. E or B? Two Aspects of same phenomenon Bill (frame S) Force up: Sharon (frame S’) is moving along with charge so v=0:

11. E or B? Two Aspects of same phenomenon E field in frame S’ from E and B fields in frame S How do the B-fields tranform from one frame to another?

12. B-field transformation: Biot Savart Law

13. The Galilean field transformation equations are where V is the velocity of frame S' relative to frame S and where the fields are measured at the same point in space by experimenters at rest in each reference frame. NOTE: These equations are only valid if V << c. E or B? Two Aspects of same phenomenon

14. Something is wrong with Galilean transformation:

18. Magnetic Gauss’s Law Since there are NO magnetic monopoles (only dipoles and conglomerates of dipoles), Net number of field lines piercing any closed surface is zero

21. Modification to Ampere’s Law

22. Changing B-field induces E-field, Lenz’s law gives direction Changing E-field induces B- field, Opposite of Lenz’s law gives B-field direction

26. Quickly Review of Traveling Waves

41. Homework set #4 Due Tuesday September 29 th by 5PM Same day as Exam I No late homework accepted Exam I – September 29 th Chapter 33-36 omitting section 36.6 Make-up exams are oral; only valid excuses

42. Last time E-fields and B-fields transform into one another with relative velocity between inertial reference Frames.

43. Last time Review of traveling waves E&M Plane waves:

44. Last time http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/0 7-EBlight/EB_Light.mpg

45. Last time

46. MIT simulation of EM waves G3-01: SHIVE WAVE MACHINE - TRAVELING WAVES M7-04: MALUS' LAW K8-05: ELECTROMAGNETIC PLANE WAVE MODEL K8-42: RADIOWAVES - ENERGY AND DIPOLE PATTERN http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/ 07-EBlight/07-EB_Light_320.html

50. Energy and momentum of EM radiation

52. Radiation Pressure:

53. Polarization and Malus’s law

55. Producing and Receiving EM waves Which way is the charge moving?

56. Producing and Receiving EM waves Which way is charge moving? To Left!

57. Producing and Receiving EM waves At large distances, E becomes ‘flat’  Plane waves

58. Producing and Receiving EM waves

59. (in the “far field”)

60. Producing and Receiving EM waves No radiation along axis of dipole: Biot-Savart law state there is no B-field along y if there is current parallel to r-hat

61. General derivation of EM wave equation