1. P09 - 1 WARNING: Exam 1 Week from Thursday

2. P09 - 2 Class 09: Outline Hour 1: Conductors & Insulators Expt. 4: Electrostatic Force Hour 2: Capacitors

3. P09 - 3 Last Time: Gauss’s Law

4. P09 - 4 Gauss’s Law In practice, use symmetry: Spherical (r) Cylindrical (r, ) Planar (Pillbox, A)

5. P09 - 5 Conductors

6. P09 - 6 Conductors and Insulators A conductor contains charges that are free to move (electrons are weakly bound to atoms) Example: metals An insulator contains charges that are NOT free to move (electrons are strongly bound to atoms) Examples: plastic, paper, wood

7. P09 - 7 Conductors Conductors have free charges  E must be zero inside the conductor  Conductors are equipotential objects

8. P09 - 8 Conductors in Equilibrium Conductors are equipotential objects: 1) E = 0 inside 2) Net charge inside is 0 3) E perpendicular to surface 4) Excess charge on surface

9. P09 - 9 Conductors as Shields

10. P09 - 10 Hollow Conductors Charge placed INSIDE induces balancing charge INSIDE

11. P09 - 11 Hollow Conductors Charge placed OUTSIDE induces charge separation on OUTSIDE

12. P09 - 12 PRS Setup What happens if we put Q in the center?

13. P09 - 13 PRS Questions: Point Charge Inside Conductor

14. P09 - 14 Demonstration: Conductive Shielding

15. P09 - 15 Field Enhancement E field is enhanced at sharp points!

16. P09 - 16 Demonstration: Field Enhancement

17. P09 - 17 Experiment 4: Electrostatic Force

18. P09 - 18 Demonstration: Capacitor

19. P09 - Capacitors and Capacitance

20. P09 - Capacitors: Store Electric Energy Capacitor: two isolated conductors with equal and opposite charges Q and potential difference  V between them. Units: Coulombs/Volt or Farads

21. P09 - 21 Parallel Plate Capacitor

22. P09 - 22 Calculating E (Gauss’s Law) Alternatively could have superimposed two sheets

23. P09 - 23 Parallel Plate Capacitor C depends only on geometric factors A and d

24. P09 - 24 Spherical Capacitor Two concentric spherical shells of radii a and b Gauss’s Law  E ≠ 0 only for a < r < b, where it looks like a point charge: What is E?

25. P09 - 25 Spherical Capacitor For an isolated spherical conductor of radius a: Is this positive or negative? Why?

26. P09 - 26 Capacitance of Earth For an isolated spherical conductor of radius a: A Farad is REALLY BIG! We usually use pF (10 -12 ) or nF (10 -9 )

27. P09 - 27 PRS Question: Changing C Dimensions

28. P09 - 28 Demonstration: Changing C Dimensions

29. P09 - 29 Energy Stored in Capacitor

30. P09 - 30 Energy To Charge Capacitor 1.Capacitor starts uncharged. 2.Carry +dq from bottom to top. Now top has charge q = +dq, bottom -dq 3.Repeat 4.Finish when top has charge q = +Q, bottom -Q

31. P09 - 31 Work Done Charging Capacitor At some point top plate has +q, bottom has –q Potential difference is  V = q / C Work done lifting another dq is dW = dq  V

32. P09 - 32 So work done to move dq is: Total energy to charge to q = Q: Work Done Charging Capacitor

33. P09 - 33 Energy Stored in Capacitor Since Where is the energy stored???

34. P09 - 34 Energy Stored in Capacitor Parallel-plate capacitor: Energy stored in the E field!

35. P09 - 35 PRS Question: Changing C Dimensions Energy Stored

36. P09 - 36 Batteries & Elementary Circuits

37. P09 - 37 Ideal Battery Fixes potential difference between its terminals Sources as much charge as necessary to do so Think: Makes a mountain

38. P09 - 38 Batteries in Series V1V1 V2V2 Net voltage change is  V =  V 1 +  V 2 Think: Two Mountains Stacked

39. P09 - 39 Batteries in Parallel Net voltage still  V Don’t do this!

40. P09 - 40 Capacitors in Parallel

41. P09 - 41 Capacitors in Parallel Same potential!

42. P09 - 42 Equivalent Capacitance ?

43. P09 - 43 Capacitors in Series Different Voltages Now What about Q?

44. P09 - 44 Capacitors in Series

45. P09 - 45 Equivalent Capacitance (voltage adds in series)

46. P09 - 46 Dielectrics

47. P09 - 47 Demonstration: Dielectric in Capacitor

48. P09 - 48 Dielectrics A dielectric is a non-conductor or insulator Examples: rubber, glass, waxed paper When placed in a charged capacitor, the dielectric reduces the potential difference between the two plates HOW???

49. P09 - 49 Molecular View of Dielectrics Polar Dielectrics : Dielectrics with permanent electric dipole moments Example: Water

50. P09 - 50 Molecular View of Dielectrics Non-Polar Dielectrics Dielectrics with induced electric dipole moments Example: CH 4

51. P09 - 51 Dielectric in Capacitor Potential difference decreases because dielectric polarization decreases Electric Field!

52. P09 - 52 Gauss’s Law for Dielectrics Upon inserting dielectric, a charge density  ’ is induced at its surface What is  ’?

53. P09 - 53 Dielectric Constant  Dielectric weakens original field by a factor  Gauss’s Law with dielectrics: Dielectric constants Vacuum1.0 Paper 3.7 Pyrex Glass 5.6 Water 80

54. P09 - 54 Dielectric in a Capacitor Q 0 = constant after battery is disconnected Upon inserting a dielectric:

55. P09 - 55 Dielectric in a Capacitor V 0 = constant when battery remains connected Upon inserting a dielectric:

56. P09 - 56 PRS Questions: Dielectric in a Capacitor

57. P09 - 57 Group: Partially Filled Capacitor What is the capacitance of this capacitor?