WARNING:

1. WARNING: Exam 1 Week from Thursday

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

3. Last Time:Gauss’s Law

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

5. Conductors

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

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. Conductors as Shields

10. Hollow Conductors Charge placed INSIDE induces balancing charge INSIDE

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

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

13. PRS Questions:Point Charge Inside Conductor

14. Demonstration:Conductive Shielding

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

16. Demonstration:Field Enhancement

17. Experiment 4:Electrostatic Force

18. Demonstration:Capacitor

19. Capacitors and Capacitance

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

21. Parallel Plate Capacitor

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

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

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

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

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. PRS Question:Changing C Dimensions

28. Demonstration:Changing C Dimensions

29. Energy Stored in Capacitor

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

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

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

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

35. PRS Question:Changing C DimensionsEnergy Stored

36. Batteries & Elementary Circuits

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

38. DV1 DV2 Batteries in Series Net voltage change is DV = DV1 + DV2 Think: Two Mountains Stacked

39. Batteries in Parallel Net voltage still DV Don’t do this!

40. Capacitors in Parallel

41. Capacitors in Parallel Same potential!

42. ? Equivalent Capacitance

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

44. Capacitors in Series

45. Equivalent Capacitance (voltage adds in series)

46. Dielectrics

47. Demonstration:Dielectric in Capacitor

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

50. Molecular View of Dielectrics Non-Polar Dielectrics Dielectrics with induced electric dipole moments Example: CH4