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Overview of Electrostatics: Conductors, Insulators, Capacitors, and Energy Storage

This outline covers key concepts from Electrostatics relevant for the upcoming exam in week one. It explores the properties and behaviors of conductors and insulators, emphasizing the movement of charges and the electric field within these materials. The discussion includes Gauss's Law applications, the design and function of capacitors, and how energy is stored within electric fields. Additionally, it addresses the role of dielectrics in capacitors, examining their impact on potential difference and capacitance. Prepare effectively for your exam with this comprehensive review of essential topics.

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Overview of Electrostatics: Conductors, Insulators, Capacitors, and Energy Storage

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Presentation Transcript

  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

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