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CAPACITANCE III

CAPACITANCE III. RECAP. The electrostatic energy stored in the capacitor. Capacity increases if the dielectric material is introduced. If the battery is connected If the capacitor is charged, disconnected from battery, and then dielectric is introduced. Capacities with the dielectric.

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CAPACITANCE III

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  1. CAPACITANCE III

  2. RECAP The electrostatic energy stored in the capacitor

  3. Capacity increases if the dielectric material is introduced. • If the battery is connected • If the capacitor is charged, disconnected from battery, and then dielectric is introduced

  4. Capacities with the dielectric • Parallel plate capacitor • Spherical capacitor • Cylindrical capacitor

  5. Electrostatic pressure • Force on a plate of capacitor

  6. Today’s plan • Energy stored before and after the dielectric is filled. • Force on a dielectric

  7. Energy stored before and after • Before  • Since C = kC0 • Why U´< U ?? Where does this energy go?

  8. Reason Dielectric, when inserted, gets pulled into the device. External agent do negative work to prevent the dielectric from accelerating. Work = U-U

  9. The nonuniform electric field (fringing field) near the edges causes a dielectric to be pulled into the capacitor.

  10. Fringing Field The bound charges tend to accumulate near the free charges of opposite sign.

  11. + + + + + + + + + + + + - - - - - - - - - - - - - - If no external agent works, slab will be accelerated.

  12. + + + + + + + + + + + + - - - - - - - - - - - - - - + + + + + + + + + + + +

  13. + + + + + + + + + + + + - - - - - - - - - - - - - -

  14. + + + + + + + + + + + + - - - - - - - - - - - - - -

  15. + + + + + + + + + + + + - - - - - - - - - - - - - -

  16. + + + + + + + + + + + + - - - - - - - - - - - - - -

  17. + + + + + + + + + + + + - - - - - - - - - - - - - - Slab oscillates between the ends

  18. + + + + + + + + + + + + - - - - - - - - - - - - - - Slab oscillates between the ends

  19. + + + + + + + + + + + + - - - - - - - - - - - - - - Slab oscillates between the ends

  20. + + + + + + + + + + + + - - - - - - - - - - - - - - Slab oscillates between the ends

  21. + + + + + + + + + + + + - - - - - - - - - - - - - - Slab oscillates between the ends

  22. To calculate the force due to electric field on the dielectric material

  23. + + + + + + + + + + + + - - - - - - - - - - - - - - Let the external agent pulls the dielectric out by a infinitesimal displacement dx Plate area is L x L x Fext dW = Fext dx Fext = dW/dx Electric force on the dielectric = -Fext

  24. Charge on the plates is constant

  25. If the battery maintains a constant potential The force simply depends only upon the fringing field and free and bound charges

  26. Two coaxial metal tubes stand vertically in a tank of dielectric oil (susceptibility e and mass density . Tubes are maintained at a potential difference of V. To what height (h) does the oil rise in the space between the tubes. Problem Griffiths Problem 4.28, page 196 vol 3.

  27. Calculate the electrostatic energy stored between the plates of the cylindrical capacitor using the relation

  28. r: a to b : 0 to 2 Z: 0 to L

  29. c a b Problem 4.21 Griffiths • A certain coaxial cable consists of a copper wire , radius a , surrounded by a concentric copper tube of inner radius c. The space between is partially filled (from b out to c) with a material of dielectric constant ke. Findthe capacitance per unit length of this cable.

  30. a b c Findthe capacitance per unit length of this cable Dielectric Material

  31. c a b

  32. A parallel plate capacitor is filled with a dielectric of dielectric constant ke. The ke varies parallel to an edge as • Where x is the distance from the left end. Calculate the capacitance.

  33. Twelve capacitors, each have capacity C are connected to form a cube. Find the Ceq B A

  34. B F A E

  35. B Isolated system Total charge zero Q/3 F Q/6 A E Q/3

  36. B Q/3 F Q/6 A E Q/3

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