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Chapter 29

Chapter 29. Electric Potential and Field. Overview Force, field, energy, potential. Force, field, energy, potential. or. Fields and potentials.

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Chapter 29

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  1. Chapter 29 Electric Potential and Field Phys 133 – Chapter 29

  2. Overview Force, field, energy, potential Phys 133 – Chapter 29

  3. Force, field, energy, potential or Phys 133 – Chapter 29

  4. Fields and potentials 1. a) E = 0 V/m in throughout some region of space, can you conclude that the potential V = 0 in this region?b) V = 0 V throughout some region of space. Can you conclude that the electric field E = 0 V/m in this region? Phys 133 – Chapter 29

  5. Graphically convert between E and V2. The top graph shows Ex vs. x for an electric field parallel to the x-axis.a) Draw the graph of V vs. x in this region of space. Let V = 0 at x = 0m. Add an appropriate scale on the vertical axis. (Hint: integration is the area under the curve)b) Draw a contour map above the x-axis on a diagram like the one below-right and label your equipotential lines every 20 V. 0V has been drawn already.C) Draw several electric field vectors on top of the contour map. Ex (V/m) 0 V 40 20 0 1 2 3 4 2 4 x(m) x(m) Phys 133 – Chapter 29

  6. Problem: Potential of sphere --Find the electric potential everywhere for a sphere (radius R) with charge (Q) uniformly distributed. Take V=0 at infinity. --Sketch V vs r and Er vs r. From Chap 27 E field is: Phys 133 – Chapter 29

  7. Vr Vr V∞ ∆V r VR Vr ∆V Problem: Potential of sphere (ans) Finding Vr definition For all r For r < R For R < r Phys 133 -- Chapter 30

  8. Find the electric potential everywhere for a sphere (radius R) with charge (Q) uniformly distributed. Problem: Potential of sphere (ans) Phys 133 – Chapter 29

  9. Problem: Field from Potential Find the x,y and z components of the electric field, given that the electric potential of a disk is given by Phys 133 – Chapter 29

  10. Problem: Field from Potential (Answer) Find the z component of the electric field, given that the electric potential of a disk is given by Phys 133 – Chapter 29

  11. Geometry of potential/field  is perp to equipotential surfaces points downhill (decreasing V) --strength proportional to spacing equipotentials Phys 133 – Chapter 29

  12. Kirchhoff’s loop rule(Conservation of energy) Phys 133 – Chapter 29

  13. Conductor in equilibrium: field and potential --field is zero inside conductor --field is perpendicular at surface --conductor is at equipotential (no work to move) Phys 133 – Chapter 29

  14. Conductor in equilibrium: equipotentials --equipotentials are parallel to nearby conductor Phys 133 – Chapter 29

  15. Do Workbook 30.4, 6, 11, & 12a Phys 133 – Chapter 29

  16. Problem: Finding Potential --Find the electric potential everywhere for a point charge (q) at the center of a hollow metal sphere (inner radius a, outer radius b) with charge Q. (Take V=0 at infinity.) --Sketch V vs r and Er vs r. Phys 133 – Chapter 29

  17. Vr V∞ ∆V r Va Vr ∆V Problem: Finding Potential (ans) Finding Vr For all r For r < a For b < r For a < r < b Phys 133 -- Chapter 30

  18. Problem: finding Potential (Answer) not origin Phys 133 -- Chapter 30

  19. -charge separation -not sustained Sources of potential: Capacitor Phys 133 -- Chapter 30

  20. Sources of potential: Battery --sustained -- Phys 133 -- Chapter 30

  21. charge separation on capacitor Capacitors Apply to capacitor Phys 133 -- Chapter 30

  22. Circuit geometry --generic circuit elements --imagine battery connection parallel series Phys 133 -- Chapter 30

  23. Capacitors: series equivalent Phys 133 -- Chapter 30

  24. Capacitors: parallel equivalent Phys 133 -- Chapter 30

  25. Capacitors Phys 133 -- Chapter 30

  26. Do Workbook 30.26 & 27 Phys 133 -- Chapter 30

  27. Energy in capacitor --work done charge separation --or in electric field Phys 133 -- Chapter 30

  28. Problem --Find the charge on (Q) and potential difference (V) across each capacitor. --What is the total energy stored in the system? Phys 133 -- Chapter 30

  29. Problem (ans) Phys 133 -- Chapter 30

  30. Problem (ans) Phys 133 -- Chapter 30

  31. Dielectrics change the potential difference • The potential between to parallel plates of a capacitor changes when the material between the plates changes. It does not matter if the plates are rolled into a tube as they are in Figure 24.13 or if they are flat as shown in Figure 24.14.

  32. Table 24.1—Dielectric constants

  33. Field lines as dielectrics change • Moving from part (a) to part (b) of Figure 24.15 shows the change induced by the dielectric. In vacuum, energy density is In dielectric

  34. Examples to consider, capacitors with and without dielectrics • If capacitor is disconnected from circuit, inserting a dielectric changes decreases electric field, potential and increases capacitance, but the amount of charge on the capacitor is unchanged. • If the capacitor is hooked up to a power supply with constant voltage, the voltage must remain the same, but capacitance and charge increase

  35. Q24.8 You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the charges on the plates remain constant. What effect does adding the dielectric have on the potential difference between the capacitor plates? A. The potential difference increases. B. The potential difference remains the same. C. The potential difference decreases. D. not enough information given to decide

  36. A24.8 You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the charges on the plates remain constant. What effect does adding the dielectric have on the potential difference between the capacitor plates? A. The potential difference increases. B. The potential difference remains the same. C. The potential difference decreases. D. not enough information given to decide

  37. Q24.9 You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the charges on the plates remain constant. What effect does adding the dielectric have on the energy stored in the capacitor? A. The stored energy increases. B. The stored energy remains the same. C. The stored energy decreases. D. not enough information given to decide

  38. A24.9 You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the charges on the plates remain constant. What effect does adding the dielectric have on the energy stored in the capacitor? A. The stored energy increases. B. The stored energy remains the same. C. The stored energy decreases. D. not enough information given to decide

  39. Q24.10 You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the potential difference between the plates remains constant. What effect does adding the dielectric have on the amount of charge on each of the capacitor plates? A. The amount of charge increases. B. The amount of charge remains the same. C. The amount of charge decreases. D. not enough information given to decide

  40. A24.10 You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the potential difference between the plates remains constant. What effect does adding the dielectric have on the amount of charge on each of the capacitor plates? A. The amount of charge increases. B. The amount of charge remains the same. C. The amount of charge decreases. D. not enough information given to decide

  41. Q24.11 You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the potential difference between the plates remains constant. What effect does adding the dielectric have on the energy stored in the capacitor? A. The stored energy increases. B. The stored energy remains the same. C. The stored energy decreases. D. not enough information given to decide

  42. A24.11 You slide a slab of dielectric between the plates of a parallel-plate capacitor. As you do this, the potential difference between the plates remains constant. What effect does adding the dielectric have on the energy stored in the capacitor? A. The stored energy increases. B. The stored energy remains the same. C. The stored energy decreases. D. not enough information given to decide

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