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Chapter 28

Chapter 28. Electric Potential. Looking ahead. New force (Chapter 25). New potential energy (Chapter 28). Electric Potential Energy ( U elec ). Potential energy Gravitational Uniform electric field Point charge. Gravitational potential (energy). Defined. Then defined.

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Chapter 28

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  1. Chapter 28 Electric Potential Phys 133 – Chapter 30

  2. Looking ahead New force (Chapter 25) New potential energy (Chapter 28) Phys 133 -- Chapter 29

  3. Electric Potential Energy (Uelec) • Potential energy • Gravitational • Uniform electric field • Point charge Phys 133 -- Chapter 29

  4. Gravitational potential (energy) Defined Then defined For the gravitational force In general Phys 133 -- Chapter 29

  5. Uniform field: Electric potential energy where Phys 133 -- Chapter 29

  6. Lower potential energy Lower potential energy s s Direction of lower potential energy depends on type of charge Uniform field: Electric potential energy Positive charge Negative charge Phys 133 -- Chapter 29

  7. Do Workbook 29.6 Phys 133 -- Chapter 29

  8. A proton is released from rest at the positive plate of a parallel plate capacitor. It crosses the capacitor and reaches the negative plate with a speed of 50,000 m/s. What will be the speed if the experiment is repeated with double the amount of charge on the capacitor plates? (Ans: 7.07x104 m/s) Problem 29.3 Phys 133 -- Chapter 29

  9. Electrical Potential Energy of Two Point Charges where Phys 133 -- Chapter 29

  10. a) Two point charges (both +Q) have their separation increased. Does the electric potential energy of the system (A) increase, (B) decrease or (C) remain the same? Question b) Two point charges (+/- Q) have their separation increased. Does the electric potential energy of the system (A) increase, (B) decrease or (C) remain the same? Phys 133 -- Chapter 29

  11. Question ans Like charges Opposite charges Phys 133 -- Chapter 29

  12. Do Workbook 29.3 Phys 133 -- Chapter 29

  13. Problem An electron (q=-e) is sent from very far away towards a charged sphere (Q=-0.25 nC). It gets to a distance of 1.10 mm from the center of the sphere before turning around. What is the initial speed of the electron? (Ans: 2.68x107m/s) What was the speed of the same electron with same initial conditions when it was 2.20 mm away? e=1.6x10-19C, me=9.1x10-31 kg, K=9x109 Nm2/C2 Phys 133 -- Chapter 29

  14. Problem ans Phys 133 -- Chapter 29

  15. Electric Potential (Velec) • Potential • Gravitational • Uniform electric field • Point charge Phys 133 -- Chapter 29

  16. Electric Potential (Velec) Charge creates potential define Potential only depends on source charges • Look at • Gravitational • Uniform electric field • Point charge Phys 133 -- Chapter 29

  17. object environment Environment only Gravitational Potential Phys 133 -- Chapter 29

  18. object environment Environment only s 0 (from before) Electric potential capacitor Phys 133 -- Chapter 29

  19. Capacitor: potential representations Phys 133 -- Chapter 29

  20. Draw V(x) for the two equipotential surfaces Draw U(x) for a proton in these potentials Draw U(x) for an electron in these potentials Phys 133 -- Chapter 29

  21. A proton is at x=0, moving to the right with 5x10-18 J of kinetic energy. What is its kinetic energy at point a? What if it were an electron? Workbook 29.18b extension Phys 133 -- Chapter 29

  22. Workbook 29.18b extension ans electron proton Not enough energy to reach a Phys 133 -- Chapter 29

  23. Problem 29.21 Modified In the figure which capacitor plate, left or right, is the positive plate? What is the electric potential energy of a proton at the midpoint of the capacitor? What is the electric field strength inside the capacitor? In general What is the electric field strength inside the capacitor in terms of  and o? What is the electric field strength inside the capacitor in terms of ∆V and d (the distance between the plates? Phys 133 -- Chapter 29

  24. Only potential difference matters Phys 133 -- Chapter 29

  25. (from before) Electric potential two point charges Phys 133 -- Chapter 29

  26. Point particle: potential representations Phys 133 -- Chapter 29

  27. Do Workbook 29.21 Phys 133 -- Chapter 29

  28. Electric Potential: multiple charges No vectors Phys 133 -- Chapter 29

  29. Do Workbook 29.25 Phys 133 -- Chapter 29

  30. Problem a) Find an expression for the electric potential V(x,y) for a dipole with point charges +/- Q at y= +/- a. b) Use the result for the dipole to find the electric potential at x=2 m, y=7 m when a=2 m, and Q=2 nC. c) What is the potential energy of a proton placed there? Phys 133 -- Chapter 29

  31. r+ y-a x r- y+a x Problem ans Phys 133 -- Chapter 29

  32. Problem plot Phys 133 -- Chapter 29

  33. Problem ans b) Use the result for the dipole to find the electric potential at x=7 m, y=2 m when a=2 m, and Q=2 nC. c) What is the potential energy of a proton placed there? Phys 133 -- Chapter 29

  34. where Potential of continuous charge distribution Then let solve Phys 133 -- Chapter 29

  35. The figure shows a thin rod of length L and charge Q. Find an expression for the electric potential a distance x away from the center of the rod on the axis of the rod. Problem 29.69 Phys 133 -- Chapter 29

  36. y P (d,0) x ith d xi ri Sum up contribution from each charge at P Problem 29.69 Find potential at P due to ith bit of charge Phys 133 -- Chapter 29

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