1. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric potential energy Electric potential Conservation of energy Chapter 21 Electric Potential Topics: Sample question: Shown is the electric potential measured on the surface of a patient. This potential is caused by electrical signals originating in the beating heart. Why does the potential have this pattern, and what do these measurements tell us about the heart’s condition?

2. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Announcements Mastering Physics Grades are still being updated Solution to Exam 1 had issues, will post today by 9 PM, Grading key available on MP Katie cannot make her office hours today. She will have make-up hours tomorrow (Tuesday) from 10-11 AM Dr. Saul will not have office hours today from 3-4 PM today Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

3. How many of you are in lab? A - Yes B - No Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

4. Reading Quiz 3. The electric potential inside a parallel-plate capacitor A.is constant. B.increases linearly from the negative to the positive plate. C.decreases linearly from the negative to the positive plate. D.decreases inversely with distance from the negative plate. E.decreases inversely with the square of the distance from the negative plate. Slide 21-10

5. Answer 3. The electric potential inside a parallel-plate capacitor A.is constant. B.increases linearly from the negative to the positive plate. C.decreases linearly from the negative to the positive plate. D.decreases inversely with distance from the negative plate. E.decreases inversely with the square of the distance from the negative plate. Slide 21-11

6. The Potential Inside a Parallel-Plate Capacitor Slide 21-25

7. Reading Quiz 4.The electric field A.is always perpendicular to an equipotential surface. B.is always tangent to an equipotential surface. C.always bisects an equipotential surface. D.makes an angle to an equipotential surface that depends on the amount of charge. Slide 21-12

8. Answer 4.The electric field A.is always perpendicular to an equipotential surface. B.is always tangent to an equipotential surface. C.always bisects an equipotential surface. D.makes an angle to an equipotential surface that depends on the amount of charge. Slide 21-13

9. Connecting Potential and Field Slide 21-31

10. Equipotential Maps (Contour Maps) Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 5. At which point is the magnitude of the electric field the greatest? 6. Is it possible to have a zero electric field, but a non-zero electric potential? 7. Is it possible to have a zero electric potential, but a non-zero electric field? 1.Describe the charges that could create equipotential lines such as those shown above. 2.Describe the forces a proton would feel at locations A and B. 3. Describe the forces an electron would feel at locations A and B 4.Where could an electron be placed so that it would not move?

11. 3D view Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

12. Electric Potential of a Point Charge Slide 21-27

13. Electric Potential: Charged Sphere Outside of a sphere of charge Q the potential has the same form as for a point charge Q: If the sphere has radius R and the potential at its surface is V 0, then the potential a distance r from its center can also be written Slide 21-28

14. Graphical Representations of Electric Potential Slide 21-13

15. Assembling a square of charges Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

16. Analyzing a square of charges Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Energy to Assemble W me =  PE E = PE Ef - PE Ei (PE Ei = 0 J) PE Ef = q 1 V nc@1 + q 2 V 1@2 + q 3 V 12@3 + q 4 V 123@4 V 123@4 = V 1@4 +V 2@4 + V 3@4 Energy to move (Move 2q from Corner to Center) W me =  PE E = PE Ef - PE Ei = q 2q V 123@center - q 2q V 123@corner

17. A.What is the potential at point A? At which point, A, B, or C, does the electric field have its largest magnitude? B.Is the magnitude of the electric field at A greater than, equal to, or less than at point D? Example Problem Source charges create the electric potential shown. C.What is the approximate magnitude of the electric field at point C? D.What is the approximate direction of the electric field at point C? Slide 21-33

18. Example Problem A proton is released from rest at point a. It then travels past point b. What is its speed at point b? Slide 21-23

19. Example Problem A parallel-plate capacitor is held at a potential difference of 250 V. A proton is fired toward a small hole in the negative plate with a speed of 3.0 x 10 5 m/s. What is its speed when it emerges through the hole in the positive plate? (Hint: The electric potential outside of a parallel-plate capacitor is zero). Slide 21-26

20. What is Q 2 ? Example Problem Slide 21-35

21. Electric Potential Energy Example Problem The electric field between two charged plates is uniform with a strength of 4 N/C. Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. a. Draw several electric field lines in the region between the plates. b. Determine the change in electrical potential energy in moving a positive 4 microCoulomb charge from A to B. c. Determine the change in electrical potential energy in moving a negative 12 microCoulomb charge from A to B.

22. Gravitational Potential Energy: Example Problem 2 A spacecraft is launched away from earth Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. a. Draw several gravitational field lines in the region around Earth. b. Determine the change in gravitational potential energy when the spacecraft moves from A to B, where A is 10 million miles from Earth and B is 30 million miles from Earth.

23. Electric Potential Energy: Example Problem 3 A small charge moves farther from a positive source charge. Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. a. Draw several electric field lines in the region around the source charge. b. Determine the change in electrical potential energy in moving a positive 4 nC charge from A to B, where A is 3 cm from the source charge and B is 10 cm away. c. Determine the change in electrical potential energy in moving a negative 4 nC charge from A to B.

24. Electric Potential Energy & Electric Potential: Example Problem 4 A proton has a speed of 3.5 x 10 5 m/s at a point where the electrical potential is 600 V. It moves through a point where the electric potential is 1000 V. What is its speed at this second point? Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.