1. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric potential energy Electric potential Conservation of energy Capacitors and Capacitance 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. 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

3. 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

4. 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

5. 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

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

7. 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.

8. 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.

9. 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.

10. 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.

11. Define Capacitance Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

12. The Capacitance of a Parallel-Plate Capacitor Slide 21-31

13. Capacitance and Capacitors The charge ±Q on each electrode is proportional to the potential difference ΔV C between the electrodes: Slide 21-29

14. Discuss Batteries Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

15. Batteries The potential difference between the terminals of a battery, often called the terminal voltage, is the battery’s emf. Slide 22-12 ∆ V bat = =  W chem q ____

16. Charging a Capacitor Slide 21-30

17. Dielectrics and Capacitors Slide 21-32

18. Dielectric Constant With a dielectric between its plates, the capacitance of a parallel-plate capacitor is increased by a factor of the dielectric constant κ: Slide 21-33

19. Energy stored in Capacitor – Storing Energy in E-field Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

20. A Conductor in Electrostatic Equilibrium Slide 21-27