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? Slide 21-1

2. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Discussion of other units for Energy and E-field Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. eV – electron Volts => Unit of energy for particle accelerators The energy gained by an electron that goes through a potential difference of one volt 1 eV = 1.60 x 10 -19 J V/m – Volts per meter => Unit of Electric Field |Delta V| = |E||Delta r| => |E| = |Delta V| / |Delta r| [E] = V / m

3. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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 ____

4. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Parallel Plate Capacitor Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A capacitor consists of two conductors that are close but not touching. A capacitor has the ability to store electric charge.

5. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Define Capacitor further Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

6. Parallel Plate Capacitor Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. (a) Parallel-plate capacitor connected to battery. (b) Battery and Capacitor in a circuit diagram. Relationship of E-field & Delta V? Delta V

7. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Define Capacitance Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitance is a measure of how much charge can be stored in a capacitor for a given amount of voltage

8. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Capacitance of a Parallel-Plate Capacitor Slide 21-31

9. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitance and Capacitors The charge ±Q on each electrode is proportional to the potential difference ΔV C between the electrodes: Slide 21-29

10. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Charging a Capacitor Slide 21-30

11. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitors Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Note: Battery is a source of constant potential What happens when you pull the plates of a capacitor apart? With a Battery connected With no Battery connected Do the following quantities (a) increase, (b) decrease, or (c) remain the same: Charge E-Field Delta V

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

13. Energy stored in Capacitor – Storing Energy in E-field Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A charged capacitor stores electric energy; the energy stored is equal to the work done to charge the capacitor.

14. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A Conductor in Electrostatic Equilibrium Slide 21-27

15. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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

16. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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

17. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Graphical Representations of Electric Potential Slide 21-13

18. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Potential Inside a Parallel-Plate Capacitor Slide 21-25

19. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Potential of a Point Charge Slide 21-27

20. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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

21. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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

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

23. Analyzing a square of charges Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Energy to Assemble W me = ΔPE 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 = ΔPE E = PE Ef - PE Ei = q 2q V 123@center - q 2q V 123@corner

24. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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

25. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. What is Q 2 ? Example Problem Slide 21-35