1. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric energy (Electric Potential Energy) Electric potential Gravitation Energy & 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. Electricity key concepts (Chs. 20 & 21) - Slide 1 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. General Concepts - These are always true Electric Force and Field Model Charge Model E-field Definition E-field vectors E-field lines Superposition (note that for forces and fields, we need to work in vector components)

3. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electricity key concepts (Chs. 20 & 21) - Slide 2 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. General Concepts - These are always true Energy, Electric Potential Energy, and Electric Potential Energy Definitions: KE, PE e, Pe g, W, E sys, E th and V Conservation of Energy Work by Conservative force = -- change of PE Electric Potential Energy and Electric Potential Energy

4. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Chapter 21 Key Equations (2) Key Energy Equations from Physics 152 Work done by a conservative force (F g, F s, & F e ) Also work done by conservative force is path independent Electric Potential Energy for 2 point charges (zero potential energy when charges an infinite distance apart)  elta Potential Energy for a uniform infinite plate For one plate, zero potential energy is at infinity For two plates, zero potential energy is at one plate or in between the two plates Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

5. Chapter 21 Key Equations (3) Key Points about Electric Potential Electric Potential is the Electric Potential Energy per Charge Electric Potential increases as you approach positive source charges and decreases as you approach negative source charges (source charges are the charges generating the electric field) A line where  V= 0 V is an equipotential line (The electric force does zero work on a test charge that moves on an equipotential line and  PE e = 0 J) Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

6. Chapter 21 Key Equations (2) Key Energy Equations from Physics 152 Electric Potential Energy for 2 point charges (zero potential energy when charges an infinite distance apart)  Elta Potential Energy for a uniform infinite plate For one plate, zero potential energy is at infinity For two plates, zero potential energy is at one plate or in between the two plates Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

7. Chapter 21 Key Equations (3) Key Points about Electric Potential Electric Potential is the Electric Potential Energy per Charge Electric Potential increases as you approach positive source charges and decreases as you approach negative source charges (source charges are the charges generating the electric field) A line where  V= 0 V is an equipotential line (The electric force does zero work on a test charge that moves on an equipotential line and  PE e = 0 J) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

8. Electric Potential and E-Field for Three Important Cases Slide 21-25 For a point charge For very large charged plates, must use

9. E-field lines and Equipotential lines Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. E-field Lines Go from + charges to - charges Perpendicular at surface of conductor or charged surface E-field in stronger where E-field lines are closer together More charge means more lines Equipotential Lines Parallel to conducting surface Perpendicular to E-field lines Near a charged object, that charges influence is greater, then blends as you to from one to the other E-field is stronger where Equipotential lines are closer together Spacing represents intervals of constant  V Higher potential as you approach a positive charge; lower potential as you approach a negative charge

10. Connecting Potential and Field Slide 21-31

11. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Checking Understanding Rank in order, from largest to smallest, the electric potentials at the numbered points. Slide 21-14

12. 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

13. 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

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

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

16. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Potential: Charged Sphere Outside of a sphere of charge Q the potential has the same form as for a point charge Q: Slide 21-28

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

18. 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

19. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example Problem 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.

20. Slide 21-15 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

21. 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

22. 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

23. A Topographic Map Slide 21-12

24. Topographic Maps Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 3. If a ball were placed at location D and another ball were placed at location C and both were released, which would have the greater acceleration? Which has the greater potential energy when released? Which will have a greater speed when at the bottom of the hill? 4. What factors does the speed at the bottom of the hill depend on? What factors does the acceleration of the ball depend on? 5. Is it possible to have a zero acceleration, but a non-zero height? Is it possible to have a zero height, but a non-zero acceleration? 1. Describe the region represented by this map. 2. Describe the directions a ball would roll if placed at positions A – D.

25. 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. 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 Where could an electron be placed so that it would not move?