1. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Conservation of energy Work and Delta PE Electric potential energy Electric potential Contour Maps E-Field and Equipotential Conductors & Fields 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? Slide 21-1

2. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Chapter 21 Key Energy Equations Key Energy Equations from Physics 151 and Ch. 21 so far Definition of Work Where Work done by a conservative force (F g, F s, & F e ) Also work done by conservative force is path independent => W ext = - W e Conservation of Energy Equation (can ignore U g and U s unless they are relevant) Electric Energy – Special Cases (Similar equations for gravity) 2 Point Charges Charge in a Uniform E-field Note: The angle is between electric force and the displacement Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

3. Chapter 21 Key Equations (3) Key Points about Electric Potential Electric Potential is the Electric 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  U e = 0 J) For multiple source charges V POI = V 1@POI + V 2@POI + … Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

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

5. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A Topographic Map Slide 21-12

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

7. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Equipotential surfaces: Representing the V field The lines represent surfaces of constant electric potential V, called equipotential surfaces. The surfaces are spheres (they look like circles on a two-dimensional page).

8. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Contour maps: An analogy for equipotential surfaces

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

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

11. Graphical Representations of Electric Potential Slide 21-13

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

13. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Connecting Potential and Field Slide 21-31

14. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Deriving a relation between the E field and ΔV We attach a small object with charge +q to the end of a very thin wooden stick and place the charged object and stick in the electric field produced by the plate. The only energy change is the system's electric potential energy, because the positively charged object moves farther away from the positively charged plate.

15. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Connecting Potential and Field Slide 21-31 E = Delta V / d

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

17. 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

18. 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

19. 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

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

21. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A.Rank the Electric Fields at points A, B, C, and D A.Rank the Electric Potentials at points A, B, C, and D Example Problem Source charges create the electric potential shown below. Slide 21-33

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

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

24. 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.

25. Analyzing a square of charges Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Energy to Assemble W me =  E = U Ef - U Ei (U Ei = 0 J) U 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 =  E = U Ef - U Ei = q 2q V 123@center - q 2q V 123@corner

26. 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