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

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Key Equations and Physics Models Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Charge Model General Point Charge E-field Model General Point Charge Plates of Charge Energy & Potential Modem General Point Charge Plates Equipotential Lines Conductor - everywhere on a conductor is at constant potential

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Analyzing a square of charges Slide 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 + q 2 V + q 3 V + q 4 V V = V +V + V Energy to move (Move 2q from Corner to Center) W me =  PE E = PE Ef - PE Ei = q 2q V - q 2q V

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Analyzing 2 Plates of Charge Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. E-field For 1 plate E = Q / 2A  0 Between Plates E = E 1 + E 2 = 2E 1 plate = 2Q / 2A  0 = Q / A  0 Outside the plates E = 0 Potential (going from lower potential to higher potential)  V = - |E||  r| cos  d = Q / A  0 * d = Qd / A  0 What happens if we pull the plates apart further? What changes and what stays the same? Define Capacitance - capacity to hold a certain amount of charge for a certain amount of energy (units Farad = C / V) C = Q /  V

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

Example Problem 5 A.The potential at points a and b.The potential difference between a and b. B.The potential energy of a proton at a and b. C.The speed at point b of a proton that was moving to the right at point a with a speed of 4.0 x 10 5 m/s. D.The speed at point a of a proton that was moving to the left at point b with a speed of 4.0 x 10 5 m/s. For the situation shown in the figure, find Slide 21-22

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

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Topographic Maps Slide 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.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Equipotential Maps (Contour Maps) Slide 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?

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

E-field lines and Equipotential lines Slide 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

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