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Chapter 21 Electric Potential Topics: • Electric potential energy • Electric potential • Conservation of energy 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? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-1 Key Equations and Physics Models 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. Slide 21-16 Analyzing a square of charges Energy to Assemble Wme = PEE = PEEf - PEEi (PEEi = 0 J) PEEf = q1Vnc@1 + q2V1@2 + q3V12@3 + q4V123@4 V123@4 = V1@4 +V2@4 + V3@4 Energy to move (Move 2q from Corner to Center) Wme = PEE = PEEf - PEEi = q2qV123@center - q2qV123@corner Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Analyzing 2 Plates of Charge E-field For 1 plate E = Q / 2A0 Between Plates E = E1 + E2 = 2E1 plate = 2Q / 2A0 = Q / A0 Outside the plates E = 0 Potential (going from lower potential to higher potential) V = - |E||r| cos d = Q / A0 * d = Qd / A0 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. Slide 21-16 Electric Potential Energy & Electric Potential: Example Problem 4 A proton has a speed of 3.5 x 105 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? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Example Problem 5 For the situation shown in the figure, find 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 105 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 105 m/s. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-22 A Topographic Map Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-12 Topographic Maps 1. Describe the region represented by this map. 2. Describe the directions a ball would roll if placed at positions A – D. 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? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Equipotential Maps (Contour Maps) 1.Describe the charges that could create equipotential lines such as those shown above. 2. 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. 4.Where could an electron be placed that is it would not 5. At whichsopoint the magnitude of the electric field the greatest? move? 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? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 3D view Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 E-field lines and Equipotential lines 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. Slide 21-16 Graphical Representations of Electric Potential Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-13