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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 Chapter 21 Key Equations (Physics 151) Key Energy Equations from Physics 151 Definition of Work Work W = F i Dr = F Dr cos a Where a = angle between the vectors Work- Energy Theorem (only valid when particle model applies) Wnet = DKE Work done by a conservative force (Fg, Fs, & Fe) Also work done by conservative force Wg = -DPEg is path independent Conservation of Energy Equation KEi + å PEi + D Esys = KE f + different types Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. å PE f + DEth different types Slide 21-16 Electric Potential Energy Case A - Book starts & stops at rest WNet = DEK = 0J Whand + Wg = 0 Þ Whand = -Wg = DEg Case C - Charge at rest at A and B WNet = DEK = 0J Whand + We = 0 Þ Whand = -We = DEe Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-9 Chapter 21 Key Equations (2) Key Energy Equations from Physics 152 q1q2 PEe = k r12 Electric Potential Energy for 2 point charges (zero potential energy when charges an infinite distance apart) Potential Energy for a uniform infinite plate DPEe = -We = - éë Fe × Dr cos a ùû = - ( q E ) Dr cos a For one plate, zero potential energy is at infinity For two plates, zero potential energy is at one plate or inbetween the two plates Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Path Independence Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Changes in Electric Potential Energy ΔEe Is the change ∆PEe of a + charged particle positive, negative, or zero as it moves from i to f? (a) Positive (b) Negative (c) Zero (d) Can’t tell Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-11 Electric Potential Uelec = qV; V = U elec / q Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-10 Chapter 21 Key Equations (3) Key Points about Electric Potential Electric Potential is the Electric Potential Energy per Charge PEe V= qtest DPEe We DV = =qtest qtest 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 PEe= 0 J) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Electric Potential and E-Field for Three Important Cases For a point charge q 1 q V=K = r 4pe 0 r For very large charged plates, must use DPEe We Fe i Dr qtest E i Dr DV = ==== -E i Dr = - E Dr cos a qtest qtest qtest qtest Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-25 Checking Understanding Rank in order, from largest to smallest, the electric potentials at the numbered points. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-14 Example Problem 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 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 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 Connecting Potential and Field Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-31 Reading Quiz 4. The electric field A. B. C. D. is always perpendicular to an equipotential surface. is always tangent to an equipotential surface. always bisects an equipotential surface. makes an angle to an equipotential surface that depends on the amount of charge. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-12 Answer 4. The electric field A. B. C. D. is always perpendicular to an equipotential surface. is always tangent to an equipotential surface. always bisects an equipotential surface. makes an angle to an equipotential surface that depends on the amount of charge. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-13 Example Problem Source charges create the electric potential shown. 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? 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? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-33 Graphical Representations of Electric Potential Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-13 The Potential Inside a Parallel-Plate Capacitor Uelec Q V= = Ex = x q Î0 A Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-25 Electric Potential of a Point Charge Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-27 Reading Quiz 3. The electric potential inside a parallel-plate capacitor A. B. C. D. E. is constant. increases linearly from the negative to the positive plate. decreases linearly from the negative to the positive plate. decreases inversely with distance from the negative plate. decreases inversely with the square of the distance from the negative plate. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-10 Answer 3. The electric potential inside a parallel-plate capacitor A. B. C. D. E. is constant. increases linearly from the negative to the positive plate. decreases linearly from the negative to the positive plate. decreases inversely with distance from the negative plate. decreases inversely with the square of the distance from the negative plate. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-11