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Chapter 21 Electric Potential Topics: • Electric energy (Electric Potential Energy) • Electric potential • Gravitation Energy & 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. Chapter 21 Key Ideas (Physics 151) Dot Product Method for multiplying two vectors to get a scalar Definition of Work consta nt Work is how forces add energy to or take away energy from a system. It is the effect of a force applied over a displacement. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Chapter 21 Key Equations (Physics 151) Key Energy Equations from Physics 151 Types of Energy Conservation of Energy Equation (key concept) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Energy Bar Graph 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 (Fg, Fs, & Fe) Also work done by conservative force Wg = -DPEg is path independent q1q2 PEe = k r12 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 inbetween the two plates Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Changes in Electric Potential Energy elta PEe For each situation below, identify which arrangement (final or initial) has more electrical potential energy within the system of charges and their field. Initial (A) Final (B) (a) (b) (c) (d) Hydrogen Atom Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Greatest Delta PEe Changes in Electric Potential Energy elta PEe For each situation below, identify which arrangement (final or initial) has more electrical potential energy within the system of charges and their field. Initial (A) Final (B) (e) (f) (g) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Greatest elta PEe Changes in Electric Potential Energy elta PEe 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 Energy Example Problem The electric field between two charged plates is uniform with a strength of 4 N/C. a. Draw several electric field lines in the region between the plates. b. Determine the change in electrical potential energy in moving a positive 4 microCoulomb charge from A to B. c. Determine the change in electrical potential energy in moving a negative 12 microCoulomb charge from A to B. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Gravitational Potential Energy: Example Problem 2 A spacecraft is launched away from earth a. Draw several gravitational field lines in the region around Earth. b. Determine the change in gravitational potential energy when the spacecraft moves from A to B, where A is 10 million miles from Earth and B is 30 million miles from Earth. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Electric Potential Energy: Example Problem 3 A small charge moves farther from a positive source charge. a. Draw several electric field lines in the region around the source charge. b. Determine the change in electrical potential energy in moving a positive 4 nC charge from A to B, where A is 3 cm from the source charge and B is 10 cm away. c. Determine the change in electrical potential energy in moving a negative 4 nC charge from A to B. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Electric Potential Model Worksheet 2: Energy and Potential in Uniform Fields Rank the change in gravitational potential energy for the following lettered objects in the Earth’s gravitational field. a. . most _______ _________ ________ ________ _______ _______ ________ b. Explain your ranking, stating why each is greater than, less than, or equal to its neighbors. c. Where is the energy stored? What gains or loses energy as the masses move from one place to another? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 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 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 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 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-15 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 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.Where could an electron be placed so that it would not move? 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? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16