1. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric energy (Electric Potential Energy) Electric potential Gravitation Energy & 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?

2. 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 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. consta nt

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

4. Energy Bar Graph

5. 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 (F g, F s, & F e ) Also work done by conservative force is path independent 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.

6. Changes in Electric Potential Energy  PE e 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) Greatest Delta PE e (a) (b) (c) (d)Hydrogen Atom

7. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Changes in Electric Potential Energy  PE e 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) Greatest  PE e (e) (f) (g)

8. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Changes in Electric Potential Energy  PE e Is the change ∆PE e 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 Slide 21-11

9. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Potential Energy Example Problem The electric field between two charged plates is uniform with a strength of 4 N/C. Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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.

10. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Gravitational Potential Energy: Example Problem 2 A spacecraft is launched away from earth Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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.

11. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Potential Energy: Example Problem 3 A small charge moves farther from a positive source charge. Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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.

12. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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. Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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?

13. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Potential Slide 21-10

14. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Chapter 21 Key Equations (3) Key Points about Electric Potential Electric Potential is the Electric Potential 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  PE e = 0 J) Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

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

16. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Checking Understanding Rank in order, from largest to smallest, the electric potentials at the numbered points. Slide 21-14

17. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example Problem 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 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

18. Slide 21-15 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

19. 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

20. A Topographic Map Slide 21-12

21. 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.

22. 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. 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 Where could an electron be placed so that it would not move?