1. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Conservation of energy Work and Delta PE Electric potential energy Electric potential 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

2. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Applications of Electric Forces and Fields In electrophoresis, what force causes DNA fragments to migrate through the gel? How can an investigator adjust the migration rate?

3. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Force & Field Applications To get the colored lines produced by gel electrophoresis of a sample of DNA, you put the sample of DNA into a solution, then cut the DNA into fragments by enzymes. In the solution, the fragments have a negative charge. Drops of the solution (with DNA fragments) are placed in wells at one end of a container of gel.

4. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Force & Field Applications Electrodes at opposite ends of the container of gel produce an electric field that exerts an electric force on the DNA fragments. Drag forces cause some fragments of different sizes to migrate at different rates.

5. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Force & Field Applications After time, the fragments sort into distinct lines, creating a “genetic fingerprint.” Two identical DNA samples would produce the same fragments and therefore the same pattern. It is extremely unlikely that two unrelated DNA samples would produce the same pattern.

6. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Dipoles An electric dipole is two equal but opposite charges with a separation between them.

7. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Dipoles When the polarization is caused by an external charge, the atom has become an induced electric dipole. Because the negative end of the dipole is slightly closer to the positive charge in this figure, the attractive force on the negative end exceeds the repulsive force on the positive end. There is a net force toward the external charge.

8. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Hydrogen Bonding Some molecules have an asymmetry in their charge distribution that makes them permanent electric dipoles. In a water molecule, bonding between the hydrogen and oxygen atoms results in an unequal sharing of charge that leaves the hydrogen atoms with a small positive charge and the oxygen atom with a negative charge.

9. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Hydrogen Bonding A hydrogen bond is the weak bond between the hydrogen atom of one molecule of water and the negative oxygen atom in the second molecule. These weak bonds give water its “stickiness” responsible for properties such as expansion on freezing.

10. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Hydrogen Bonding Hydrogen bonds are extremely important in biological systems. The nucleotides, the four molecules guanine, thymine, adenine, and cytosine, on one strand of a DNA helix form hydrogen bonds with the nucleotides on the opposite strand. The nucleotides bond only in certain pairs. This preferential bonding is due to hydrogen bonds. The positive hydrogen atoms on one nucleotide attract the negative oxygen or nitrogen atoms on another.

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

12. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Electric Field of the Heart The surface of the heart is positive on one side of the boundary between tissue that is polarized and tissue that is not yet depolarized, negative on the other. The heart is a large electric dipole. The orientation and strength of the dipole change during each beat of the heart.

13. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Chapter 21 Key Energy Equations Key Energy Equations from Physics 151 and Ch. 21 so far Definition of Work Where Work done by a conservative force (F g, F s, & F e ) Also work done by conservative force is path independent Conservation of Energy Equation (can ignore U g and U s unless they are relevant) Electric Energy – Special Cases (Similar equations for gravity) 2 Point Charges Charge in a Uniform E-field Note: in both cases of Electric Energy must assume where U e = 0 Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

14. Voting question If two charged point-like objects have electric potential energy U, and the distance between them is doubled, the electric potential energy is: a)Quartered. b)Halved. c)Doubled. d)Quadrupled.

15. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Voting question If two charged point-like objects have electric potential energy U, and the distance between them is doubled, the electric potential energy is: a)Quartered. b)Halved. c)Doubled. d)Quadrupled.

16. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Voting question Based on this graph of the electric potential energy of two objects, what can you conclude about those two objects? a) The two objects have the same type of charge. b) The two objects have unlike charges. c) Only one of the two objects is charged. d) There isn't enough information in the graph to reach any of these conclusions.

17. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Voting question Based on this graph of the electric potential energy of two objects, what can you conclude about those two objects? The two objects have the same type of charge. The two objects have unlike charges. Only one of the two objects is charged. There isn't enough information in the graph to reach any of these conclusions.

18. 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.

19. 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.

20. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The V field Can we describe electric fields using the concepts of work and energy? To do so, we need to describe the electric field not as a force-related E field, but as an energy-related field.

21. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Potential Slide 21-10 <= Replace before using

22. 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.

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

24. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Finding the electric potential energy when the V field is known If we know the electric potential at a specific location, we can rearrange the definition of the V field to determine the electric potential energy:

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

26. The superposition principle and the V field due to multiple charges where Q 1, Q 2, Q 3, … are the source charges (including their signs) creating the field and r 1, r 2, r 3, … are the distances between the source charges and the location where we are determining the V field. So Electric Potentials (V) add just like Electric Potential Energies

27. 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

28. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Quantitative Example Suppose that the heart's dipole charges −Q and +Q are separated by distance d. Write an expression for the V field due to both charges at point A, a distance d to the right of the +Q charge. 1. Simplify and diagram. 2. Represent mathematically.

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

30. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Particles in a potential difference A positively charged object accelerates from regions of higher electric potential toward regions of lower potential (like an object falling to lower elevation in Earth's gravitational field). A negatively charged particle tends to do the opposite, accelerating from regions of lower potential toward regions of higher potential.

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

32. A Topographic Map Slide 21-12

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

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

35. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Reading Quiz 4.The electric field A.is always perpendicular to an equipotential surface. B.is always tangent to an equipotential surface. C.always bisects an equipotential surface. D.makes an angle to an equipotential surface that depends on the amount of charge. Slide 21-12

36. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Answer 4.The electric field A.is always perpendicular to an equipotential surface. B.is always tangent to an equipotential surface. C.always bisects an equipotential surface. D.makes an angle to an equipotential surface that depends on the amount of charge. Slide 21-13

37. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Connecting Potential and Field Slide 21-31

38. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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 4.Where could an electron be placed so that it would not move?

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

40. Graphical Representations of Electric Potential Slide 21-13

41. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Reading Quiz 3. The electric potential inside a parallel-plate capacitor A.is constant. B.increases linearly from the negative to the positive plate. C.decreases linearly from the negative to the positive plate. D.decreases inversely with distance from the negative plate. E.decreases inversely with the square of the distance from the negative plate. Slide 21-10

42. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Answer 3. The electric potential inside a parallel-plate capacitor A.is constant. B.increases linearly from the negative to the positive plate. C.decreases linearly from the negative to the positive plate. D.decreases inversely with distance from the negative plate. E.decreases inversely with the square of the distance from the negative plate. Slide 21-11

43. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Potential Inside a Parallel-Plate Capacitor Slide 21-25

44. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A.Rank the Electric Fields at points A, B, C, and D A.Rank the Electric Potentials at points A, B, C, and D Example Problem Source charges create the electric potential shown below. Slide 21-33

45. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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? Example Problem Source charges create the electric potential shown. 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? Slide 21-33

46. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example Problem A proton is released from rest at point a. It then travels past point b. What is its speed at point b? Slide 21-23

47. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Assembling a square of charges Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

48. Analyzing a square of charges Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Energy to Assemble W me =  E = U Ef - U Ei (U Ei = 0 J) U Ef = q 1 V nc@1 + q 2 V 1@2 + q 3 V 12@3 + q 4 V 123@4 V 123@4 = V 1@4 +V 2@4 + V 3@4 Energy to move (Move 2q from Corner to Center) W me =  E = U Ef - U Ei = q 2q V 123@center - q 2q V 123@corner

49. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example Problem A parallel-plate capacitor is held at a potential difference of 250 V. A proton is fired toward a small hole in the negative plate with a speed of 3.0 x 10 5 m/s. What is its speed when it emerges through the hole in the positive plate? (Hint: The electric potential outside of a parallel-plate capacitor is zero). Slide 21-26

50. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. What is Q 2 ? Example Problem Slide 21-35

51. 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.