Electrostatics. Typeset by FoilTEX 1

Transcription

1 Electrostatics Typeset by FoilTEX 1

2 Question 1 A plastic rod is rubbed and touched to a small metal ball. After this the rod is observed to repel the ball. Which of the following is correct? 1. The force exerted by the rod on the ball is a contact force. 2. The force exerted by the rod on the ball is a gravitational force. 3. The force exerted by the rod on the ball is not a gravitational force since only Earth can exert gravitational forces. 4. The force exerted by the rod on the ball is not a gravitational force since it is repulsive. Typeset by FoilTEX 2

3 Question 2 A plastic rod is rubbed and touched to a small metal ball. After this the rod is observed to repel the ball. Which of the following is correct? 1. The force exerted by the rod on the ball is a contact force. 2. The force exerted by the rod on the ball is a gravitational force. 3. The force exerted by the rod on the ball is not a gravitational force since only Earth can exert gravitational forces. 4. The force exerted by the rod on the ball is not a gravitational force since.... Typeset by FoilTEX 3

4 Question 3 Congratulations! You now know how to navigate the course website. The following is a photograph of a well-known city. Describe as accurately as you can the name of this city, its country and continent. Typeset by FoilTEX 4

5 Question 4 Two balls are suspended and are observed to repel each other. Which of the following is true? 1. One ball is positive, the other negative. 2. Both are positive. 3. Both are negative. 4. Either both are positive or else both are negative. Typeset by FoilTEX 5

6 Question 5 Two pairs of balls are suspended next to each other. Each pair is observed to repel and the green ball is the same in both cases. The red and blue balls are placed near to each other. Which of the following will be observed? 1. The red and blue repel each other. 2. The red and blue attract each other. 3. The red does not exert a force on the blue but the blue does exert a force on the red. 4. The blue does not exert a force on the red but the red does exert a force on the blue. 5. Neither ball exerts a force on the other. Typeset by FoilTEX 6

7 Question 6 A small metal sphere is initially neutral. It is placed into contact with a small negatively charged metal cube and then released. Which of the following is true after the two objects have been in contact? 1. They attract each other and stay in contact. 2. They repel each other and move apart. 3. Theyneitherattractnorrepelbut stillstay in contact. Typeset by FoilTEX 7

8 Question 7 Two negatively charged metal balls are connected by a metal wire and suspended over a wooden (insulating) peg as illustrated. Which of the following best describes the rod? 1. The rod is positively charged. 2. The rod is negatively charged. 3. The rod is uncharged. 4. The rod is magic. A rod is brought near to but not touching the peg and it is observed that the separation of the balls increases. Typeset by FoilTEX 8

9 Question 8 A negatively charged rod is held near to a neutral oval object, which becomes polarized as illustrated. Which of the following is true about the forces exerted by the rod on the oval object? 1. The force on the right edge (of the oval) is the same as that on the left edge (of the oval) since the charges at the edges are the same The force on the right edge is larger than as that on the left edge. 3. The force on the right edge is smaller than as that on the left edge. Typeset by FoilTEX 9

10 Question 9 A positively charged rod is held above a metal ball on an insulating stand. The ball is connected to the earth by a wire. While the rod is in place, the wire is removed. After this, the rod is removed Which of the following best describes the charge on the ball at the end of this procedure? 1. Positive. 2. Negative. 3. No net charge but polarized. 4. No net charge and not polarized. 5. There is not enough information. It is important to note that the earth can supply or remove plentiful electrons from any object with which it is in contact. Typeset by FoilTEX 10

11 Question 10 Two identical subatomic particles, labeled X, are separately placed near to two different particles, labeled A and B. The forces exerted by X on either A or B are as illustrated. Which of the following is true? 1. The charge of X in case 1 is opposite to that of X in case 2. Case 1 X Case 2 X A B 2. The charge of X in the same in both cases. 3. The charge of X is larger in case 1 than in case The charge of X is smaller in case 1 than in case 2. Typeset by FoilTEX 11

12 Question 11 An isolated particle has charge +16 C. Consider the following statements: A) The particle always exerts a force of 16N but can feel a force of any size. B) The particle always feels a force of 16N but can exert a force of any size. C) The particle always exerts a force of 16N and always feels a force of 16N. Which of the statements are true? 1. Only A. 2. Only B. 3. Only C. 4. None of them. Typeset by FoilTEX 12

13 Question 12 A point particle, named Zog, has charge +16 C and is in the vicinity of another point charged particle. Consider the following statements: A) Zog definitely exerts a force of 16N but the force Zog feels could be of another size. B) Zog definitely feels a force of 16N but the force Zog exerts could be of another size. Which of the statements are true? 1. Only A. 2. Only B. 3. Only C. 4. None of them. C) Zog definitely exerts a force of 16N and definitely feels a force of 16N. Typeset by FoilTEX 13

14 Question 13 A proton gun fires a proton toward another subatomic particle. After it leaves the gun, it travels in a straight line with constant speed toward another particle. +? The two particles are isolated and the gravitational forces between them are negligible (i.e. ignore the gravitational forces). Which of the following is true? 1. The particle on the right is positively charged. 2. The particle on the right is negatively charged. 3. The particle on the right contains absolutely no charge. Typeset by FoilTEX 14

15 Question 14 Two charges are aligned as illustrated. Denote the electrostatic force exerted by the blue charge on the red charge as F blue on red and that by the red on blue as F red on blue. Which of the following is true regarding the magnitude of the two forces? 1. F red on blue = F blue on red +2C + 4C 2. F red on blue > F blue on red 3. F red on blue < F blue on red 4. The sizes of forces depends on the masses of the particles. Typeset by FoilTEX 15

16 Question 15 Two metal balls are supported on fixed insulating stands and they are given distinct charges. Which of the following correctly illustrates the electrostatic forces on the two balls? + + Case Case Case Case Case Typeset by FoilTEX 16

17 Question 16 Three charges are aligned as illustrated. +2C + 2C 4C Which of the following gives the direction of the net force exerted on the charge at the right? Zero net force. Typeset by FoilTEX 17

18 Question 17 Three charges are aligned as illustrated. +2C + 2C +4C + Which of the following gives the direction of the net force exerted on the blue charge? Zero net force. Typeset by FoilTEX 18

19 Question 18 In which of the following is the magnitude of the net electrostatic force exerted on the blue charge largest? All distances between the red and blue charges are equal. 2. +e +e e 1. e 3. +e e +e +e +e Typeset by FoilTEX 19

20 Question 19 Two particles with charges that are identical in magnitude but opposite in sign are placed along the x axis as illustrated. q y Q +q A negatively charged particle is placed along the y axis. x Which of the following best represents the direction of the net force exerted on the charge on the y axis? ր 4.ց 5. Typeset by FoilTEX 20

21 Question 20 Two identically charged particle are placed along the x axis as illustrated. y Q Which vector best represents the direction of the net force exerted on the charge on the y axis? 1. î 2. ĵ +q +q x 3. ĵ A negatively charged particle is placed along the y axis. 4. î ĵ 5. î+ĵ Typeset by FoilTEX 21

22 Question 21 The electric field produced by a hidden charge collection of charged particles (sources) is illustrated below. Initially a probe charge with charge 5C is placed at point P. This is removed and replaced by a new probe charge with charge 10C, also placed at P. Which is true at point regarding the electric field produced by the sources at P and the forces on the probe charges? 1. Field is same (for both probes), force is same (for both probes). 2. Field is same, force differs. 3. Field differs, force is same. 4. Field differs, force differs. P Typeset by FoilTEX 22

23 Question 22 A positively charged plate is placed in the vicinity of a negatively charged ring. The plate and ring are held fixed as illustrated and the charges are evenly distributed on each. P Consider the statement regarding the electric field produced by the ring and the plate: The electric field at point P describes, or is used to describe, whether the plate attracts or repels the ring. Is this statement true or false? 1. True 2. False 3. Depends on the situation. Typeset by FoilTEX 23

24 Question 23 A positively charged plate is placed in the vicinity of a negatively charged ring. The plate and ring are held fixed as illustrated and the charges are evenly distributed on each. P Consider the statement regarding the electric field produced by the ring and the plate: The electric field at point P is always the force exerted at P. Is this statement true or false? 1. True 2. False 3. Depends on the situation. Typeset by FoilTEX 24

25 Question 24 A positively charged plate is placed in the vicinity of a negatively charged ring. The plate and ring are held fixed as illustrated and the charges are evenly distributed on each. Consider the statement regarding the electric field produced by the ring and the plate: The electric field consists of two vectors, one indicating a downward attraction on the ring and the other an upward attraction on the plate. Is this statement true or false? P True 2. False 3. Depends on the situation. Typeset by FoilTEX 25

26 Question 25 A positively charged plate is placed in the vicinity of a negatively charged ring. The plate and ring are held fixed as illustrated and the charges are evenly distributed on each. Consider the statement regarding the electric field produced by the ring and the plate: The electric field at P produced by the plate and ring consists of one vector and this is the same regardless of any other charge which is placed at P. Is this statement true or false? P True 2. False 3. Depends on the situation. Typeset by FoilTEX 26

27 Question 26 A positively charged plate is placed in the vicinity of a negatively charged ring. The plate and ring are held fixed as illustrated and the charges are evenly distributed on each. Consider the statement regarding the electric field produced by the ring and the plate: The electric field at P produced by the plate and ring consists of one vector and thus will exert the same force on a charge placed at P as on any other charge placed at P. Is this statement true or false? P True 2. False 3. Depends on the situation. Typeset by FoilTEX 27

28 Question 27 A positively charged plate is placed in the vicinity of a negatively charged ring. The plate and ring are held fixed as illustrated and the charges are evenly distributed on each. P Which of the following best represents the direction of the electric field produced by the ring and the plate at P? 1. for positive probe charge for negative probe charge. 2. for positive probe charge for negative probe charge. 3. for any probe charge. 4. for any probe charge. 5. Zero field. Typeset by FoilTEX 28

29 Question 28 The electric field produced by a hidden charge collection of charged particles (sources) is illustrated below. A charged particle is placed at point P. Which of the following is true of the force exerted by the electric field on the charged particle? 1. The force will definitely be to the right. 2. The force will definitely be to the left. P 3. The force could be either right or left. 4. The force depends on the direction of motion of the particle. Typeset by FoilTEX 29

30 Question 29 The electric field produced by a hidden charge collection of charged particles is illustrated below. Which of the following is true? 1. The magnitude of the force exerted on a charge at P is always larger than that exerted on another charge at Q. P Q 2. The magnitude of the force exerted on a charge at P is always smaller than that exerted on another charge at Q. 3. The magnitude of the force exerted on a charge at P could be larger or smaller than that exerted on another charge at Q. 4. The magnitude of the force exerted on a charge at P can never be the same as that exerted on another charge at Q. Typeset by FoilTEX 30

31 Question 30 A positive charge, labeled A, of magnitude +5C, and another charge B, of magnitude 8 C, are placed as illustrated. The distance between the charges is 10m. A + B Which of the following is true for the electric field produced by A at the location of B? 1. E = k 8C (10m) 2 2. E = k 8C (10m) 2 3. E = k 5C (10m) 2 4. E = k 5C (10m) 2 5. E = k 40C2 (10m) 2 Typeset by FoilTEX 31

32 Question 31 A positive charge, Zog, is placed in the vicinity of a collection of source charges. The net force exerted on the positive charge is as illustrated. Zog is replaced by another charge, Geraldine, of the same magnitude but of opposite sign. The source charges are unaltered. Which of the following is true regarding the electric field produced by the source charges, E, and the force on Geraldine compared to those when Zog was present? + Zog F 1. Force same direction, E same direction. 2. Force same direction, E reverses direction. 3. Force reverses direction, E same direction. 4. Force reverses direction, E reverses direction. Typeset by FoilTEX 32

33 Question 32 In the following separate scenarios two source charges produce electric fields. Consider the magnitude of the field at the location midway between the two source charges. +4C Case A + +4C + Which of the following describes the rank of the magnitudes of the fields at the midpoint? 1. E C > E A = E B 2. E A = E B = E C 3. E A = E B > E C +2C Case B + +2C + 4. E A > E B > E C 5. E C > E A > E B +2C Case C + 2C Typeset by FoilTEX 33

34 Question 33 Two point charges of equal magnitude but opposite sign are located as illustrated. A + P B A third charge, Z, is placed at point P. Which of the following best represents the net electric field produced by A and B at the location of Z? 1. if Z is positive; if Z is negative. 2. if Z is positive; if Z is negative. 3. if Z is positive; if Z is negative. 4. if Z is positive; if Z is negative. Typeset by FoilTEX 34

35 Question 34 Two plates, held m apart are charged. The electric field between them is uniform and points down with a magnitude of 1200N/C. A small ball of 100 electrons is placed between the plates. Which of the following represents the magnitude of the force exerted by the field on the ball of electrons? 1. F = 100N 2. F = 1200N 3. F = N 4. F = k C 100C (0.050m) 2 5. None of the above. Typeset by FoilTEX 35

36 Question 35 The electric field produced by a hidden charge collection of charged particles is illustrated below. Which vector best represents the direction of the force exerted on a positively charged particle placed at (1, 1)? 1. î+ĵ 1 y 2. î ĵ x 3. î+ĵ 4. î ĵ 5. None of the above/not enough info. Typeset by FoilTEX 36

37 Question 36 The electric field produced by a hidden charge collection of charged particles is illustrated below. Which vector best represents the direction of the force exerted on a negatively charged particle placed at (1, 1)? 1. î+ĵ 1 y 2. î ĵ x 3. î+ĵ 4. î ĵ 5. None of the above/not enough info. Typeset by FoilTEX 37

38 Question 37 Two particles with charges that are identical in magnitude but opposite in sign are placed along the x axis as illustrated. y Which vector best represents the direction of the Electric field at the origin? 1. î 2. ĵ q +q x 3. ĵ 4. î 5. None of the above. Typeset by FoilTEX 38

39 Question 38 Two point charges of equal magnitude but opposite sign are located as illustrated. + Which of the following best represents the net electric field produced by A and B at the location of Z? -3 A B 1. if Z is positive; if Z is negative. 2. if Z is positive; if Z is negative. A third charge, Z, is placed at (1,0). 3. if Z is positive; if Z is negative. 4. if Z is positive; if Z is negative. Typeset by FoilTEX 39

40 Question 39 Four charged particles are arranged as illustrated where distances are in meters. Which of the following best represents the electric field at the origin? 4 y +q 1. k q 8 î 2 2. k q 8 î +q 2q x 3. k 3q 8 î k q 4 î -4 +q 5. None of the above/not enough info. Typeset by FoilTEX 40

41 Question 40 The illustrated arc contains a uniform distribution of positive charge. y Which of the following best describes the direction of the electric field at the center of the arc? x 1. î 2. -î 3. ĵ 4. -ĵ 5. î+ĵ Typeset by FoilTEX 41

42 Question 41 The illustrated arc of radius R contains a uniform distribution of positive charge. Consider the contribution of the portion located at angle θ and containing charge dq as illustrated. y θ x Which of the following best describe the components of d E produced by this segment? 1. de x = k dq R 2 cosθ 2. de x = k dq R 2 cosθ 3. de x = k dq R 2 cosθ 4. de x = k dq R 2 cosθ 5. de x = k dq R 2 sinθ de y = k dq R 2 sinθ de y = k dq R 2 sinθ de y = k dq R 2 sinθ de y = k dq R 2 sinθ de y = k dq R 2 cosθ Typeset by FoilTEX 42

43 Question 42 The illustrated arc of radius R contains a uniform distribution of positive charge. y Which of the following best describe the x component of the electric field E produced by the entire arc? 1. E x = kλ R R 0 cosθdθ α x 2. E x = kλ R (π α/2) π α/2 cosθdθ 3. E x = kλ R π α/2 (π α/2) cosθdθ 4. E x = kλ R α 0 cosθdθ 5. E x = kλ R 2π 0 cosθdθ Typeset by FoilTEX 43

44 Question 43 A proton enters a region of constant electric field as illustrated. Which of the following best represents the trajectory of the proton while it is in the field? E Case 1 Case 2 Case 3 Case 4 Case 5 Typeset by FoilTEX 44

45 Question 44 The following diagrams illustrate a dipole placed in electric fields. In which of these cases is the net force on the dipole equal to zero? Case (a) + Case (c) + Case (b) + Case (d) + 1. (a) and (b) 2. (a) and (c) 3. (c) and (d) 4. (b) and (d) 5. (c) only Typeset by FoilTEX 45

46 Warm Up Question 1 Some molecules such as water have what is known as a permanent electric dipole. Consider the example of a permanent electric dipole as illustrated in the text. Is it possible for a permanent electric dipole to have a net (total) charge of zero? Explain your answer. 1. No. The dipole will not be symmetrical and so there will be an imbalance of forces. 2. No. There is positive and negative charge so the dipole is charged and cannot have a charge of zero. 3. Yes. The molecule is divided into a positive side and a negative side, each with equal magnitude, the molecule as a whole has a neutral charge. 4. Yes. The force exerted by the positive cancels that exerted by the negative. Typeset by FoilTEX 46

47 Warm Up Question 2 Go to the course website at: dacollin/teaching/2011spring/phys112 Look in the navigation bar on the left and click Calendar. This will open a new page with a day-by-day listing of the course activities. Click on the link for the Quiz on 19 January. You should see the quiz questions that were covered in the class. Now answer question 2. Typeset by FoilTEX 47

48 Warm Up Question 3 A charge of interest, Zog, is placed in the vicinity of a collection of charged metal objects. The force exerted by Zog is determined to point directly up. Is is true that the electric field at Zog s location and produced by the charged metal objects points directly up? Explain your answer. 1. Yes. The force points away from Zog, so Zog is positive and the field must also point away. 2. No. The charges of the metal objects point opposite to Zog. 3. No. Depending on the charges on the metal objects, Zog could be pulled up or down. 4. No. There could be many objects producing fields in all directions. These could add up to a net force upwards. 5. No. Zog s charge is not known. If it s charge is positive then the field would be up. However, if it s charge is negative the field would be down. Typeset by FoilTEX 48

49 Warm Up Question 4 Source charges are placed on two differently sized and separated balls and kept fixed. Various probe charges are placed at the location exactly midway between the two balls. Will the electric field produced (by the charged balls) at this location point one way for a positive probe charge and the other way for a negative probe charge? Explain your answer. 1. Yes. The electric field points away from a positive charge and toward a negative charge. 2. Yes. The field depends on whether the probe is attracted or repelled. This depends on the probe charge. 3. No. The electric field produced by the source charges is dependent solely upon the source charges. The probe charges do not influence the source charge electric field. 4. This depends on the sources. If they are like then the fields point away. If opposite toward. Typeset by FoilTEX 49

50 Warm Up Question 5 A vacuum is a region in which there is absolutely no matter, not even a single electron. Is it possible to establish an electric field in a box, inside which there is a vacuum? Explain your answer. 1. No. There is no matter inside the box so there is nothing to produce a field. 2. Yes. One can have an electron without mass. This would not be matter and could produce a field. 3. Yes. There is gravity in a vacuum. The formula for gravity is very similar to the formula for electrostatic force. 4. Yes. If the vacuum is surrounded by charged particles, the electric field can travel through the into the vacuum, even without any particles being in the vacuum. Typeset by FoilTEX 50

51 Warm Up Question 6 During a thunderstorm in the middle of a flat prairie, you have the choice of sitting inside either a small fiberglass trailer or else an aluminum trailer (Airstream!). Inside which of these will you be safer from a lightening strike? Explain your answer. 1. Airstream. Aluminum is a better conductor of electricity. A conductor can shield the inside from external electric fields. 2. Fiberglass. Fiberglass insulates and cannot carry charges. 3. Airstream because Airstreams rule! Typeset by FoilTEX 51

52 Electrostatic Potential Typeset by FoilTEX 52

53 Question 45 A positively charged particle (source) is held fixed. Another charged particle, Zog, fired toward the source a long time ago, moves toward the source particle. Assume that the only force acting on Zog is the electrostatic force due to the positively charged particle. Which of the following is true during this motion? + Zog: final Zog: initial 1. U elec > 0 regardless of Zog s charge. 2. U elec < 0 regardless of Zog s charge. 3. U elec > 0 for positive Zog, U elec < 0 for negative Zog. 4. U elec < 0 for positive Zog, U elec > 0 for negative Zog. Typeset by FoilTEX 53

54 Question 46 A negatively charged particle (source) is held fixed. Another charged particle, Zog, fired toward the source a long time ago, moves toward the source particle. Assume that the only force acting on Zog is the electrostatic force due to the negatively charged particle. Which of the following is true during this motion? Zog: final Zog: initial 1. U elec > 0 regardless of Zog s charge. 2. U elec < 0 regardless of Zog s charge. 3. U elec > 0 for positive Zog, U elec < 0 for negative Zog. 4. U elec < 0 for positive Zog, U elec > 0 for negative Zog. Typeset by FoilTEX 54

55 Question 47 A hidden collection of fixed charges produces the uniform electric field as illustrated. A positively charged particle moves in a straight line from the indicated initial to final location. Which of the following is true regarding the work done by the electric field on the particle? 1. W > 0. Initial + Final + 2. W < W = W depends on the speed of the charge. Typeset by FoilTEX 55

56 Question 48 A hidden collection of fixed charges produces the uniform electric field as illustrated. A negatively charged particle moves in a straight line from the indicated initial to final location. Which of the following is true regarding the work done by the electric field on the particle? 1. W > W < 0. Final Initial 3. W = W depends on the speed of the charge. Typeset by FoilTEX 56

57 Question 49 A hidden collection of fixed charges produces the uniform electric field as illustrated. A charged particle moves in a straight line from the indicated initial to final location. Final Initial Which of the following is true regarding the work done by the electric field on the particle? 1. W > 0 in all cases. 2. W < 0 in all cases. 3. W > 0 for positive charge and W < 0 for negative charge. 4. W < 0 for positive charge and W > 0 for negative charge. 5. W = 0 in all cases. Typeset by FoilTEX 57

58 Question 50 A positively charged particle (source) with charge +Q is held fixed. Another object, Zog, with charge +q, fired toward the source a long time ago, moves as illustrated. Assume that the only force acting on the positively charged particle is the electrostatic force due to the source. Which of the following is true for Zog during this motion? +Q + +q + +q + 1. W elec = 0 and K = W elec > 0 and K > 0. Zog: final Zog: initial 3. W elec > 0 and K < W elec < 0 and K > W elec < 0 and K < 0. Typeset by FoilTEX 58

59 Question 51 A negatively charged particle (source) with charge Q is held fixed. Positive probe charges move between the same points as illustrated. Probe A has charge 2.0C and probe B had charge 10.0C Which of the following is true? Q +q + Probe: final +q + Probe: initial 1. Work done on probe A is same as that on probe B. 2. Work done on probe B is 5 times larger than on probe A. 3. Work done on probe B is more than 5 times larger than on probe A. 4. Work done on probe B is more between 1 and 5 times larger than on probe A. 5. Work done on probe B is smaller than on probe A. Typeset by FoilTEX 59

60 Question 52 A positively charged object with charge +Q is held fixed and a negatively charged object, Zog, with charge q is released in such a way that at a later instant it is closer to the positive charge. Assume that the only force acting on the negatively charged particle is the electrostatic force due to the positively charged particle. Which of the following is true for Zog during this motion? +Q + q Zog: final q Zog: initial 1. K > 0 and U elec > K > 0 and U elec < K < 0 and U elec > K < 0 and U elec < Not enough info/none of the above. Typeset by FoilTEX 60

61 Question 53 Consider the following arrangements of charges. The source charge is the same in all cases and charge Zog was moved at constant speed from infinitely far away to its illustrated final location. Which of the following is true for the electrostatic potential energy stored in the system? 1. U A = U B < U C. Case A +Q + +6C + 2. U B < U C < U A. 3. U C < U B < U A. Case B +Q + +3C + 4. U B = U C < U A. 5. U B < U C = U A. Case C +Q + +3C + Typeset by FoilTEX 61

62 Question 54 Consider the following arrangements of charges. The source charge is at rest on the left and the probe charge was moved from the right at constant speed from infinitely far away to its illustrated final location. Which of the following is true for the electrostatic potential energy stored in the system? 1. U C < U A < U B. Case A +40C + +4C + 2. U A < U C = U B. 3. U C < U A = U B. Case B +40C + +8C + 4. U A < U C < U B. 5. U B < U A < U C. Case C +10C + +8C + Typeset by FoilTEX 62

63 Question 55 Two metal plates are charged in such a way that the electric potential at each is as indicated. On each plate the electric potential is constant. Separately, two particles with identical charges of +10 C move as illustrated. Which of the following is true regarding the change in electric potential energy? 1. U elec A = U elec B and V A = V B. 2. U elec A < U elec B and V A = V B. 12V 2V 3. U elec A > U elec B and V A = V B. 4. U elec A < U elec B and V A < V B. 5. U elec A = U elec B and V A < V B. Particle B Particle A Typeset by FoilTEX 63

64 Question 56 Two metal plates are charged in such a way that the electric potential at each is as indicated. On each plate the electric potential is constant. Separately, two positively charged particles move as illustrated. Particle A has a smaller charge than that of particle B. Which of the following is true? 1. U elec A = U elec B and V A = V B. 2. U elec A < U elec B and V A = V B. 3. U elec A > U elec B and V A = V B. 2V 12V + 4. U elec A < U elec B and V A < V B. 5. U elec A = U elec B and V A < V B. + Particle B + + Particle A Typeset by FoilTEX 64

65 Question 57 Two metal plates are charged in such a way that the electric potential at each is as indicated. On each plate the electric potential is constant. Separately, two particles move as illustrated. Particle A has charge of +5C and particle B has charge +10 C. Which of the following is true? 1. U elec A = U elec B and V A = V B. 2. U elec A < U elec B and V A = V B. 3. U elec A > U elec B and V A = V B. 2V 12V + 4. U elec A < U elec B and V A < V B. 5. U elec A = U elec B and V A < V B. + Particle B + + Particle A Typeset by FoilTEX 65

66 Question 58 Hidden source charges produce an electric potential. Another positively charged particle moves from a location where the electric potential is +20V to a location where it is 50V. Which of the following is true of the kinetic energy of the particle between these two locations? 1. K = 0 +20V + Initial 50V + Final 2. K > 0 3. K < 0 Typeset by FoilTEX 66

67 Question 59 A hidden source produces the following electrostatic potential. A charge, Zog, is at rest at the indicated location. V Zog is made to move toward the origin. Which of the following is true? 1. U elec > 0 regardless of Zog s charge. 2. U elec < 0 regardless of Zog s charge. 3. U elec = 0 regardless of Zog s charge. 4. U elec > 0 for positive Zog, U elec < 0 for negative Zog. 5. U elec < 0 for positive Zog, U elec > 0 for negative Zog. Zog: initial Typeset by FoilTEX 67

68 Question 60 A source charge produces the following electrostatic potential. Another charge, Z, is at rest at the indicated location on the x axis. The charge Z can move left or right along the x axis. V Z is released. In which direction does the charge Z move? 1. Left. 2. Right. 3. Left if Z is positive and right if Z is negative. 4. Right if Z is positive and left if Z is negative. 5. This cannot be determined without more information about the source charge. Zog: initial x Typeset by FoilTEX 68

69 Question 61 An infinite line of charge and two point charges produce an electric potential, which, along the x-axis has the following form. An electron moves, purely under the influence of these charge distributions, from the indicated intial to final points along the x axis. V Which is true of the electron s speed? 1. v i = v f 2. v i > v f 3. v i < v f 4. Not enough information. initial final x Typeset by FoilTEX 69

70 Question 62 A collection of fixed source particles produce an electric potential. Separately, two probe charges are placed in the potential (without altering the source charges). They are each placed at the same initial location and move to the same final location. The first probe particle Zog, has charge +4.0C and the second, Geraldine, has charge +8.0 C. Which of the following is true regarding the change in electric potential (between initial and final locations) for the probe charges? 1. V Zog = 1 4 V Geraldine 2. V Zog = 1 2 V Geraldine + initial + final 3. V Zog = V Geraldine 4. V Zog = 2 V Geraldine 5. V Zog = 4 V Geraldine Typeset by FoilTEX 70

71 Question 63 A charged particle, Zog, is in the vicinity of various source charges. The only forces exerted on Zog are those exerted by the source charges. Initially Zog is at location A and moves with speed 20m/s. Later Zog is at location B and moves with speed 5m/s. Which of the following is true regarding the electric potential difference V = V B V A where V A is the potential at A, etc,...? 1. V = V > 0 always. 3. V < 0 always. 4. V > 0 for positive Zog, V < 0 for negative Zog. 5. V < 0 for positive Zog, V > 0 for negative Zog. Typeset by FoilTEX 71

72 Question 64 Hidden source charges produce an electric potential which has equipotentials as illustrated. Probe charges moving through the initial location reach the indicated final location 10V 30V 50V initial final Which of the following is true regarding the probe charge? 1. K = 0 regardless of charge. 2. K < 0 regardless of charge. 3. K > 0 regardless of charge. 4. K > 0 for positive probe, K < 0 for negative probe. 5. K < 0 for positive probe, K > 0 for negative probe. Typeset by FoilTEX 72

73 Question 65 Two metal plates are charged as illustrated A B C D Which of the following is true regarding the potentials (note that negative is always less than positive, e.g. 50V < 10V)? 1. V A = V B = V C = V D 2. V A > V B = V C > V D 3. V A < V B = V C < V D 4. V A < V B < V C < V D 5. V A > V B > V C > V D Typeset by FoilTEX 73

74 Question 66 A positive source charge produces an electric potential. C Which of the following is the correct rank of the electric potential at the various points (a negative potential ranks lower than a positive potential, i.e. 20V < 10V)? 1. V A = V B = V C = V D A + Source B 2. V A = V B < V C = V D 3. V C = V D < V A = V B 4. V D < V A = V B < V C D 5. V A < V D = V C < V B Typeset by FoilTEX 74

75 Question 67 A negative source charge produces an electric potential. C Which of the following is the correct rank of the electric potential at the various points (a negative potential ranks lower than a positive potential, i.e. 20V < 10V)? 1. V A = V B = V C = V D A Source B 2. V A = V B < V C = V D 3. V C = V D < V A = V B 4. V D < V A = V B < V C D 5. V A < V D = V C < V B Typeset by FoilTEX 75

76 Question 68 An electron moves away from a positive source charge as illustrated. Final Initial + Source Which of the following is true regarding the electric potential (produced by the source) felt by the electron between initial and final locations? 1. V = 0 2. V > 0 3. V < 0 4. It depends on how fast the electron is moving. Typeset by FoilTEX 76

77 Question 69 An electron moves away from a positive source charge as illustrated. Which of the following is true regarding the electric potential energy of the electron between initial and final locations? Final Initial + Source 1. U elec = 0 2. U elec > 0 3. U elec < 0 4. It depends on how fast the electron is moving. Typeset by FoilTEX 77

78 Question 70 Two source charges are located as illustrated. Consider the following statement regarding the potential produced by the pair of charges: + +2C 10C The potential produce by these charges is negative since the negatively charged particle has a larger magnitude of charge. Is this statement correct? 1. Correct. 2. Incorrect. 3. Neither. Typeset by FoilTEX 78

79 Question 71 Two source charges are located as illustrated. The magnitudes of the charges are equal but their signs are opposite. Which of the following represents the rank of the potentials at the various points? 1. V A = V B = V C = V D A 2. V A = V B < V C = V D + +q D B C q 3. V D < V A = V B < V C 4. V C < V A = V B < V D Typeset by FoilTEX 79

80 Question 72 Two source charges are located as illustrated. The magnitudes of the charges are equal but their signs are opposite. Which of the following represents the rank of the potentials at the various points? 1. V A < V B = V C 2. V B < V C < V A + +q C A B q 3. V C < V B < V A 4. V A < V B < V C 5. V B < V A < V C Typeset by FoilTEX 80

81 Question 73 Two arrangements of source charges are illustrated. Which of the following is true of the potentials at the various points? + +q B A q 1. V A > V B 2. V A < V B 3. V A = V B 0 4. V A = V B = 0 + +q q Typeset by FoilTEX 81

82 Question 74 Two source charges are located as illustrated. The magnitudes of the charges are equal but their signs are opposite. Which of the following represents the rank of the potentials at the various points? 1. V A < V B = V C 2. V B < V C < V A + +q C A B q 3. V C < V B < V A 4. V A < V B < V C 5. V B < V A < V C Typeset by FoilTEX 82

83 Question 75 A positive point charge, S, is located at the origin as illustrated. C O Z A Which of the following best represents the rank of the electrostatic potential differences between each point and O, e.g. V AO = V A V O? 1. V BO > V AO = V CO 2. V AO = V CO > V BO B 3. V AO > V BO > V CO 4. V CO > V BO > V AO Typeset by FoilTEX 83

84 Question 76 Two charged particles A with charge q A and B with charge q B are located as illustrated below. A third particle Z with charge q Z is placed at the indicated location. Distances are measured in meters. A B Z The electrostatic potential energy of Z is to be calculated using U elec = q Z V. Which of the following represents V that should be used here? 1. V = k q A 4 + kq B 1 2. V = k q A 5 + kq B 1 3. V = k q A 4 + kq B 1 + kq Z 1 4. V = k q A 5 + kq B V = k q Aq Z 5 + k q Bq Z 1 Typeset by FoilTEX 84

85 Question 77 Four source charges are placed at the corners of a square as illustrated. The point P is a distance r from each corner. Which of the following is true for the electric potential at the point P in the center of the square? 1C + +1C P 1C + +2C 1. V = 0C 2. V = +1C 3. V = k 1C r 4. V = k 1C r 5. V = k 5C r Typeset by FoilTEX 85

86 Question 78 Two source charges are located as illustrated. Which of the following represents the electric potential at point P? 1. V = 3V + +1C d + +2C d P 2. V = k 1C d 3. V = k 3C d 4. V = k 2C d + k1c d 5. V = k 2C d + k1c 2d Typeset by FoilTEX 86

87 Question 79 The diagrams illustrate arrangements of charges where the symbols Q and q represent particular fixed values of charge. Rank the situations in order of increasing electrostatic potential energy. A Q q 1. A > B > C 2. A > B = C 3. A > C > B B 4. C > B > A Q +q + 5. C = B > A C Q +4q + Typeset by FoilTEX 87

88 Question 80 Two source charges are located as illustrated. The magnitudes of the charges are equal but their signs are opposite. A B D C Which represents an equipotential? 1. A only. 2. B only. 3. C only. 4. D only. + +q q 5. B and C. Typeset by FoilTEX 88

89 Question 81 The following diagram illustrates evenly spaced (in terms of voltage) equipotentials for a negative source charge. C Identical positively charged particles are successively moved from C to another point. Which of the following are true regarding the change in the electric potential energy of the positively charged particle? 1. U elec (C A) > U elec (C B) A B 2. U elec (C A) < U elec (C B) 3. U elec (C A) = U elec (C B) 4. U elec (C A) = U elec (C B) 5. None of the above/not enough info. Typeset by FoilTEX 89

90 Question 82 Source charges produce equipotential lines as illustrated. B Which of the following represents the rank of the magnitude of the electric field at the illustrated points? 1. E A = E B = E C C A 2. E A < E B < E C 3. E C < E B < E A 4. E B < E C < E A 5. E B < E A < E C Typeset by FoilTEX 90

91 Question 83 An electric field produced by some sources charges is as illustrated. Which of the following represents the rank of the magnitude of the electric potential at the illustrated points? A B C 1. V A = V B = V C 2. V A > V B > V C 3. V A < V B < V C 4. V A = V B < V C 5. V A < V B = V C Typeset by FoilTEX 91

92 Question 84 The electric field lines produced by a charge distribution are as illustrated. Which of the following represents an equipotential line? Case 1 Case 2 Case 3 Case 4 Typeset by FoilTEX 92

93 Question 85 Three pairs of uniformly charged infinite plates are separated by the same distance. Each plate is held at a constant voltage as indicated. Which of the following is the correct ranking of the magnitude of the force exerted on an proton placed between the plates? 200V 100V 50V 200V 180V 10V 1. A > B > C 2. A > C > B 3. B > A > C 4. B > C > A A B C Typeset by FoilTEX 93

94 Question 86 A simple electron gun is configured as illustrated. An electron is at rest on the left electrode. Each electrode is at a fixed electric potential. The electron must be accelerated from the left to the right electrode. For this to happen which of the followings must be true? Left electrode Right electrode 1. V L = V R 2. V L < V R 3. V L > V R V L V R Typeset by FoilTEX 94

95 Question 87 A simple electron gun is configured as illustrated. An electron moves between the electrodes, each of which is held at the fixed electric potentials. The distance between the potentials is 0.20 m. The electron is initially at rest at the left electrode and moves to the right. Left electrode 0V Right electrode 250V The electron is midway between the two electrodes and we would like to determine the electron s speed. Which electric potential is most useful in this regard? 1. V = 250V 2. V = 125V 3. V = 0V 4. V = kq r 5. V = kq r = = Typeset by FoilTEX 95

96 Question 88 A small neutral conductor is placed near to a positively charged sheet Which of the following best describes the subsequent motion of the ball? 1. The ball is immediately repelled from the plate. 2. The ball is attracted to the plate and then adheres to the plate. 3. The ball is attracted to the plate, then moves away from the plate, coming to rest at an angle to the left of vertical. 4. The ball is attracted to the plate, then moves away from the plate, coming to rest in a vertical position. 5. The ball is attracted to the plate, then moves away from the plate, coming to rest at an angle to the right of vertical. Typeset by FoilTEX 96

97 Question 89 Two capacitor plates are closely separated. A conducting ball is placed between them. The plates are connected to a power supply, allowed to charge and then disconnected from the power supply Which of the following is subsequently true? 1. The ball sticks to the plate to which it was attracted. 2. The ball is repelled and hangs midway between the plates 3. The ball is repelled to the opposite plate and sticks to that plate. 4. The ball bounces back and forth between the plates. The ball is initially attracted to one of the plates. Typeset by FoilTEX 97

98 Question 90 Two oppositely charged plates are closely separated. A conducting ball is placed between them Initially the ball bounces repeatedly, with very gradually diminishing frequency, between the two plates. A wire is connected from one plate to the other. Which of the following is true? 1. The ball continues to bounce with no change in frequency. 2. The rate at which the ball bounces slows to a lower steady rate. 3. The ball bounces a few more times and then stops. 4. The ball bounces a few more times, stops briefly and resumes bouncing. Typeset by FoilTEX 98

99 Warm Up Question 7 An electron is fired toward a negatively charged metal plate. As the electron approaches the plate does its electric potential energy decrease, increase or stay the same? Explain your answer. 1. Increase. The kinetic energy is decreasing meaning that the potential energy is increasing as it come closer to the metal plate. 2. Decrease. The negative charges repel the electron and this must decrease the potential. 3. Decrease. As a charge moves toward a negative plate, its energy always decreases. 4. Stay same. Typeset by FoilTEX 99

100 Warm Up Question 8 Consider the scenario illustrated in Fig Suppose that the plates are charged as illustrated in b) and an electron (negatively charged) moves from the right plate to the left. Will the electric potential energy of the electron increase, decrease or stay the same? Explain your answer. 1. Increase. If a negative electron moves from point B to point A, its potential energy will increase because it is moving closer to the negative side from which it experiences a stronger and stronger repulsive force. 2. Increase. A force of a hand would have to do work on the electron to bring it closer to the capacitor. 3. Decrease. Since U elec = W elec and W elec is positive. 4. Stay the same. No force is needed to move the electron. Typeset by FoilTEX 100

101 Warm Up Question 9 The text describes the mechanism by which lightning is produced. Consider a lightning strike between the bottom of the cloud and ground. Suppose that the lightning consists of a stream of moving electrons. In which direction (cloud to ground or ground to cloud) do the electrons travel? Does the electric potential energy (U elec ) of the electron increase, decrease or stay constant during this process? Is the electric potential (V) higher or lower at the bottom of the cloud than at the ground? Explain your answers. 1. U elec decreases, V decreases. There must be a higher V at the bottom of the cloud where the charge build up occurs. 2. U elec decreases, V decreases. The electric potential is converted to KE and so must be smaller at the bottom of the cloud. 3. U elec decreases, V decreases. The electric potential energy is converted to KE and so must be smaller at the bottom of the cloud - the same is true for electric potential. 4. U elec decreases, V increases. The electric potential energy is released as increasing kinetic energy. Typeset by FoilTEX 101

102 Warm Up Question 10 An ion is an atom from which charge has been removed or added. Various ions can be accelerated by placing them in a region where there is an electric potential difference. Suppose that a sodium ion (neutral sodium atom with one electron removed) is accelerated from rest through the same electric potential difference as a potassium ion (a potassium atom with one electron removed). How will their kinetic energies compare? Explain your answer, describing which equation in the text is most useful for this problem. 1. Potassium KE larger since potassium is heavier. 2. Different. Since the atoms have different charge arrangements, they will produce different electric potentials. 3. Both ions would have the same kinetic energies as they both have the same charge (each is missing a single electron) and the problem states that the Vs are the same. Using K = q V gives same KE. Typeset by FoilTEX 102

103 Warm Up Question 11 An electric field between two charged metal plates consists of vectors which all have the same size and point up. Which way are the equipotential lines oriented? 1. Perpendicular to the electric field and thus horizontal. 2. There is only one equipotential and it is located midway between the plates. 3. Same direction as the electric field and thus up. 4. Opposite to the electric field and thus down. Typeset by FoilTEX 103

104 Warm Up Question 12 A sphere made of a perfect conductor is neutral and is placed to the left of a single positive point charge. How does the electric potential on the left side (farthest from the point charge) of the sphere compare to that on the right side (closer to the point charge)? Explain your answer. 1. The same. The whole surface of the sphere is a has the same potential and is a equipotential surface. Pg. 693 states that any two points inside a conductor in electrostatic equilibrium are at the same potential. 2. Right side higher potential since V = kq r and r is smaller for the right side which is closer to the positive charge. 3. Left side higher potential since the sphere becomes polarized, sending positive charge to the left. Typeset by FoilTEX 104

105 Warm Up Question 13 Look at Problem 25 on page 707. Consider points 1 and 3 in the accompanying figure (P21.25). During which point in the heart s cycle is V 3 V 1 negative? Explain your answer. 1. Stage c. Here V 3 is positive and V 1 is negative. 2. Stage b. V 3 V 1 will be negative during septal depolarization. This is because V 3 will be negative and V 1 will be positive. 3. Stage b. The blood flows from the top, closer to 1, to the bottom, closer to 3. Since the blood flows down the potential at 3 must be lower. 4. Stage b. The charge at 1 is positive and at 3 negative. Typeset by FoilTEX 105

106 Warm Up Question 14 A parallel-plate capacitor consists of two metal plates that are parallel to each other. The distance between the plates is held steady and their area stays constant. Suppose that the electric potential difference across the capacitor is increased. Does the capacitance increase, decrease or stay constant? Explain your answer. 1. Response 2. Response Typeset by FoilTEX 106

107 Currents and Circuits Typeset by FoilTEX 107

108 Question 91 Charged particles pass along wires as illustrated. In each case, the number of charged particles that pass through the end of the wire is N, the charge of each particle is q and the time during which this is observed is t. Rank the situations in order of magnitude of current through the shaded end of the wire. 1. I A > I B > I C Case A N = 40 q = 6C t = 4s 2. I A > I C > I B 3. I B = I C > I A 4. I B > I C > I A Case B N = 100 q = 1C t = 4s 5. I C > I B > I A Case C N = 100 q = 2C t = 4s Typeset by FoilTEX 108

109 Question 92 Charged particles pass along wires as illustrated. In each case, the number of charged particles that pass through the end of the wire is N, the charge of each particle is q and the time during which this is observed is t. Rank the situations in order of magnitude of current through the shaded end of the wire. 1. I A = I B = I C Case A N = 40 q = 6C t = 4s 2. I A > I B > I C 3. I A > I C > I B 4. I B > I C > I A Case B N = 100 q = 1C t = 4s 5. I C > I B > I A Case C N = 100 q = 2C t = 4s Typeset by FoilTEX 109