positively charged - Colorado Mesa University

Electrostatics – Typeset by FoilTEX – 1 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 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 Question 3 Congratulations! You now know how to navigate the course website. The following is a photograph of a well-known city. – Typeset by FoilTEX – Describe as accurately as you can the name of this city, its country and continent. 4 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 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 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. They neither attract nor repel but still stay in contact. – Typeset by FoilTEX – 7 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 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. − – Typeset by FoilTEX – + − − − − 2. 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. 9 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 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. A – Typeset by FoilTEX – 3. The charge of X is larger in case 1 than in case 2. 4. The charge of X is smaller in case 1 than in case 2. Case 2 X 1. The charge of X in case 1 is opposite to that of X in case 2. 2. The charge of X in the same in both cases. Case 1 X Which of the following is true? B 11 Question 11 An isolated particle has charge +16 C. Consider the following statements: Which of the statements are true? 1. Only A. A) The particle always exerts a force of 16 N but can feel a force of any size. B) The particle always feels a force of 16 N but can exert a force of any size. 2. Only B. 3. Only C. 4. None of them. C) The particle always exerts a force of 16 N and always feels a force of 16 N. – Typeset by FoilTEX – 12 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: Which of the statements are true? A) Zog definitely exerts a force of 16 N but the force Zog feels could be of another size. 2. Only B. B) Zog definitely feels a force of 16 N but the force Zog exerts could be of another size. 4. None of them. 1. Only A. 3. Only C. C) Zog definitely exerts a force of 16 N and definitely feels a force of 16 N. – Typeset by FoilTEX – 13 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 Question 14 Two charges are aligned as illustrated. Denote the electrostatic force exerted by the ~blue on red blue charge on the red charge as F ~red on blue . and that by the red on blue as F Which of the following is true regarding the magnitude of the two forces? 1. Fred on blue = Fblue on red 2. Fred on blue > Fblue on red +2 C + – Typeset by FoilTEX – −4 C − 3. Fred on blue < Fblue on red 4. The sizes of forces depends on the masses of the particles. 15 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 1 + + + + – Typeset by FoilTEX – + + + + + + Case 4 + + Case 2 + + + + Case 3 + + + + + + Case 5 + + + + + + + + 16 Question 16 Three charges are aligned as illustrated. +2 C + −2 C − −4 C − Which of the following gives the direction of the net force exerted on the charge at the right? 1. 2. 3. 4. → ← ↑ ↓ 5. Zero net force. – Typeset by FoilTEX – 17 Question 17 Three charges are aligned as illustrated. +2 C + −2 C − +4 C + Which of the following gives the direction of the net force exerted on the blue charge? 1. 2. 3. 4. → ← ↑ ↓ 5. Zero net force. – Typeset by FoilTEX – 18 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. 1. −e +e – Typeset by FoilTEX – 2. +e +e −e +e −e +e 3. +e 19 Question 19 Two particles with charges that are identical in magnitude but opposite in sign are placed along the x axis as illustrated. Which of the following best represents the direction of the net force exerted on the charge on the y axis? y 1. −Q −q 2. 3. +q x 4. A negatively charged particle is placed along the y axis. – Typeset by FoilTEX – 5. → ← ր ց ↑ 20 Question 20 Two identically charged particle are placed along the x axis as illustrated. y 3. −ĵ 4. î − ĵ 5. î + ĵ +q x A negatively charged particle is placed along the y axis. – Typeset by FoilTEX – 2. î ĵ 1. −Q +q Which vector best represents the direction of the net force exerted on the charge on the y axis? 21 Question 21 The electric field produced by a hidden charge collection of charged particles (sources) is illustrated below. Initially a probe charge with charge 5 C is placed at point P. This is removed and replaced by a new probe charge with charge 10 C, 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 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. −−− − − −−− 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 P× +++++++++++++++++++++ – Typeset by FoilTEX – 2. False 3. Depends on the situation. 23 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. −−− − − −−− 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 P× 3. Depends on the situation. +++++++++++++++++++++ – Typeset by FoilTEX – 24 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× +++++++++++++++++++++ 1. True 2. False 3. Depends on the situation. – Typeset by FoilTEX – 25 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× +++++++++++++++++++++ 1. True 2. False 3. Depends on the situation. – Typeset by FoilTEX – 26 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× +++++++++++++++++++++ 1. True 2. False 3. Depends on the situation. – Typeset by FoilTEX – 27 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. −−− − − −−− Which of the following best represents the direction of the electric field produced by the ring and the plate at P? 1. 2. ↑ ↓ for ↓ ↑ for for positive probe charge negative probe charge. for positive probe charge negative probe charge. ↑ for any probe charge. 4. ↓ for any probe charge. 3. P× +++++++++++++++++++++ 5. Zero field. – Typeset by FoilTEX – 28 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 × – Typeset by FoilTEX – 3. The force could be either right or left. 4. The force depends on the direction of motion of the particle. 29 Question 29 The electric field produced by a hidden charge collection of charged particles is illustrated below. Q × P × 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. 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 Question 30 A positive charge, labeled A, of magnitude +5 C, and another charge B, of magnitude −8 C, are placed as illustrated. The distance between the charges is 10 m. A + – Typeset by FoilTEX – B − Which of the following is true for the electric field produced by A at the location of B? ~ =k 1. E 8C (10 m)2 → ~ =k 2. E 8C (10 m)2 ← ~ =k 3. E 5C (10 m)2 → ~ =k 4. E 5C (10 m)2 ← 2 40 C ~ =k 5. E (10 m)2 ← 31 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 ~ F 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 ~ and the force on Geraldine compared to charges, E, those when Zog was present? ~ same direction. 1. Force same direction, E ~ reverses direction. 2. Force same direction, E ~ same direction. 3. Force reverses direction, E ~ reverses direction. 4. Force reverses direction, E – Typeset by FoilTEX – 32 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. Case A +4 C + × +4 C + Which of the following describes the rank of the magnitudes of the fields at the midpoint? 1. EC > EA = EB 2. EA = EB = EC 3. EA = EB > EC Case B +2 C + Case C +2 C + – Typeset by FoilTEX – × +2 C + × −2 C − 4. EA > EB > EC 5. EC > EA > EB 33 Question 33 Two point charges of equal magnitude but opposite sign are located as illustrated. A + P × B − Which of the following best represents the net electric field produced by A and B at the location of Z? 1. A third charge, Z, is placed at point P. 2. 3. 4. – Typeset by FoilTEX – → if Z is positive; ← if Z is negative. ← if Z is positive; → if Z is negative. → if Z is positive; → if Z is negative. ← if Z is positive; ← if Z is negative. 34 Question 34 Two plates, held 0.050 m apart are charged. The electric field between them is uniform and points down with a magnitude of 1200 N/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 = 100 N 2. F = 1200 N 3. F = 120000 N 1.6 × 10−17 C × 100 C 4. F = k (0.050 m)2 5. None of the above. – Typeset by FoilTEX – 35 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 2. î − ĵ 3. −î + ĵ 4. −î − ĵ y 1 -2 -1 1 -1 2 x 5. None of the above/not enough info. – Typeset by FoilTEX – 36 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 2. î − ĵ 3. −î + ĵ 4. −î − ĵ y 1 -2 -1 1 -1 2 x 5. None of the above/not enough info. – Typeset by FoilTEX – 37 Question 37 Two particles with charges that are identical in magnitude but opposite in sign are placed along the x axis as illustrated. Which vector best represents the direction of the Electric field at the origin? 2. î ĵ 3. −ĵ 4. −î 1. y −q +q x 5. None of the above. – Typeset by FoilTEX – 38 Question 38 Two point charges of equal magnitude but opposite sign are located as illustrated. + -3 – -2 A -1 0 1 2 3 B A third charge, Z, is placed at (1, 0). Which of the following best represents the net electric field produced by A and B at the location of Z? 1. 2. 3. 4. – Typeset by FoilTEX – → if Z is positive; ← if Z is negative. ← if Z is positive; → if Z is negative. → if Z is positive; → if Z is negative. ← if Z is positive; ← if Z is negative. 39 Question 39 Four charged particles are arranged as illustrated where distances are in meters. y 4 q î 8 q 2. −k î 8 1. k +q 2 +q -4 -2 2 -2 -4 – Typeset by FoilTEX – +q Which of the following best represents the electric field at the origin? −2q 4 x 3q î 8 q 4. k î 4 3. k 5. None of the above/not enough info. 40 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? 3. î -î ĵ 4. -ĵ 5. î + ĵ 1. x – Typeset by FoilTEX – 2. 41 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 Which of the following best describe the components ~ produced by this segment? of dE 1. dEx = k dq 2. dEx = −k 2 cos θ R 3. dEx = k θ – Typeset by FoilTEX – x dq cos θ R2 dq cos θ R2 dEy = k dq sin θ R2 dq dEy = k 2 sin θ R dEy = −k dq sin θ R2 4. dEx = −k dq cos θ R2 dEy = −k 5. dEx = −k dq sin θ 2 R dEy = −k dq sin θ R2 dq cos θ 2 R 42 Question 42 The illustrated arc of radius R contains a uniform distribution of positive charge. y α – Typeset by FoilTEX – x Which of the following best describe the x component of the electric field E produced by the entire arc? kλ 1. Ex = − R Z R kλ 2. Ex = − R Z −(π−α/2) kλ 3. Ex = − R Z π−α/2 kλ 4. Ex = − R Z α kλ 5. Ex = − R Z 2π cos θ dθ 0 cos θ dθ π−α/2 cos θ dθ −(π−α/2) cos θ dθ 0 cos θ dθ 0 43 Question 43 A proton enters a region of constant electric field as illustrated. b 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 Question 44 The following diagrams illustrate a dipole placed in electric fields. Case (a) Case (b) −+ + − In which of these cases is the net force on the dipole equal to zero? 1. (a) and (b) 2. (a) and (c) 3. (c) and (d) 4. (b) and (d) Case (c) Case (d) 5. (c) only −+ – Typeset by FoilTEX – + − 45 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 Warm Up Question 2 Go to the course website at: http://myhome.mesastate.edu/∼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 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 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 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 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 Electrostatic Potential – Typeset by FoilTEX – 52 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? 1. ∆Uelec > 0 regardless of Zog’s charge. 2. ∆Uelec < 0 regardless of Zog’s charge. + Zog: final Zog: initial 3. ∆Uelec > 0 for positive Zog, ∆Uelec < 0 for negative Zog. 4. ∆Uelec < 0 for positive Zog, ∆Uelec > 0 for negative Zog. – Typeset by FoilTEX – 53 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? 1. ∆Uelec > 0 regardless of Zog’s charge. 2. ∆Uelec < 0 regardless of Zog’s charge. − Zog: final Zog: initial 3. ∆Uelec > 0 for positive Zog, ∆Uelec < 0 for negative Zog. 4. ∆Uelec < 0 for positive Zog, ∆Uelec > 0 for negative Zog. – Typeset by FoilTEX – 54 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. 2. W < 0. 3. W = 0. Initial + – Typeset by FoilTEX – Final + 4. W depends on the speed of the charge. 55 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 > 0. 2. W < 0. 3. W = 0. Final − – Typeset by FoilTEX – Initial − 4. W depends on the speed of the charge. 56 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 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? 1. Welec = 0 and ∆K = 0. +q + +q + 2. Welec > 0 and ∆K > 0. Zog: final Zog: initial 3. Welec > 0 and ∆K < 0. +Q + 4. Welec < 0 and ∆K > 0. 5. Welec < 0 and ∆K < 0. – Typeset by FoilTEX – 58 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 2.0 C and probe B had charge 10.0 C Which of the following is true? 1. Work done on probe A is same as that on probe B. +q + +q + Probe: final Probe: initial −Q − 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 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? 1. ∆K > 0 and ∆Uelec > 0. +Q + −q − Zog: final −q − Zog: initial 2. ∆K > 0 and ∆Uelec < 0. 3. ∆K < 0 and ∆Uelec > 0. 4. ∆K < 0 and ∆Uelec < 0. 5. Not enough info/none of the above. – Typeset by FoilTEX – 60 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. +Q Case A + +6 C + – Typeset by FoilTEX – 1. UA = UB < UC . 2. UB < UC < UA . 3. UC < UB < UA . +Q Case B + +Q Case C + Which of the following is true for the electrostatic potential energy stored in the system? +3 C + 4. UB = UC < UA . 5. UB < UC = UA . +3 C + 61 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. +40 C +4 C + Case A + +40 C +8 C + Case B + Which of the following is true for the electrostatic potential energy stored in the system? 1. UC < UA < UB . 2. UA < UC = UB . 3. UC < UA = UB . 4. UA < UC < UB . 5. UB < UA < UC . +10 C +8 C + Case C + – Typeset by FoilTEX – 62 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. 12 V 2V Which of the following is true regarding the change in electric potential energy? 1. ∆Uelec A = ∆Uelec B and ∆VA = ∆VB . 2. ∆Uelec A < ∆Uelec B and ∆VA = ∆VB . 3. ∆Uelec A > ∆Uelec B and ∆VA = ∆VB . 4. ∆Uelec A < ∆Uelec B and ∆VA < ∆VB . 5. ∆Uelec A = ∆Uelec B and ∆VA < ∆VB . Particle B Particle A – Typeset by FoilTEX – 63 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. 2V 12 V + Which of the following is true? 1. ∆Uelec A = ∆Uelec B and ∆VA = ∆VB . 2. ∆Uelec A < ∆Uelec B and ∆VA = ∆VB . 3. ∆Uelec A > ∆Uelec B and ∆VA = ∆VB . 4. ∆Uelec A < ∆Uelec B and ∆VA < ∆VB . 5. ∆Uelec A = ∆Uelec B and ∆VA < ∆VB . + Particle B + + Particle A – Typeset by FoilTEX – 64 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 +5 C and particle B has charge +10 C. 2V 12 V + Which of the following is true? 1. ∆Uelec A = ∆Uelec B and ∆VA = ∆VB . 2. ∆Uelec A < ∆Uelec B and ∆VA = ∆VB . 3. ∆Uelec A > ∆Uelec B and ∆VA = ∆VB . 4. ∆Uelec A < ∆Uelec B and ∆VA < ∆VB . 5. ∆Uelec A = ∆Uelec B and ∆VA < ∆VB . + Particle B + + Particle A – Typeset by FoilTEX – 65 Question 58 Hidden source charges produce an electric potential. Another positively charged particle moves from a location where the electric potential is +20 V to a location where it is −50 V. +20 V + Initial – Typeset by FoilTEX – Which of the following is true of the kinetic energy of the particle between these two locations? 1. ∆K = 0 2. ∆K > 0 −50 V + Final 3. ∆K < 0 66 Question 59 A hidden source produces the following electrostatic potential. A charge, Zog, is at rest at the indicated location. Zog is made to move toward the origin. Which of the following is true? 1. ∆Uelec > 0 regardless of Zog’s charge. V 2. ∆Uelec < 0 regardless of Zog’s charge. 3. ∆Uelec = 0 regardless of Zog’s charge. 4. ∆Uelec > 0 for positive Zog, ∆Uelec < 0 for negative Zog. 5. ∆Uelec < 0 for positive Zog, ∆Uelec > 0 for negative Zog. Zog: initial – Typeset by FoilTEX – 67 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. Z is released. In which direction does the charge Z move? 1. Left. 2. Right. V 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 – Typeset by FoilTEX – x 68 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. Which is true of the electron’s speed? 1. vi = vf 2. vi > vf 3. vi < vf V 4. Not enough information. initial – Typeset by FoilTEX – final x 69 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 +4.0 C and the second, Geraldine, has charge +8.0 C. + final + initial – Typeset by FoilTEX – Which of the following is true regarding the change in electric potential (between initial and final locations) for the probe charges? 1. ∆VZog = 1 ∆VGeraldine 4 2. ∆VZog = 1 ∆VGeraldine 2 3. ∆VZog = ∆VGeraldine 4. ∆VZog = 2∆VGeraldine 5. ∆VZog = 4∆VGeraldine 70 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 20 m/s. Later Zog is at location B and moves with speed 5 m/s. Which of the following is true regarding the electric potential difference ∆V = VB − VA where VA is the potential at A, etc, . . . ? 1. ∆V = 0. 2. ∆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 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 Which of the following is true regarding the probe charge? 1. ∆K = 0 regardless of charge. 2. ∆K < 0 regardless of charge. 10 V 30 V 3. ∆K > 0 regardless of charge. 4. ∆K > 0 for positive probe, ∆K < 0 for negative probe. initial final – Typeset by FoilTEX – 50 V 5. ∆K < 0 for positive probe, ∆K > 0 for negative probe. 72 Question 65 Two metal plates are charged as illustrated. + + + + A + + + + b b b B C − − − D− − − − − b Which of the following is true regarding the potentials (note that negative is always less than positive, e.g. −50 V < 10 V)? 1. VA = VB = VC = VD 2. VA > VB = VC > VD 3. VA < VB = VC < VD 4. VA < VB < VC < VD 5. VA > VB > VC > VD – Typeset by FoilTEX – 73 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. −20 V < 10 V)? 1. VA = VB = VC = VD A × + Source B × 2. VA = VB < VC = VD 3. VC = VD < VA = VB 4. VD < VA = VB < VC D × – Typeset by FoilTEX – 5. VA < VD = VC < VB 74 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. −20 V < 10 V)? 1. VA = VB = VC = VD A × − Source B × 2. VA = VB < VC = VD 3. VC = VD < VA = VB 4. VD < VA = VB < VC D × – Typeset by FoilTEX – 5. VA < VD = VC < VB 75 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 Question 69 An electron moves away from a positive source charge as illustrated. − Final − Initial + Source Which of the following is true regarding the electric potential energy of the electron between initial and final locations? 1. ∆Uelec = 0 2. ∆Uelec > 0 3. ∆Uelec < 0 4. It depends on how fast the electron is moving. – Typeset by FoilTEX – 77 Question 70 Two source charges are located as illustrated. + +2 C − −10 C Consider the following statement regarding the potential produced by the pair of charges: “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 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. VA = VB = VC = VD 2. VA = VB < VC = VD A × 3. VD < VA = VB < VC B × + +q D × – Typeset by FoilTEX – C × − −q 4. VC < VA = VB < VD 79 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. VA < VB = VC 2. VB < VC < VA 3. VC < VB < VA A × + +q C × – Typeset by FoilTEX – B × − −q 4. VA < VB < VC 5. VB < VA < VC 80 Question 73 Two arrangements of source charges are illustrated. A × + +q Which of the following is true of the potentials at the various points? 1. VA > VB − −q 2. VA < VB 3. VA = VB 6= 0 4. VA = VB = 0 B × + +q – Typeset by FoilTEX – − −q 81 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. VA < VB = VC 2. VB < VC < VA 3. VC < VB < VA A × + +q C × – Typeset by FoilTEX – B × − −q 4. VA < VB < VC 5. VB < VA < VC 82 Question 75 A positive point charge, S, is located at the origin as illustrated. C 4 3 Which of the following best represents the rank of the electrostatic potential differences between each point and O, e.g. ∆VAO = VA − VO ? O 2 1. ∆VBO > ∆VAO = ∆VCO 1 Z 0 A 2. ∆VAO = ∆VCO > ∆VBO -1 3. ∆VAO > ∆VBO > ∆VCO B -2 4. ∆VCO > ∆VBO > ∆VAO -3 -4 -4 -3 -2 – Typeset by FoilTEX – -1 0 1 2 3 4 83 Question 76 Two charged particles A with charge qA and B with charge qB are located as illustrated below. A third particle Z with charge qZ 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 Uelec = qZ V. Which of the following represents V that should be used here? 2. V = 3. V = 4. V = 5. V = – Typeset by FoilTEX – qA qB +k 4 1 qA qB k +k 5 1 qB qZ qA +k +k k 4 1 1 qA qB k 2 +k 2 5 1 qA qZ qB qZ k +k 5 1 1. V = k 84 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. − −1 C b − −1 C Which of the following is true for the electric potential at the point P in the center of the square? 1. V = 0 C 2. V = +1 C P 3. V = k + +1 C + +2 C 4. V = −k 5. V = k – Typeset by FoilTEX – 1C r 1C r 5C r 85 Question 78 Two source charges are located as illustrated. Which of the following represents the electric potential at point P? 1. V = 3 V + +1 C d – Typeset by FoilTEX – + +2 C d P × 2. V = k 1C d 3. V = k 3C d 4. V = k 1C 2C +k d d 5. V = k 2C 1C +k d 2d 86 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. 1. A > B > C A −Q − 2. A > B = C −q − 3. A > C > B 4. C > B > A B −Q − +q + 5. C = B > A C −Q − – Typeset by FoilTEX – +4q + 87 Question 80 Two source charges are located as illustrated. The magnitudes of the charges are equal but their signs are opposite. A B D Which represents an equipotential? 1. A only. 2. B only. 3. C only. C + +q – Typeset by FoilTEX – − −q 4. D only. 5. B and C. 88 Question 81 The following diagram illustrates evenly spaced (in terms of voltage) equipotentials for a negative source charge. 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? C 1. ∆Uelec (C → A) > ∆Uelec (C → B) A − B 2. ∆Uelec (C → A) < ∆Uelec (C → B) 3. ∆Uelec (C → A) = ∆Uelec (C → B) 4. ∆Uelec (C → A) = −∆Uelec (C → B) 5. None of the above/not enough info. – Typeset by FoilTEX – 89 Question 82 Source charges produce equipotential lines as illustrated. Which of the following represents the rank of the magnitude of the electric field at the illustrated points? b B b C 1. EA = EB = EC A b 2. EA < EB < EC 3. EC < EB < EA 4. EB < EC < EA 5. EB < EA < EC – Typeset by FoilTEX – 90 Question 83 An electric field produced by some sources charges is as illustrated. A b B b C b Which of the following represents the rank of the magnitude of the electric potential at the illustrated points? 1. VA = VB = VC 2. VA > VB > VC 3. VA < VB < VC 4. VA = VB < VC 5. VA < VB = VC – Typeset by FoilTEX – 91 Question 84 The electric field lines produced by a charge distribution are as illustrated. – Typeset by FoilTEX – Which of the following equipotential line? represents Case 1 Case 2 Case 3 Case 4 an 92 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? 1. A > B > C −200 V 100 V 50 V 200 V −180 V −10 V 2. A > C > B 3. B > A > C 4. B > C > A A – Typeset by FoilTEX – B C 93 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. Left electrode Right electrode The electron must be accelerated from the left to the right electrode. For this to happen which of the followings must be true? 1. VL = VR 2. VL < VR 3. VL > VR − VL – Typeset by FoilTEX – VR 94 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. 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 = 250 V 2. V = 125 V Left electrode Right electrode −19 kq −9 −1.6 × 10 4. V = = 9.0 × 10 r 0.20 − 0V – Typeset by FoilTEX – 3. V = 0 V 250 V −19 kq −9 −1.6 × 10 5. V = = 9.0 × 10 r 0.10 95 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 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 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. – Typeset by FoilTEX – 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. 98 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. decreases. As a charge moves toward a negative plate, its energy always 4. Stay same. – Typeset by FoilTEX – 99 Warm Up Question 8 Consider the scenario illustrated in Fig 21.4. 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 ∆Uelec = −Welec and Welec is positive. 4. Stay the same. No force is needed to move the electron. – Typeset by FoilTEX – 100 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 (Uelec ) 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. Uelec decreases, V decreases. There must be a higher V at the bottom of the cloud where the charge build up occurs. 2. Uelec decreases, V decreases. The electric potential is converted to KE and so must be smaller at the bottom of the cloud. 3. Uelec 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. Uelec decreases, V increases. increasing kinetic energy. – Typeset by FoilTEX – The electric potential energy is released as 101 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 ∆V s are the same. Using ∆K = −q∆V gives same KE. – Typeset by FoilTEX – 102 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 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 = which is closer to the positive charge. kq r and r is smaller for the right side 3. Left side higher potential since the sphere becomes polarized, sending positive charge to the left. – Typeset by FoilTEX – 104 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 V3 − V1 negative? Explain your answer. 1. Stage c. Here V3 is positive and V1 is negative. 2. Stage b. V3 − V1 will be negative during septal depolarization. This is because V3 will be negative and V1 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 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 Currents and Circuits – Typeset by FoilTEX – 107 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. Case A b b b b b b N = 40 q = 6 C ∆t = 4 s b b Rank the situations in order of magnitude of current through the shaded end of the wire. 1. IA > IB > IC 2. IA > IC > IB 3. IB = IC > IA 4. IB > IC > IA Case B Case C b b b b b b b b b – Typeset by FoilTEX – b b b b b b b N = 100 q = 1 C ∆t = 4 s b b b b b b b b 5. IC > IB > IA N = 100 q = 2 C ∆t = 4 s 108 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. Case A b b b b b b N = 40 q = −6 C ∆t = 4 s b b Rank the situations in order of magnitude of current through the shaded end of the wire. 1. IA = IB = IC 2. IA > IB > IC 3. IA > IC > IB 4. IB > IC > IA Case B Case C b b b b b b b b b – Typeset by FoilTEX – b b b b b b b N = 100 q = 1 C ∆t = 4 s b b b b b b b b 5. IC > IB > IA N = 100 q = 2 C ∆t = 4 s 109 Question 93 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. Case A b b b b b b N = 40 q = −6 C ∆t = 10 s b b Rank the situations in order of magnitude of current through the shaded end of the wire. 1. IC > IB > IA 2. IA > IC > IB 3. IA > IC = IB 4. IB = IC > IA Case B Case C b b b b b b b b b – Typeset by FoilTEX – b b b b b b b N = 100 q = 1 C ∆t = 5 s b b b b b b b b 5. IB > IA = IC N = 100 q = 2 C ∆t = 10 s 110 Question 94 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. Case A b b b b b b N = 40 q = −5 C ∆t = 10 s b b Which of these currents are identical (both in magnitude and direction)? 1. All of them. 2. None of them. 3. A and B. 4. A and C. b Case B Case C b b b b b b b b – Typeset by FoilTEX – b b b b b b b N = 100 q = −2 C ∆t = 10 s b b b b b b b b 5. B and C. N = 100 q = 2 C ∆t = 10 s 111 Question 95 Consider circuit devices (e.g. bulb) with two connecting ends. Several conceivable current flow scenarios are illustrated. In which case/s does charge accumulate within the device as time passes? 1. It accumulates in all of these. Case A 10 A Case B 10 A Case C 10 A 2. Only A. 3. Only B. 4. Only C. 10 A – Typeset by FoilTEX – 10 A 20 A 5. Only B and C. 112 Question 96 A bulb is connected to a battery as illustrated. A b b C Which of the following is true for the currents at different points? 1. IA = Ibulb = IC 2. IA > Ibulb > IC 3. IA = IC > Ibulb 4. IA < Ibulb < IC – Typeset by FoilTEX – 113 Question 97 A bulb is connected to a battery as illustrated. A thicker wire is used to connect one terminal of the bulb to the battery. Which of the following represents the rank of the magnitude of the currents? 1. IA = IB – Typeset by FoilTEX – b A b B 2. IA > IB 3. IB > IA 114 Question 98 Two identical batteries are connected in two different scenarios as illustrated. In the scenario on the left a thicker wires (smaller resistance) are used. b A b C Which of the following represents the rank of the magnitude of the currents? 1. IA = IB = IC 2. IA = IB > IC 3. IC > IA = IB b B 4. IB > IA = IC 5. IC = IA > IB – Typeset by FoilTEX – 115 Question 99 Two identical bulbs are connected to identical batteries in two different scenarios as illustrated. In the scenario on the left a thicker wire (smaller resistance) is used to connect one terminal of the bulb to the battery. Which of the following represents the rank of the magnitude of the currents? 1. IA = IC 2. IA > IC 3. IC > IA b – Typeset by FoilTEX – A b C 116 Question 100 Two resistors are connected to a battery. R1 = 100 Ω b It is found that 1000 electrons pass point A in 1.0 s. How many electrons pass point B in 2.0 s? 1. 250 B R2 = 200 Ω b A 2. 500 3. 1000 4. 2000 5. 4000 – Typeset by FoilTEX – 117 Question 101 A bulb is connected to a battery as illustrated. Which of the following is true? 1. In 10 s the total charge that flows through the bulb is 3 C and through the battery 3 C. 5V 3A The current through the bulb and potential difference across the battery are indicated. The wires offer negligible resistance. 2. In 10 s the total charge that flows through the bulb is 5 C and through the battery 5 C. 3. In 10 s the total charge that flows through the bulb is 30 C and through the battery 5 C. 4. In 10 s the total charge that flows through the bulb is 30 C and through the battery 30 C. 5. In 10 s the total charge that flows through the bulb is 30 C and through the battery 50 C. – Typeset by FoilTEX – 118 Question 102 A bulb is connected to a battery as illustrated. 5V 3A In 2 s a total of 6 C moves from the positive to negative terminal of the battery. Which of the following is true? 1. The energy lost by this charge is 0 J. 2. The energy lost by this charge is 3 J. The current and potential difference across the battery are indicated. The wires offer negligible resistance. 3. The energy lost by this charge is 5 J. 4. The energy lost by this charge is 6 J. 5. The energy lost by this charge is 30 J. – Typeset by FoilTEX – 119 Question 103 A bulb is connected to a battery as illustrated. 6V 3Ω Which of the following represents the power produced by the bulb? 1. 0 W 2. 0.5 W 3. 2 W The wires offer negligible resistance. 4. 6 W 5. 12 W – Typeset by FoilTEX – 120 Question 104 Two resistors are connected to a battery. Which of the following is true? 1. I1 = I2. R1 = 10 Ω 15 V R2 = 5 Ω 2. I1 is larger than I2. 3. I1 is smaller than I2 . Let I1 and I2 denote the current through resistors 1 and 2 respectively. Similarly V1 and V2 denote the potential differences across resistors 1 and 2 respectively. – Typeset by FoilTEX – 121 Question 105 Two resistors are connected to a battery. Which of the following is true? 1. V1 = V2 = 15 V. R1 = 10 Ω 2. V1 = V2 = 7.5 V. R2 = 5 Ω 3. V1 = V2 but both are some other value than the previous options. 15 V 4. V1 is larger than V2 . Let V1 and V2 denote the electric potential differences across resistors 1 and 2 respectively. – Typeset by FoilTEX – 5. V1 is smaller than V2 . 122 Question 106 Two identical resistors are connected to a battery. b b b a 5Ω c 10 V b b e b 5Ω – Typeset by FoilTEX – d Which of the following concerning voltages is correct? 1. ∆Ve→a = 10 V ∆Vb→c = 5 V 2. ∆Ve→a = 10 V ∆Vb→c = −5 V 3. ∆Ve→a = −10 V ∆Vb→c = −5 V 4. ∆Ve→a = −10 V ∆Vb→c = 5 V 5. None of the above/not enough info. 123 Question 107 Consider the following circuit. R1 = 5 Ω 10 V R2 = 15 Ω – Typeset by FoilTEX – Which of the following best represents the potential difference across each of the resistors? 1. ∆V1 = 1 3 ∆V2 2. ∆V1 = 1 2 ∆V2 3. ∆V1 = ∆V2 4. ∆V1 = 3∆V2 5. Not enough info/none of the above. 124 Question 108 Several identical bulbs are connected in a circuit as illustrated. Which of the following is true? 1. A is brighter than E. A 2. A is dimmer than E. B D 3. A and E have the same brightness. C E The relative brightnesses of these bulbs depend only on the relative currents which flow through them. – Typeset by FoilTEX – 125 Question 109 Several identical bulbs are connected in a circuit as illustrated. A D Which of the following statements about brightness is true (choose one)? 1. A > B > C B 2. A < B < C C 3. A > B = C E 4. A < B = C 5. A = B = C The relative brightnesses of these bulbs depend only on the relative currents which flow through them. – Typeset by FoilTEX – 126 Question 110 Several identical bulbs are connected in a circuit as illustrated. A D Which of the following statements about brightness is true (choose one)? 1. A > B > D B 2. A > D > B C 3. A > B = D E 4. A = D > B 5. A = B = D The relative brightnesses of these bulbs depend only on the relative currents which flow through them. – Typeset by FoilTEX – 127 Question 111 Consider the following circuit, R1 = 5 Ω and R1 = 10 Ω. ∆V R1 where Let ∆V1 be the potential difference across R1 and ∆V2 be the potential difference across R2 . How are these related? (Hint: Consider energy between points on the circuit). R2 1. ∆V1 = ∆V2 2. ∆V1 = 2∆V2 3. ∆V1 = – Typeset by FoilTEX – 1 2 ∆V2 128 Question 112 Consider the following R1 = R2 = R3 . circuit, where Consider the current through resistor 3 when the switch is open versus when it is closed. 1. Iclosed = 2 3 Iopen 2. Iclosed = Iopen ∆V – Typeset by FoilTEX – R1 R2 R3 3. Iclosed = 3 2 Iopen 129 Question 113 Consider the following circuit, R1 = R2 = 10 Ω, R3 = 20 Ω. where Which of the following is true of the equivalent resistance of the entire combination? 1. Req > 40 Ω ∆V R1 R2 R3 2. 40 Ω > Req > 20 Ω 3. 20 Ω > Req > 10 Ω 4. 10 Ω > Req > 5 Ω 5. 5 Ω > Req – Typeset by FoilTEX – 130 Question 114 Consider the following circuit, where R1 = 10 Ω, R2 = 6 Ω, R2 = 12 Ω and ∆V = 7 V. The current through the battery is 0.5 A. Which of the following is true? 1. ∆V2 = 7 V R1 2. ∆V2 = 5 V ∆V R2 R3 3. ∆V2 = 3.5 V 4. ∆V2 = 2 V – Typeset by FoilTEX – 131 Question 115 Consider the following circuit. R1 Suppose that resistor 4 is removed from the circuit. Which of the following happens to the current through the battery? R2 1. The current through the battery increases. ∆V 2. The current through the battery decreases. R3 – Typeset by FoilTEX – R4 3. The current through the battery does not change. 132 Question 116 A parallel plate capacitor is connected to a battery. The distance between the plates is increased. Which of the following is true? 1. The charge on the capacitor decreases. Initial ∆V – Typeset by FoilTEX – Final ∆V 2. The charge on the capacitor increases. 3. The charge on the capacitor stays the same. 133 Question 117 A parallel plate capacitor is connected to a battery and allowed to charge. The capacitor is then disconnected, without any charge leaking from the capacitor, and the distance between the plates is doubled. Initial Final Which of the following is true regarding the potential difference across the plates? 1. ∆Vafter = 4∆Vbefore 2. ∆Vafter = 2∆Vbefore 3. ∆Vafter = ∆Vbefore ∆V – Typeset by FoilTEX – 4. ∆Vafter = 1 ∆Vbefore 2 5. ∆Vafter = 1 ∆Vbefore 4 134 Question 118 Two capacitors are connected in parallel as illustrated. Suppose that C1 6= C2. Which of the following is true? 1. ∆V1 = ∆V2 and q1 = q2 C1 C2 2. ∆V1 = ∆V2 and q1 6= q2 3. ∆V1 6= ∆V2 and q1 = q2 Let ∆V1 and q1 be the potential difference across and the charge on capacitor 1. Let ∆V2 and q2 be the potential difference across and the charge on capacitor 2. – Typeset by FoilTEX – 4. ∆V1 6= ∆V2 and q1 6= q2 135 Question 119 A parallel plate capacitor is connected to a battery which provides a potential difference of 10 V. The capacitor is allowed to charge and the then the battery is disconnected. After this, the plates of the capacitor are pulled apart. Which of the following are true of the energy stored in the capacitor during this process? 1. The energy increases. 2. The energy decreases. 3. The energy stays constant. 4. Not enough information to answer. – Typeset by FoilTEX – 136 Question 120 A parallel plate capacitor is connected to a battery which provides a potential difference of 10 V. There is a dielectric between the capacitor plates. The capacitor is allowed to charge and the then the battery is disconnected. After this, the dielectric is removed. Which of the following are true of the energy stored in the capacitor during this process? 1. The energy increases. 2. The energy decreases. 3. The energy stays constant. 4. Not enough information to answer. – Typeset by FoilTEX – 137 Warm Up Question 15 A battery can succeed in pushing positive charges around a circuit. As described on page 718, these charges move through a wire from the positive terminal (at higher V) to the negative terminal (at lower V). Consider one of these charges as it completes a circuit. As the charge moves through the wire, does its electric potential energy increase, decrease or stay constant? As the charge moves through battery from the negative to positive terminal, does its electric potential energy increase, decrease or stay constant? 1. Constant in wire, increase in battery. The V is the same throughout the wire but increases from positive to negative in the battery. 2. Constant in the wire since the charges move at a constant rate. Increasing teh the battery. 3. Stays constant since the V produced by the battery stays constant. 4. Decrease in wire, increase in battery. If positive charge flows from positive to negative in wire then ∆V is negative and q∆V is negative. – Typeset by FoilTEX – 138 Warm Up Question 16 One wire is made from copper and the other from tungsten, whose resistivity is larger. Suppose that the wires have the same length. It is claimed that the resistance of the tungsten wire is larger because its resistivity is higher. Is this claim true or not? Explain your answer. 1. True. Higher resistivity implies higher resistance in all cases. 2. True. Higher resistivity and identical lengths gives higher resistance. 3. Not necessarily. The areas could be different. If tungsten had a larger area it could have a lower resistance. – Typeset by FoilTEX – 139 Warm Up Question 17 A conventional light bulb operates by passing current through a narrow strand of tungsten wire. This causes the tungsten’s temperature to rise, eventually becoming hot enough to glow. The resistivity of tungsten changes as its temperature increases (there is a table which indicates this in the text). Suppose that such a bulb is connected to a power source which provides a constant voltage. What will happen to the current as time passes (increase, decrease or stay constant)? Explain your answer. 1. Decrease. As tungsten heats up it resists more or it gets harder to push charges through the tungsten. 2. Decrease. The potential provided by the battery drops. 3. Decrease. The current will initially flow but eventually the entire circuit will be charged and current will stop. 4. Increase. The resistivity decreases, so resistance decreases and current increases. 5. Stay constant. Whatever current enters the bulb must leave the bulb too. – Typeset by FoilTEX – 140 Magnetic Fields and Forces – Typeset by FoilTEX – 141 Question 121 Which of the following correctly illustrates the magnetic field in the vicinity of the north pole of a bar magnet? Case 1 Case 3 Case 2 Case 4 – Typeset by FoilTEX – 142 Question 122 Two current carrying wires point out of the page as illustrated. The currents are equal in magnitude but flow in opposite directions. Which of the following best indicates the direction of the magnetic field at the midpoint? ↑ 2. ↓ 3. ← 4. → 1. × b b 5. Magnitude is zero ⇒ no direction. – Typeset by FoilTEX – 143 Question 123 In two separate scenarios, three current carrying wires point out of the page as illustrated. The currents are equal in magnitude. Which of the following is true? 1. The magnetic field at A is larger than at B. 2. The magnetic field at A is smaller than at B. b × × b – Typeset by FoilTEX – B × 3. The magnetic field at A is the same as B. A × b b 144 Question 124 Three current carrying wires point out of the page as illustrated. The currents are equal in magnitude. Which of the following is true? 1. The magnetic field at A is larger than at B. 2. The magnetic field at A is smaller than at B. × A × – Typeset by FoilTEX – b B × b 3. The magnetic field at A is the same as B. 145 Question 125 Two current-carrying wires are arranged as illustrated. Which of the following is true regarding the net direction of the magnetic field at the location midway between the wires? 1. Definitely into the board/page. I1 I2 2. Definitely out of the board/page. 3. Either into or out of the board/page. 4. Clockwise. 5. Counter clockwise. – Typeset by FoilTEX – 146 Question 126 Two current-carrying wires are arranged as illustrated. The loop is situated at a specific location so that the net magnetic field is zero. Suppose that the loop is moved to another location further away from the wire. Which of the following is true regarding the net direction of the magnetic field? 1. Into the board/page. I1 I2 2. Out of the board/page. 3. It remains zero. 4. Clockwise. 5. Counter clockwise. – Typeset by FoilTEX – 147 Question 127 Two current-carrying wires are placed near each other. The straight wire is infinitely long. The currents are such that the net magnetic field at the center of the loop is zero. What is the direction of the current in the circular wire? 1. Clockwise 2. Counter-clockwise 3. Current is zero. I – Typeset by FoilTEX – 148 Question 128 A solenoid carries current and is placed next to a bar magnet. When viewed from its right end, the current circulates as illustrated. N S Which of the following is true regarding the force exerted by the solenoid on the magnet? 1. Left 2. Right 3. Up Right end 4. Down 5. No force. – Typeset by FoilTEX – 149 Question 129 Two infinitely long solenoids each carry the same current. Each has the same length and the same number of coils. The radius of the outer solenoid is double that of the inner solenoid. One solenoid is inside the other. When viewed end-on, they appear as illustrated. Which of the following is true? 1. The magnetic field inside the inner solenoid is the same as that between the two solenoids and is non-zero. 2. The magnetic field inside both solenoids is zero. 3. The magnetic field inside the inner solenoid is zero and that between the two solenoids is non-zero. 4. The magnetic field inside the inner solenoid is non-zero and that between the two solenoids is zero. – Typeset by FoilTEX – 150 Question 130 Identical positively charged particles move through identical magnetic fields with identical speeds, in directions indicated by black vectors, as illustrated. Case A Case B Case C Ranking the cases in order of magnitude of magnetic force, which is correct? 1. B > A = C 2. C > B > A 3. B > A > C ~ B + + + 4. C > A > B 5. A > C > B – Typeset by FoilTEX – 151 Question 131 Identical positively charged particles move through identical magnetic fields with identical speeds, in directions indicated by black vectors, as illustrated. Case A Case B Case C Ranking the cases in order of magnitude of magnetic force, which is correct? 1. B > A = C 2. C > B > A 3. B > A > C + + + 4. C > A > B 5. A > C > B ~ B – Typeset by FoilTEX – 152 Question 132 A negatively charged particle moves vertically down at the instant that a magnetic field is turned on. The relative directions are indicated below. Determine the direction of the force exerted by the magnetic field on the charged particle. 1. 2. 3. − ~ B → ← ↓ 4. Into the screen/board. 5. Out of the screen/board. – Typeset by FoilTEX – 153 Question 133 A positively charged particle, whose mass is not zero, moves horizontally at one moment as illustrated. + An experimenter attempts to provide an external magnetic field which will prevent the particle from falling under the influence of the earth’s gravity. What must the direction of this field be? 1. 2. 3. → ↑ ↓ 4. Into the screen/board. 5. Out of the screen/board. – Typeset by FoilTEX – 154 Question 134 A negatively charged particle (with charge −8 C) moves as illustrated at the instant that a magnetic field is turned on. The particle is moving at an angle of 70◦ above the horizontal and the magnetic field is vertical. Which of the following is the magnitude of the force exerted by the magnetic field on the particle? 1. F = 8vB sin (20◦) 2. F = 8vB sin (70◦) ~ B − – Typeset by FoilTEX – 3. F = −8vB sin (20◦) 4. F = −8vB sin (70◦) 5. F = 8vB cos (20◦) 155 Question 135 An alpha particle (two protons and two neutrons) is fired into the gap between two closely spaced magnets as illustrated. ← 2. → b N – Typeset by FoilTEX – Which of the following best represents the direction of the force exerted by the magnets on the alpha particle while it is between them? 1. S 3. Into the board 4. Out of the board 156 Question 136 Two charged particles each move with constant speed in a region containing a uniform and constant magnetic field. Their trajectories when viewed from above are as illustrated. Which is true regarding the charges of the particles? 1. Both are positive. ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 2. Both are negative. ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ A B ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 3. They are opposite but one cannot say which is positive. ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 4. A is positive, B is negative. ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ~ B ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 5. B is positive, A is negative. – Typeset by FoilTEX – 157 Question 137 Two positively charged particles each move with constant speed in a region in which a constant magnetic field points directly out of the board/screen. Their trajectories are indicated below. b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b 1. mA = mB b b b b b b b b b b b b b b 3. mA > mB 4. None of the above/not enough info. A – Typeset by FoilTEX – relationship 2. mA < mB b B Which best describes the between the particle masses? 158 Question 138 A charged particle is fired into a region in which there is a uniform but time varying magnetic field. That is, at any instant the magnetic field is the same at all points but as time passes the magnetic field vectors all change in the same way. The particle is fired into the field perpendicular to the field. The direction of the field remains constant but its strength increases as time passes. Which of the following is true as time passes? 1. The particle moves with constant speed in a circle. 2. The particle moves with constant speed in a spiral of decreasing radius. 3. The particle moves with constant speed in a spiral of increasing radius. 4. The particle moves with increasing speed in a circle. 5. The particle moves with increasing speed in a spiral of decreasing radius. – Typeset by FoilTEX – 159 Question 139 A wire carries a current, consisting of moving electrons. The positive nuclei in the wire remain stationary. The wire is placed into a ~ , pointing out of the screen. magnetic field, B b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b + b b b + b b b + b b b + b b b b b + b b b + b b b b b + b b b + b b b b b b + b b b b b b ~ exerts a force on the positive charges 3. B and a force on the negative charges. The force on the negative charges is larger since they are smaller. b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b ~ B ~ exerts no force on the wire since the 1. B net charge of the wire is zero. ~ exerts a force on the positive charges 2. B and a force on the negative charges and these cancel. + b b Which of the following is true? ~ exerts a force on the negative charges 4. B but no force on the positive charges. ~ exerts a force on the positive charges 5. B but no force on the negative charges. – Typeset by FoilTEX – 160 Question 140 A current flows through wire in the indicated direction. The wire is placed in the indicated magnetic field. Which of the following describes the direction of the force exerted on the wire? ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 1. ↑ if the charges are positive and ↓ if the charges are negative, ⊗ ⊗ ⊗ ⊗I ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ b b b b b b b b b b b ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 2. ↑ if the charges are positive and ↑ if the charges are negative, 3. ↓ if the charges are positive and ↑ if the charges are negative, 4. ↓ if the charges are positive and ↓ if the charges are negative, or 5. Not enough info/none of the above. – Typeset by FoilTEX – 161 Question 141 Wires of different lengths carrying the same currents are placed in identical magnetic fields. Which of the following is true regarding the magnitudes of the magnetic forces exerted on the wires? Case B ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 1. FA = FB , ⊗ ⊗ ⊗ ⊗I ⊗ ⊗ ⊗ 2. FA < FB , or 3. FA > FB . ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ Case A ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗I ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ – Typeset by FoilTEX – 162 Question 142 An non-magnetic axle with two wheels is free to roll along two rails. The rails are connected to a battery and this is illustrated from above. The north pole of a magnet is held above the axle. The axle is initially at rest and is then released. Which of the following is true after the wheel is released? 1. It remains stationary. 2. It lifts off the rails. Battery + − 3. It rolls left. 4. It rolls right. 5. It slides down to the lower rail. – Typeset by FoilTEX – 163 Question 143 A circular loop carries a uniform current. Another long straight wire lies along the axis of the loop and this also carries a current. View along the line of the straight wire, the currents are as illustrated. Which of the following represents the force exerted by the straight wire on the loop? 1. The force is zero. 2. The force is counterclockwise. 3. The force is clockwise. × I1 I2 4. The force is out of the page/screen. 5. The force is into of the page/screen. – Typeset by FoilTEX – 164 Question 144 A rectangular loop is placed into the indicated magnetic field. ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ~ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗B ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ – Typeset by FoilTEX – Which (choose one) of the following is true? 1. There is a net force on the loop. 2. There is a net torque on the loop. 3. There is a net force and a net torque on the loop. 4. There is neither a net force nor a net torque on the loop. 165 Question 145 A rectangular loop is placed into the indicated magnetic field. Which (choose one) of the following is true? 1. The entire loop moves out of the screen. 2. The entire loop moves into of the screen. ~ B 3. The loop rotates with its center fixed. 4. The loop rotates and its center moves out of the screen. 5. The loop rotates and its center moves into the screen. – Typeset by FoilTEX – 166 Question 146 Two current-carrying wires are placed near each other. The vertical wire is infinitely long. Which of the following best represents the direction of the force exerted by the vertical wire on the horizontal wire? → 2. ← 3. ↑ 4. ↓ 1. ID IC 5. Out of the page/board. – Typeset by FoilTEX – 167 Question 147 Three wires each carry currents of identical magnitudes. The distance between adjacent wires are equal. Rank the wires in order of the magnitudes of the net magnetic force on each. 1. FA = FB 2. FA > FB = 0 3. FA > FB 6= 0 4. FB > FA = 0 A – Typeset by FoilTEX – B C 5. FB > FA 6= 0 168 Question 148 Three wires, each perpendicular to the board, carry currents of identical magnitudes. The distance between adjacent wires are equal. A B b b C × Rank the wires in order of the magnitudes of the net magnetic force on each. 1. FA = FB = FC 2. FA = FC > FB = 0 3. FC = FA > FB = 0 4. FB > FC = FA 5. FB > FC > FA – Typeset by FoilTEX – 169 Question 149 Various current carrying loops are placed in a magnetic field as illustrated. Loop A Loop B Rank the loops in order of increasing torque exerted by the magnetic field. Loop C The currents through the loops are: 1. A=B<C 2. A<B<C 3. C =A<B 4. C <A<B 5. B<C<A 6. Not enough info/none of the above. IA = 25 A IB = 25 A IC = 10 A – Typeset by FoilTEX – 170 Question 150 A loop is placed in a region of uniform magnetic field as illustrated. The left edge of the loop can slide, maintaining contact with the rest of the loop. At the instant depicted in the illustration the left edge is dragged (by hand) to the left. Which of the following is true about the current in the loop: ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 1. Counter-clockwise ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 2. Clockwise ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 3. Zero 4. None of the above/not enough info. ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ – Typeset by FoilTEX – 171 Question 151 A loop is placed in a region of uniform magnetic field as illustrated. The left edge of the loop can slide, maintaining contact with the rest of the loop. At the instant depicted in the illustration the left edge slides to the left. Which of the following is true about the current in the loop: 1. Counter-clockwise current. ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 2. Clockwise current. ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 3. Zero current. ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 4. None of the above/not enough info. ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ – Typeset by FoilTEX – 172 Question 152 A loop passes through a region of constant magnetic field at a constant speed as illustrated. At the instant depicted in the illustration the current in the loop is: 1. Counter-clockwise ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 2. Clockwise ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 3. Zero ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 4. None of the above/not enough info. ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ – Typeset by FoilTEX – 173 Question 153 A loop passes through a region of constant magnetic field at a constant speed as illustrated. At the instant depicted in the illustration the current in the loop is: 1. Counter-clockwise ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 2. Clockwise ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 3. Zero ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 4. None of the above/not enough info. ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ – Typeset by FoilTEX – 174 Question 154 A loop passes through a region of constant magnetic field at a constant speed as illustrated. At the instant depicted in the illustration the current in the loop is: 1. Counter-clockwise ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 2. Clockwise ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 3. Zero ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 4. None of the above/not enough info. ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ – Typeset by FoilTEX – 175 Question 155 A rail/rod loop is placed in a magnetic field. The diagram shows a view of this from above. The gray rod is initially at rest and is given a sharp kick directly right. The rail arrangement has a non-zero resistance. Which of the following is true? 1. The rod continues to move to the right at a constant speed. 2. The rod moves to the right with a decreasing speed. ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ 3. The rod moves to the right with an increasing speed. 4. The rod moves right, slows down, reverses direction and moves left. ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ – Typeset by FoilTEX – 176 Question 156 A loop is stationary in a region of uniform magnetic field as illustrated. The field strength decreases at a steady rate. While the field decreases, the current in the loop is: 1. Counter-clockwise ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 2. Clockwise ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 3. Zero ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 4. None of the above/not enough info. ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ – Typeset by FoilTEX – 177 Question 157 Several loops are placed in a uniform magnetic field (restricted to shaded region) as illustrated. Which of the following represents the rank of the fluxes through the loop? Loop A Loop B Loop C ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 1. ΦA = ΦB = ΦC ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 2. ΦA < ΦB < ΦC ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 3. ΦA < ΦC < ΦB ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 4. ΦC < ΦA < ΦB ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 5. ΦC = ΦA < ΦB ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ – Typeset by FoilTEX – 178 Question 158 A magnetic field is as illustrated. A square coil is situated so that only one side is visible from this perspective. Which of the following is the correct expression for the flux through the loop? 1. Φ = BA 2. Φ = BA cos 10◦ 3. Φ = BA cos 20◦ ◦ 110 ~ B 4. Φ = BA cos 110◦ 5. Φ = BA cos 120◦ 10◦ – Typeset by FoilTEX – 179 Question 159 A magnet is pulled away from a loop in the indicated direction. N S Which of the following is true as the magnet moves away from the loop? 1. The current in the loop counterclockwise (viewed from right). is 2. The current in the loop is clockwise (viewed from right). 3. There is no current in the loop. – Typeset by FoilTEX – 180 Question 160 A magnet is pushed toward a loop in the indicated direction. N S Which of the following is true as the magnet approaches the loop? 1. The current in the loop counterclockwise (viewed from right). is 2. The current in the loop is clockwise (viewed from right). 3. There is no current in the loop. – Typeset by FoilTEX – 181 Question 161 A magnet is pushed through a loop in the indicated direction. N S Which of the following is true immediately after the north pole of the magnet passes through the loop? 1. The current in the loop counterclockwise (viewed from right). is 2. The current in the loop is clockwise (viewed from right). 3. There is no current in the loop. – Typeset by FoilTEX – 182 Question 162 A magnet is pushed toward a loop in the indicated direction. N S Which of the following is true regarding the force exerted by the loop on the magnet as the magnet approaches the loop? 1. The loop exerts a force to the left. 2. The loop exerts a force to the right. 3. The loop exerts no force. 4. The loop exerts a force up. 5. The loop exerts a force down. – Typeset by FoilTEX – 183 Question 163 A magnet is pushed through a loop in the indicated direction. N S Which of the following is true immediately after the north pole of the magnet passes through the loop? 1. The loop exerts a force to the left. 2. The loop exerts a force to the right. 3. The loop exerts no force. 4. The loop exerts a force up. 5. The loop exerts a force down. – Typeset by FoilTEX – 184 Question 164 A circular loop of wire is such that it can be made to expand and contract. The loop is placed in a uniform magnetic field. The initial configuration of the loop is indicated by a dashed line; the final by a solid line. Which of the following is true while the loop expands? 1. There is no current in the loop. 2. There is a clockwise current in the loop. ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ 3. There is a counter-clockwise current in the loop. ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ – Typeset by FoilTEX – 185 Question 165 A loop is placed in an external magnetic field. The flux through the loop as time passes is plotted below. Which of the following is true regarding the magnitude of the induced EMF, E ? 1. E is largest from 0 s to 2 s 2. E is largest from 2 s to 5 s Φ in Wb 3. E is largest from 5 s to 7 s 10 5 1 2 3 −5 4 5 6 7 t in s 4. E is larger at 3 s than 4 s 5. E is larger at 4 s than 3 s −10 – Typeset by FoilTEX – 186 Question 166 A loop rotates in a uniform magnetic field with orientations as described in class. The axle of the loop is perpendicular to the magnetic field. Zog claims that: “If the speed with which the loop rotates increases steadily then the current through the loop stays constant, since the magnetic field and the area of the loop are constant.” Is this: 1. Definitely true. 2. Definitely false. 3. Possibly/partly true. 4. Possibly/partly false. – Typeset by FoilTEX – 187 Question 167 Two circular loops are initially placed perpendicular to the same magnetic field. The area of loop B is twice that of loop A. Each loop is rotated through 90◦ . The time taken to rotate loop B is twice that of loop A. ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ Initial Final ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ Loop A ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ❀ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ Initial Final ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ Which of the following is true regarding the (magnitudes of the) induced EMFs? 1. EA = EB = 0 2. EA = EB 6= 0 3. EA = 2EB 4. EA = 4EB 5. EA = 1 EB 2 ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ Loop B ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ❀ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ – Typeset by FoilTEX – 188 Warm Up Question 18 The configuration of a solenoid is described on page 788. Two long solenoids are constructed using the same type of wire. They each have the same length and the number of turns of the wire is the same along their lengths. However, solenoid A has double the diameter of solenoid B. How does the magnetic field inside A compare to that inside B (same, smaller, larger, twice as large, half as large, etc.,...)? Explain your answer. 1. A smaller than B. The current is distributed over a larger region in A and the field is more concentrated in B. 2. A larger than B. There is greater volume available for the magnetic field in A. 3. Same. The equation to calculate the magnetic field does not include area in the equation: B = µ0 I N L , so area does not matter and they will be the same. 4. Same. It is zero everywhere inside in each case. – Typeset by FoilTEX – 189 Warm Up Question 19 A proton is fired toward a current-carrying solenoid and it enters the solenoid traveling in a direction down the axis of the solenoid. Will the solenoid exert a force on the proton? Explain your answer. 1. Yes. A magnetic field always exerts a force on a moving charged particle. 2. Yes. The angle between the magnetic field and the velocity is 90◦ so there will be a force. 3. No. The solenoid exerts no force on the proton since the proton is moving down the axis of the solenoid and therefore is parallel to the magnetic field within the solenoid so there is no force. 4. No. There is no magnetic field inside a solenoid and there will be no force. 5. No. The field is uniform and so there cannot be any force. – Typeset by FoilTEX – 190 Warm Up Question 20 The cords that connect a household appliance to the mains outlet consist of two strands of wire that run parallel to each other. At any instant the current in one strand is opposite to that in the other strand. Describe the direction of the force exerted by one strand on the other. In household circuits, the currents in the strands simultaneously reverse direction many times every second. Do the wires still exert forces in the same directions in this circumstance? Explain your answer. 1. No forces. Magnetic fields do not exert forces on parallel moving charges. 2. Attractive since currents are opposite. Still attractive when reversed. 3. Repel since the currents are opposite. Still repel when reversed since currents are still opposite. 4. Repel since the currents are opposite. Forces reverse when currents are reversed. – Typeset by FoilTEX – 191 Warm Up Question 21 Consider the left loop in Fig 24.43 (pg 798) and suppose that the current flows as indicated. Suppose that the right loop has been removed and bar magnet is placed to the left of the left loop. The south pole of the bar magnet is closest to the left side of the left loop. Will it exert a force on the loop and, if so, what is the direction of the force? Explain your answer. 1. Yes. It will exert a force attracting the loop toward the bar magnet. If the current is flowing up on the side closest to us, then the magnetic field is will be flowing to the left. Therefore the south end will be or the right and the north end will be on the left closest to the south end of the bar magnet. 2. Yes. The left side of the loop will be the south end and the right side the north end. So the magnet will repel. 3. Yes. The magnet will exert a force on the current and the force will repel the current loop because magnets repel currents. 4. No force. – Typeset by FoilTEX – 192 Warm Up Question 22 A square loop of wire is held in such a way that the Earth’s magnetic field is perpendicular to the plane of the loop. The loop is held stationary relative to the Earth and the Earth’s field does not change. Two claims are made: 1) There is a non-zero flux through the loop and 2) as a result of this there is a current through the loop. Are these claims true or not? Explain your answers. 1. 1) No 2) No. The magnetic field is not changing and so there is no flux. Since there is no flux, there is no induced current. 2. 1) No 2) No. The angle is 0◦ and so the flux is zero. So there is no induced current. 3. 1) Yes 2) No. The flux through the loop is non-zero because the loop is perpendicular to the Earths magnetic field so the flux is at its greatest. There is no current through the loop however because the flux is not changing. 4. 1) Yes 2) Yes. The angle between the plane of loop and field is 90◦. Thus the flux is non-zero. A non-zero flux also implies that there is current flowing through the loop. – Typeset by FoilTEX – 193 Warm Up Question 23 A loop is held near a long straight wire as illustrated in Fig 25.17 on page 825 except that the loop is held stationary. The current in the straight wire is made to decrease gradually. Will there be a current in the loop and if so what will the direction of the current be? Explain your answer. 1. No. Because they are stationary the wire will not induce a current in the loop. 2. Yes. When the current in the straight wire decreases, the flux from the loop will decrease also. To oppose the change in the flux, this would lead to a clockwise current being induced. 3. Yes. When the current in the straight wire decreases, the flux from the loop will decrease also. To oppose the change in the flux, this would lead to a counter-clockwise current being induced. – Typeset by FoilTEX – 194 Electromagnetic Waves – Typeset by FoilTEX – 195 Question 168 The following diagrams show snapshots of electromagnetic waves. Red represents the electric field and blue the magnetic field. In which directions propagating? are the waves 1. A in +x, B in +x y 2. A in +x, B in −x Case A 3. A in −x, B in +x x 4. A in −y , B in +y 5. A in +y , B in −y y Case B x – Typeset by FoilTEX – 196 Question 169 The electric field for various electromagnetic waves at one instant is indicated. Ey Rank the waves in order of wavelength. 1. A = B = C Case A 2. A = B < C x Ey 3. A = B > C 4. A < B = C Case B 5. A < B < C x Ey Case C x – Typeset by FoilTEX – 197 Question 170 The electric field for two electromagnetic waves at one instant is indicated. These wave patterns travel to the right with the same speed. Ey Which of the following is true regarding the number of times the electric field at one position along the x axis oscillates? 1. The number of oscillations per second for A is the same as that for B. Case A x 2. The number of oscillations per second for A is half that for B. 3. The number of oscillations per second for A is twice that for B. Ey Case B 4. None of the above/not enough info. x – Typeset by FoilTEX – 198 Question 171 The electric field for an electromagnetic wave at one instant is illustrated. Ez Which of the following best represents the wavenumber? 1. k = 30 x 10 20 – Typeset by FoilTEX – 30 40 50 60 2. k = 40 2π 3. k = 20 4. k = 2π 30 5. k = 2π 40 199 Question 172 A beam of light has a circular cross section. The beam passes through a polarizing filter and the transmitted light has an electromagnetic wave whose electric field vector at each location oscillates up and down along the z axis. The transmitted light beam strikes a screen. Which of the following is true? 1. The light travels along the z axis. 2. The light travels along an axis perpendicular to the z axis and produces a circular spot on the screen. 3. The light travels along an axis perpendicular to the z axis and produces a streak (along z ) on the screen. 4. The light travels along an axis perpendicular to the z axis and produces a streak (perpendicular to z ) on the screen. – Typeset by FoilTEX – 200 Question 173 Unpolarized light of intensity Iincident is incident on a polarizer (labeled A) whose transmission axis is oriented vertically. Subsequently this light passes through a polarizer (labeled B) whose transmission axis is oriented horizontally. Which of the following represents the intensity of the light transmitted by B? 1. 0 2. 1 Iincident 4 3. 1 Iincident 2 1 4. √ Iincident 2 – Typeset by FoilTEX – 201 Question 174 Unpolarized light, whose intensity is Iincident , is incident upon a linear polarizer, whose axis of transmission is oriented horizontally. A second polarizer has transmission axis oriented vertically. Which of the following represents the intensity of the light transmitted by the final polarizer? 1. 0 2. 1 Iincident 4 3. 1 Iincident 2 1 4. √ Iincident 2 – Typeset by FoilTEX – 202 Question 175 Unpolarized light of intensity Iincident is incident on a polarizer (labeled A) whose transmission axis is oriented vertically. Subsequently this light passes through a polarizer (labeled B) whose transmission axis is oriented vertically. Which of the following represents the intensity of the light transmitted by B? 1. 0 2. 1 Iincident 4 3. 1 Iincident 2 1 4. √ Iincident 2 – Typeset by FoilTEX – 203 Question 176 Unpolarized light of intensity Iincident is incident on a polarizer (labeled A) whose transmission axis is oriented vertically. Subsequently this light passes through a polarizer (labeled B) whose transmission axis is oriented midway between horizontal and vertical. Which of the following represents the intensity of the light transmitted by B? 1. 0 2. 1 Iincident 4 3. 1 Iincident 2 1 4. √ Iincident 2 – Typeset by FoilTEX – 204 Question 177 Polarized light, whose axis of polarization is at an angle of 45◦ between the horizontal and vertical is incident upon a linear polarizer, whose axis of transmission is oriented horizontally. A second polarizer has transmission axis at an angle of 45◦ degrees above the horizontal and a third has transmission axis oriented vertically. The middle polarizer is removed. What does this do to the intensity of the light after the final polarizer? 1. Reduces the intensity. 2. Increases the intensity. 3. Intensity stays the same. – Typeset by FoilTEX – 205 Question 178 Unpolarized light is incident upon a linear polarizer, whose axis of transmission is oriented horizontally. A second polarizer has transmission axis at an angle of 45◦ degrees above the horizontal and a third has transmission axis oriented vertically. The middle polarizer is removed. What does this do to the intensity of the light after the final polarizer? 1. Reduces the intensity. 2. Increases the intensity. 3. Intensity stays the same. – Typeset by FoilTEX – 206 Question 179 A spherical wave propagates outwards in empty space. Two spherical “windows” at which the wave is observed at one instant are shown. 1. IA = IB since the energy passing through the window at A is the same as that passing through B. 2. IA < IB since the energy passing through the window at A is the same as that passing through B. Location A 3. IA > IB since the energy passing through the window at A is the same as that passing through B. 4. IA > IB since energy is lost between A and B. Location B – Typeset by FoilTEX – 207 Warm Up Question 24 A pair of sunglasses is designed so that the polarization axis is vertical when worn by someone who stands upright. The person lies down on a bench on his side with one side of his head against the bench (i.e. one ear against the bench). Will these sunglasses eliminate the glare from a horizontal reflecting surface? Explain your answer. 1. Yes. The wave is still travels perpendicular to the sunglasses and so it will still be blocked. 2. Yes. The axis of polarization is still vertical and so the glare will still be blocked. 3. No. When turned on the side the axis of polarization is now horizontal. This will allow horizontal waves to pass through and not eliminate the glare. – Typeset by FoilTEX – 208 Warm Up Question 25 Electromagnetic waves can be produced by forcing electrons in an antenna to oscillate. The strength of the waves that are produced depends on the length of the antenna and is largest when the length of the antenna is exactly a quarter wavelength (with all else the same). Using this information, determine whether antennas for radio waves are larger or smaller than those for microwaves. Explain your answer. 1. Radio antenna larger. Microwaves have a smaller wavelength inturn making the need for a smaller antena for the microwave in comparison to the radio waves. 2. Radio antenna larger. Radio waves travel further and so they must be larger and have a longer wavelength. 3. Radio antenna smaller. Larger antennas are not practical. 4. Radio antenna smaller. Radio waves are not as energetic as microwaves and they thus require smaller antennas. – Typeset by FoilTEX – 209 Warm Up Question 26 A laser produces a narrow beam of light. The diameter of the beam is noticeable. The beam is focused by a lens to a point whose diameter is much smaller than that of the beam. As the beam is focused to a point does the intensity of the beam increase, decrease or stay the same? Explain your answer in terms of energy and ignore the negligible losses of energy to the air and the lens. 1. Increases. I = P/A so if you put the same amount of power into a smaller area the I increases. 2. Decreases. The beam must be losing energy as it propagates since the distance traveled increases. 3. Same. Energy is conserved in this case. – Typeset by FoilTEX – 210 Electromagnetic Waves: Slides – Typeset by FoilTEX – 211 Electromagnetic Wave Propagation Along One Line Electromagnetic wave propagating along +x direction. Red indicates the electric field, blue the magnetic field. y x – Typeset by FoilTEX – 212 Electromagnetic Wave Propagation Along Several Directions Electromagnetic waves produced by charge oscillating up and down the y axis. Red indicates the electric field. y x – Typeset by FoilTEX – 213 Linearly Polarized Electromagnetic Waves Electromagnetic wave propagating along +x direction. Only the electric field is indicated. Horizontally Polarized x Vertically Polarized x – Typeset by FoilTEX – 214 More Linearly Polarized Electromagnetic Waves Electromagnetic wave propagating along +x direction. Only the electric field is indicated. x x – Typeset by FoilTEX – 215 Unpolarized Electromagnetic Waves Electromagnetic wave propagating along +x direction. Only the electric field is indicated. x – Typeset by FoilTEX – 216 Wave Optics – Typeset by FoilTEX – 217 Question 180 A beam of light propagates toward a screen. The beam and the envelope of the electric field are as illustrated. The screen is labeled with a vertical scale. E – Typeset by FoilTEX – 4 3 2 1 0 -1 -2 -3 -4 Which of the following is true regarding the appearance of the light at the screen? 1. A constant vertical stripe from −3 to 3. 2. A constant vertical stripe from 0 to 3. 3. A flickering vertical stripe from −3 to 3. 4. A constant vertical stripe from −1.5 to 1.5. 5. A spot in the vicinity of 0. 218 Question 181 Light passes from air (n = 1.00) into glass (n = 1.5). Which of the following most correctly represents the light wave in this case? Case 1 Air Case 2 Glass Air Glass Glass Case 3 – Typeset by FoilTEX – Air 219 Question 182 Two pulses approach each other on a string. At an initial instant the string is as illustrated and the pulses travel with speed 1 unit per second. Which of the following is an accurate depiction of the entire string at an instant 2 seconds later? Case 1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Case 2 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Case 3 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 – Typeset by FoilTEX – 220 Question 183 Two pulses approach each other on a string. At an initial instant the string is as illustrated and the pulses travel with speed 1 unit per second. Which of the following is an accurate depiction of the entire string at an instant 2 seconds later? Case 1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Case 2 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Case 3 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 – Typeset by FoilTEX – 221 Question 184 Two light waves propagate through different combinations of media as illustrated. Ez In vacuum Determine the index of refraction of the glass. 1. nglass = 0.5 2. nglass = 0.67 3. nglass = 1 Ez In glass and vacuum – Typeset by FoilTEX – 4. nglass = 1.5 5. nglass = 1.33 222 Question 185 Two light waves propagate through different combinations of media as illustrated. Ez The phase difference between the emerging waves is: In vacuum 1. 0 π 2. 2 3. π Ez In glass and vacuum 4. 3π 2 5. 2π – Typeset by FoilTEX – 223 Question 186 Two light waves propagate through different combinations of media as illustrated. Ez The phase difference between the emerging waves is: In vacuum 1. 0 π 2. 2 3. π Ez In glass and vacuum 4. 3π 2 5. 2π – Typeset by FoilTEX – 224 Question 187 Snapshots of two waves at t = 0 s in the same medium are illustrated. y1 Determine the phase difference between the waves. Wave 1 1. ∆φ = 0 π 4 π 3. ∆φ = 2 2. ∆φ = y2 Wave 2 4. ∆φ = π 5. ∆φ = – Typeset by FoilTEX – 3π 2 225 Question 188 Snapshots of two waves at t = 0 s in the same medium are illustrated. y1 Determine the phase difference between the waves. Wave 1 1. ∆φ = 0 π 4 π 3. ∆φ = 2 2. ∆φ = y2 Wave 2 4. ∆φ = π 5. ∆φ = – Typeset by FoilTEX – 3π 2 226 Question 189 Snapshots of two waves in the same medium are as illustrated. By how far is wave 2 shifted from wave 1? 1. 4λ Wave 1 2. 2λ 3. λ Wave 2 – Typeset by FoilTEX – 4. λ 2 5. λ 4 227 Question 190 Snapshots of two waves in the same medium are as illustrated. By how far is wave 2 shifted from wave 1? 1. 4λ Wave 1 2. 2λ 3. λ Wave 2 – Typeset by FoilTEX – 4. λ 2 5. λ 4 228 Question 191 Monochromatic light (of just one wavelength) is incident upon a double slit. Which of the following describes the intensity of the light at point P, which is located at the midpoint of the double-slit arrangement? 1. There is a dark spot, since the light is obstructed by the barrier. b P 2. There is a dark spot, since waves from the slits interfere destructively. 3. There is a bright spot, since waves from the slits interfere constructively. Light Barrier – Typeset by FoilTEX – 4. There is a spot of intermediate brightness. Screen 229 Question 192 Monochromatic light (of just one wavelength) is incident upon a double slit. The wavelength of the light increases. Which of the following describes what happens to the bright fringes? 1. Stay the same. 2. Spread out. 3. Squash together. 4. Stay in the same location but diminish in brightness. Light Barrier – Typeset by FoilTEX – 5. Stay in the same location but increase in brightness. Screen 230 Question 193 Monochromatic light (of just one wavelength) is incident upon a double slit. A piece of glass is placed in front of one slit. The glass absorbs negligible light and shifts the phase of the light passing through it by exactly one half wavelength. Which of the following describes what happens to the pattern? 1. The pattern disappears. 2. The bright spots are closer together. 3. The bright spots are further apart. Light Barrier 4. The bright interchanged. and dark spots are Screen 5. There are no changes. – Typeset by FoilTEX – 231 Question 194 Red light and blue light are incident upon double slits with the same slit spacing. The distance from the slits to the screen is the same for both. The wavelength of red light is larger than that for blue light. Which of the following is/are true? 1. In both cases there is a bright fringe at the center. 2. There is a bright fringe at the center only for the blue light. 3. The locations of the bright fringes are the same for red and blue. 4. Red fringes are further apart than blue. 5. Red fringes are closer together than blue. – Typeset by FoilTEX – 232 Question 195 White light is a combination of light waves of many different frequencies. The wavelengths of the light range from largest for red to smallest for blue. A beam of white light is incident upon a double-slit. Which of the following is true? 1. There is a white central bright fringe. 2. There is a bright blue fringe at the center. 3. There are only red fringes to the left of center and blue fringes to the right of center. 4. Outer bright fringes contain a range of color bands - red are further out than blue. 5. Outer bright fringes contain a range of color bands - blue are further out than red. – Typeset by FoilTEX – 233 Question 196 Red light of wavelength 632 nm is incident on a pair of narrow slits. A pattern of bright and dark fringes is observed on a screen placed beyond the slits. The separation between the slits is decreased. Which of the following describes the effect on the pattern on the screen? 1. Bright and dark fringes are interchanged. 2. Distances between adjacent dark fringes increase. 3. Distances between adjacent dark fringes decrease. 4. There is no change. – Typeset by FoilTEX – 234 Question 197 Consider four equally spaced slits and consider light waves that travel to one particular screen location. Suppose that the discrepancy in the distance traveled by the waves between adjacent slits is one wavelength. Which of the following is true regarding the difference in the distance traveled between the waves emanating from slit 1 and slit 4? 1. 2λ 2. 2.5λ 3. 3λ Slit 1 Slit 2 4. 3.5λ 5. 4λ Slit 3 Slit 4 Barrier – Typeset by FoilTEX – 235 Question 198 Consider four equally spaced slits and consider light waves that travel to one particular screen location. Suppose that the discrepancy in the distance traveled by the λ waves between adjacent slits is . 2 Slit 1 Slit 2 Slit 3 Which of the following is true? (Hint: consider combinations of various pairs of waves) 1. The waves interfere destructively ⇒ dark fringe. 2. The waves interfere constructively ⇒ bright fringe. 3. Some waves interfere destructively others constructively ⇒ intermediate fringe. Slit 4 Barrier – Typeset by FoilTEX – 236 Question 199 Consider four equally spaced slits and consider light waves that travel to one particular screen location. Suppose that the discrepancy in the distance traveled by the λ waves between adjacent slits is . 4 Slit 1 Slit 2 Slit 3 Which of the following is true? (Hint: consider combinations of various pairs of waves) 1. The waves interfere destructively ⇒ dark fringe. 2. The waves interfere constructively ⇒ bright fringe. 3. Some waves interfere destructively others constructively ⇒ intermediate fringe. Slit 4 Barrier – Typeset by FoilTEX – 237 Question 200 A narrow beam of white light is viewed through a diffraction grating whose slits are vertical. Wavelengths of light are typically 650 nm for red light 480 nm for violet. Which of the following is true in the vicinity of the region immediately opposite the beam of light? 1. The light will split into a rainbow pattern with the violet on the left and red on the right. 2. The light will split into a rainbow pattern with the violet on the right and red on the left. 3. The light will split into a rainbow pattern with the violet further from the center than red. 4. The light will split into a rainbow pattern with the violet closer to the center than red. – Typeset by FoilTEX – 238 Question 201 A diffraction grating is illuminated with yellow light at normal incidence. The pattern seen on a screen behind the grating consists of three yellow spots, one at 0◦ (straight through) and one each at ±45◦. You now add red light of equal intensity, coming in the same direction as the yellow light. The new pattern consists of: 1. red spots at 0◦ and 45◦. 2. yellow spots at 0◦ and 45◦. 3. orange spots at 0◦ and 45◦. 4. an orange spot at 0◦, yellow spots at 45◦ , and red spots slightly farther out. 5. an orange spot at 0◦, yellow spots at 45◦ , and red spots slightly closer in. – Typeset by FoilTEX – 239 Question 202 Light of wavelength 500 nm passes through a single slit of width 1800 nm. How many dark spots will appear in the diffraction pattern? 1. 3 2. 4 3. 6 4. 7 5. Infinite – Typeset by FoilTEX – 240 Question 203 Monochromatic light is incident on a small disk-shaped barrier. The disk will produce a shadow. The center of this area (marked by an arrow) is: 1. a bright spot, 2. darker than the rest of the shadow, 3. slightly lighter than the rest of the shadow, 4. bright or dark depending on the distance between the screen and the disk. Light Screen – Typeset by FoilTEX – 241 Question 204 Light of wavelength 600 nm strikes a thin film of thickness 200 nm perpendicularly and a wave passes through the film as illustrated (with the angles exaggerated). The index of refraction of the film is nfilm = 1.5. Which of the following represents the shift resulting only from the distance which the wave travels through the film? 1. 0 wavelengths 1 2. wavelengths 2 3. 1 wavelength 4. 3 wavelengths 2 5. 2 wavelengths – Typeset by FoilTEX – 242 Question 205 Light of one wavelength is incident on a thin film, whose index of refraction is 1.33. The thickness of the film is such that when the film is surrounded by air (index of refraction 1.00), the intensity of the reflected light is zero. Film Which of the following is a possible phase shift (in numbers of wavelengths) between the two reflected light waves? 1. 0 wavelengths. 1 2. wavelength. 2 3. 1 wavelength. 4 4. 1 wavelength. 5. 2 wavelengths. – Typeset by FoilTEX – 243 Question 206 Light of wavelength 600 nm strikes a thin film of thickness 200 nm perpendicularly and a waves travel as illustrated (with the angles exaggerated). The index of refraction of the film is nfilm = 1.5. The index of refraction of the surrounding medium is 1.0. Which of the following represents the shift between the two waves that emerge from the left edge of the film and travel leftwards? 1. 0 wavelengths 1 2. wavelengths 2 3. 1 wavelength 4. 3 wavelengths 2 5. 2 wavelengths – Typeset by FoilTEX – 244 Question 207 Light of wavelength 600 nm strikes a thin film of thickness 200 nm perpendicularly and a waves travel as illustrated (with the angles exaggerated). The index of refraction of the film is nfilm = 1.5. The index of refraction of the surrounding medium left of the film is 1.0 and to the right of the film 1.83. Which of the following represents the shift between the two waves that emerge from the left edge of the film and travel leftwards? 1. 0 wavelengths 1 2. wavelengths 2 3. 1 wavelength 4. 3 wavelengths 2 5. 2 wavelengths – Typeset by FoilTEX – 245 Question 208 Light is incident on a thin film of oil on water. Assume that the film of oil has a uniform thickness. The index of refraction of the oil is 1.20 and of water 1.33. Red light has a longer wavelength than blue light. Consider light that is incident in a narrow range of angles. Which of the following is true regarding the distances traveled by light through the oil that results in strongly reflected red light and strongly reflected blue light? 1. Shorter for red than blue. Oil 2. Longer for red than blue. 3. Same for red as blue. Water – Typeset by FoilTEX – 246 Question 209 White light is incident on a thin film of oil on water. Assume that the film of oil has a uniform thickness. Oil Water The index of refraction of the oil is 1.20 and of water 1.33. Red light has a longer wavelength than blue light. Which of the following is true? 1. Red and blue light will be reflected at the same angle. 2. Red light will be strongly reflected at a greater angle than blue. 3. Blue light will be reflected at a greater angle than red. – Typeset by FoilTEX – 247 Question 210 Light of one wavelength is incident on a thin film, whose index of refraction is 1.33. The thickness of the film is such that when the film is surrounded by air (index of refraction 1.00), the intensity of the reflected light is zero. Film Glass A sheet of glass (index of refraction 1.50) is placed immediately to the right of the film. Which of the following is true? 1. The intensity of the reflected light is zero because the two reflected waves interfere destructively. 2. The intensity of the reflected light is brighter because the two reflected waves interfere constructively. 3. The intensity of the reflected light is brighter because there is now only one reflected wave. 4. None of the above. – Typeset by FoilTEX – 248 Question 211 Two microscope slides are held together as illustrated. Light is incident on the slides from above. The slides are coated (black line) to prevent reflections. The upper slide is rotated away from the lower slide so that the angle of the wedge increases. What happens to the pattern of fringes? 1. Stays the same. 2. Fringes are further apart. 3. Fringes are closer together. – Typeset by FoilTEX – 249 Question 212 Light passes through a single slit whose width can be varied. As the slit width is decreased, what happens. 1. The central maximum narrows. 2. The central maximum widens. 3. The central maximum stays the same width but more dark fringes appear. 4. The central maximum stays the same width but fewer dark fringes appear. 5. Nothing changes except for the brightness of the central maximum. – Typeset by FoilTEX – 250 Warm Up Question 27 Fig 17.6 illustrates diffraction, the spreading of light as it passes through an opening. Would the double-slit experiment of Fig 17.7 display bright and dark fringes if light did NOT spread as it passed through the slits? Explain your answer. 1. Yes. The pattern would just be concentrated opposite each slit. 2. Yes. There would just be two bands opposite the slits. 3. No. The two waves are not overlapping after they pass through the slits. The overlapping of waves causes interference which is what makes the light and dark fringes. If the light does’t spread after the slits there is no interference and thus no light and dark fringes. 4. No. The spreading of the light as it passes splits it into dark and light waves. – Typeset by FoilTEX – 251 Warm Up Question 28 Suppose that two different light sources are used to produce light that is incident upon a double slit as shown in Fig 17.7. The sources produce light with distinct frequencies (distinct colors). Will the resulting interference patterns for the two colors overlap perfectly (i.e. each bright fringe for one color coincides with a bright fringe for the other color)? Explain your answer. 1. Yes. The colors fringes will over lap and produce a new color. 2. Yes. They pass through the same slits and so the patterns produced will be the same. 3. No. The waves have different wavelengths and so a crest of one will not generally meet a crest of another. 4. No. frequency changes it alters wavelength and hence alters the position (mλL/d) for positions of brightness for fringes . – Typeset by FoilTEX – 252 Warm Up Question 29 Red light of one particular wavelength is incident upon a single slit. The diffraction pattern is observed while the intensity of the intensity of the light is reduced. Describe whether the locations of the bright and dark fringes changes as the intensity is reduced. If they do, describe whether they move closer or further apart. Explain your answer. 1. Closer together. The wavelength decreases as the intensity decreases and so fringe locations are nearer the central fringe. 2. Further apart. The wavelengths increase, spacing everything further out. 3. No change. Neither a nor L change and so the locations of the dark fringes stay the same. – Typeset by FoilTEX – 253 Warm Up Question 30 Two radio waves are broadcast into a gap between two hills. One is from an AM station whose frequency is about 1000 kHz and the other from an FM radio station whose frequency is about 100 MHz. Which wave is more likely to propagate to a town that is behind one of the hills but not directly behind the gap between the hills? Explain your answer. 1. AM. AM has longer wavelength meaning that the waves travel further. 2. AM. The AM waves are larger and will travel further. 3. AM. A bigger frequency means that the waves will be stronger. 4. FM. Larger wavelength means a larger diffraction pattern. 5. FM. The larger frequency means that the signal is stronger. – Typeset by FoilTEX – 254 Wave Optics: Slides – Typeset by FoilTEX – 255 Phase Shift I Two waves overlap initially. Two crests that initially align are marked. Waves shift by different distances. Ez b Ez b Ez b Ez b – Typeset by FoilTEX – 256 Phase Shift II One possible relative shift by a whole wavelength. Ez A different but equivalent relative shift by a whole number of wavelengths. Ez b Ez b b Ez – Typeset by FoilTEX – b 257 Phase Shift III One possible wavelength. relative Ez shift by a half A different but equivalent relative shift by a half wavelength. Ez b Ez b b Ez – Typeset by FoilTEX – b 258 Interference of Pulses A snapshot of a string at t = 0 s displays two pulses traveling toward each other. The horizontal units are cm. Suppose that the pulses travel with speed 1 cm/s. At t = 1 s the pulses appear as: x x – Typeset by FoilTEX – 259 Interference of Pulses A snapshot of a string at t = 1 s is as follows. At t = 2.5 s the individual pulses and their superposition appear as: x x Add to give: x – Typeset by FoilTEX – 260 General Interference I Snapshots of two waves at t = 0 s in the same medium are illustrated whose phase difference is ∆φ = 0. y1 The superposition of the two waves is: y Individual waves Wave 1 Superposition y2 Wave 2 – Typeset by FoilTEX – ytot 261 General Interference II Snapshots of two waves at t = 0 s in the same medium are illustrated whose phase difference is ∆φ = π4 . y1 The superposition of the two waves is: y Individual waves Wave 1 Superposition y2 Wave 2 – Typeset by FoilTEX – ytot 262 General Interference III Snapshots of two waves at t = 0 s in the same medium are illustrated whose phase difference is ∆φ = π2 . y1 The superposition of the two waves is: y Individual waves Wave 1 Superposition y2 Wave 2 – Typeset by FoilTEX – ytot 263 General Interference IV Snapshots of two waves at t = 0 s in the same medium are illustrated whose phase difference is ∆φ = 3π 4 . y1 The superposition of the two waves is: y Individual waves Wave 1 Superposition y2 Wave 2 – Typeset by FoilTEX – ytot 264 General Interference V Snapshots of two waves at t = 0 s in the same medium are illustrated whose phase difference is ∆φ = π . y1 The superposition of the two waves is: y Individual waves Wave 1 Superposition y2 Wave 2 – Typeset by FoilTEX – ytot 265 Constructive Interference Snapshots of two waves at on instant in the same medium. y1 y2 Wave 1 The superposition of the two waves is: y Superposition Wave 2 – Typeset by FoilTEX – Individual waves ytot 266 Destructive Interference Snapshots of two waves at one instant in the same medium. y1 y2 Wave 1 The superposition of the two waves is: y Superposition Wave 2 – Typeset by FoilTEX – Individual waves ytot 267 March 2006 Mach-Zehnder Interferometer Detector Beam Splitter Mirror Beam Splitter – Typeset by FoilTEX – Mirror 268 Waves from Two Sources Sources coincide. Constructive interference results. Sources offset by one wavelength. Constructive interference results. λ Source 1 b Source 2 b Source 1 Superposition – Typeset by FoilTEX – b Source 2 b Superposition 269 Waves from Two Sources Sources offset by two wavelengths. Constructive interference results. Sources offset by two wavelengths. Constructive interference results. 2λ Source 1 b 2λ Source 1 Source 2 Superposition – Typeset by FoilTEX – b b Source 2 b Superposition 270 Waves from Two Sources Sources offset by a half wavelength. Destructive interference results. Sources offset by one and a half wavelengths. Destructive interference results. λ/2 Source 1 b Source 2 Superposition – Typeset by FoilTEX – 3λ/2 b Source 1 b Source 2 b Superposition 271 Waves from Two Sources: Constructive Interference Sources offset by one wavelength. Sources offset by two wavelengths. λ Source 1 λ Source 1 b Source 2 ∆l Superposition – Typeset by FoilTEX – b λ b Source 2 b ∆l Superposition 272 Waves from Two Sources: Constructive Interference Sources offset by one wavelength. Sources offset by two wavelengths. λ Source 1 λ λ Source 1 b Source 2 b b Source 2 ∆l ∆l Superposition Superposition – Typeset by FoilTEX – b 273 Waves from Two Sources: Destructive Interference Sources offset by one half wavelength. Sources offset by one and a half wavelengths. λ Source 1 λ Source 1 b Source 2 b ∆l Superposition – Typeset by FoilTEX – λ b Source 2 b ∆l Superposition 274 Waves from Two Sources: Destructive Interference Sources offset by half wavelength. Sources offset by one and a half wavelengths. λ Source 1 Source 1 b Source 2 ∆l Superposition – Typeset by FoilTEX – λ b λ b Source 2 b ∆l Superposition 275 Overlapping Waves from a Double Slit Light Intensity Light Barrier – Typeset by FoilTEX – Screen 276 Single Slit Interference I Snapshots of two waves at t = 0 s in the same medium are illustrated. The shift of one relative to the other is λ/12. y1 The superposition of the two waves is: y Individual waves Wave 1 Superposition y2 Wave 2 – Typeset by FoilTEX – ytot 277 Single Slit Interference II Interference of two waves at t = 0 s in the same medium whose successive shifts are λ/12. y Individual waves Interference of four waves at t = 0 s in the same medium whose successive whose successive shifts are λ/12. y Superposition ytot – Typeset by FoilTEX – Individual waves Superposition ytot 278 Single Slit Interference III Interference of four waves at t = 0 s in the same medium whose successive whose successive shifts are λ/12. y Individual waves Interference of eight waves at t = 0 s in the same medium whose successive whose successive shifts are λ/12. y Superposition ytot – Typeset by FoilTEX – Individual waves Superposition ytot 279 Single Slit Interference IV Interference of eight waves at t = 0 s in the same medium whose successive whose successive shifts are λ/12. y Individual waves Interference of ten waves at t = 0 s in the same medium whose successive whose successive shifts are λ/12. y Superposition ytot – Typeset by FoilTEX – Individual waves Superposition ytot 280 Single Slit Interference V Interference of ten waves at t = 0 s in the same medium whose successive whose successive shifts are λ/12. y Individual waves Interference of twelve waves at t = 0 s in the same medium whose successive whose successive shifts are λ/12. y Superposition ytot – Typeset by FoilTEX – Individual waves Superposition ytot 281 Double Slit Pattern Double slit interference pattern for two slits of negligible width. Intensity I = I max cos2 β 0 where β= θ πd sin θ. λ – Typeset by FoilTEX – 282 Single Slit Pattern Single slit interference pattern. I =I max sin α α 0 where α= Intensity 2 θ πa sin θ. λ – Typeset by FoilTEX – 283 Double Slit Pattern: Width Included Double slit interference pattern including width features. I = I max sin α α 2 cos2 β 0 θ where α= πa sin θ λ β= πd sin θ. λ and – Typeset by FoilTEX – 284 Double Slit Pattern: Width Included Double slit interference pattern including width features. I =I max sin α α 2 2 cos β where α= πa sin θ λ and πd β= sin θ. λ – Typeset by FoilTEX – 0 θ 285 Double Slit Pattern: Narrower Width Double slit interference pattern with a narrower width. I =I max sin α α 2 2 cos β where α= πa sin θ λ and πd β= sin θ. λ – Typeset by FoilTEX – 0 θ 286 Title Question 1. Response 2. Response – Typeset by FoilTEX – 287 Geometric Optics – Typeset by FoilTEX – 288 Question 213 A narrow beam of light rays is incident on a perfectly flat mirror as indicated. 1 2 4 b b b Which observer(s) can see the reflected light? 5 b 3 b – Typeset by FoilTEX – 289 Question 214 A light ray is incident on a smooth curved surface as illustrated. Which of the following indicates the reflected light ray correctly? Case 3 Case 1 – Typeset by FoilTEX – Case 4 Case 2 290 Question 215 A light ray is incident on a smooth curved surface as illustrated. Which of the following indicates the reflected light ray correctly? Case 3 Case 1 – Typeset by FoilTEX – Case 4 Case 2 291 Question 216 An observer labeled O, faces a mirror and observes a point light source S. Where is the image of S located, according to O? Where is the image of S located according to O? 1. A O C b b 2. B 3. C A S – Typeset by FoilTEX – b 4. D b B b D b 5. O cannot see an image of S. 292 Question 217 Three observers, A, B and C, and an object, labeled S, are placed in front of a mirror as illustrated. Which of the observers can see the image of the object? 1. Only C C b B b 2. Only B 3. Only B and C 4. Only A and C S A b 5. Only A and B b – Typeset by FoilTEX – 293 Question 218 An object is placed between two parallel mirrors as illustrated. The horizontal units are marked in meters. The images produced by the mirrors are located at: 1. x = 2 m, 3 m, . . . b x 2. x = ±2 m, ±3 m, ±4 m, . . . 3. x = ±2 m, ±4 m, ±6 m, . . . 4. x = ±2 m – Typeset by FoilTEX – 294 Question 219 Case 4 Plane Plane Plane Case 5 Plane – Typeset by FoilTEX – Case 2 Plane Case 1 Case 3 Two mirrors are parallel to each other as illustrated. A toy plane is placed between the mirrors. Various possibilities for some of the reflected images are illustrated. Which of these is correct? 295 Question 220 Sections of convex spherical mirrors are illustrated below. Mirror A Mirror B Which of the following best represents the rank of the radii of curvatures of the mirrors? 1. A > C > B 2. A = B > C 3. A = B < C 4. A < B = C Mirror C – Typeset by FoilTEX – 5. A < C < B 296 Question 221 Sections of convex spherical mirrors are illustrated below. Mirror A Mirror B The answer: A=B<C Mirror C – Typeset by FoilTEX – 297 Question 222 Various convex mirrors are used to produce images of the same object. Which of the following is true? 1. Convex mirrors always produce upright images. 2. Convex mirrors can produce upright or inverted images depending on the location of the object. 3. Convex mirrors always produce inverted images. 4. Convex mirrors always produce reduced size images. 5. Convex mirrors can produce enlarged or reduced images depending on the object location. – Typeset by FoilTEX – 298 Question 223 Light passes from air into water. Light travels at a smaller speed in water than in air. Which of the following is possible for the waves? Case 3 Case 1 – Typeset by FoilTEX – Case 2 299 Question 224 Light passes from air (n = 1.00) into glass (n = 1.52) and then into water (n = 1.33). Which of the following indicates a possible trajectory of the light ray? Case 3 Case 1 Case 4 Case 2 – Typeset by FoilTEX – 300 Question 225 The indices of refraction for various substances are given below: Air 1.00 Water 1.33 Benzene 1.50 Which of the following is/are true? 1. Total internal reflection is possible for light passing from any of the materials listed to any other one listed. 2. Total internal reflection is possible for light passing from benzene to air but not water to air. 3. Total internal reflection is possible for light passing from benzene to air and water to air. 4. Total internal reflection is possible for light passing from air to benzene but not air to water. 5. Total internal reflection is possible for light passing from air to benzene and air to water. – Typeset by FoilTEX – 301 Question 226 The indices of refraction for various substances are given below: Air 1.00 Water 1.33 Benzene 1.50 Which of the following is/are true? 1. Total internal reflection is possible for light passing from any of the materials listed to any other one listed. 2. Total internal reflection is possible for light passing from benzene to air but not water to air. 3. Total internal reflection is possible for light passing from benzene to air and water to air. 4. θc for the air/benzene combination is larger than that for the air/water combination. 5. θc for the air/benzene combination is smaller than that for the air/water combination. – Typeset by FoilTEX – 302 Question 227 White light enters a prism as illustrated. The light is broken into distinct colors after emerging. Which of the following is true for the index of refraction for light in glass? 1. It is the same for red and blue. 2. It is larger for red. 3. 4. It is larger for blue. – Typeset by FoilTEX – 303 Question 228 A lens focuses incoming parallel light rays in air as illustrated. The lens is then immersed in water a parallel light rays enter it. The index of refraction of water is 1.33 and for this glass 1.50. Inside the water, the rays are focused: 1. closer to the lens 2. further from the lens 3. at the same point as in the air. – Typeset by FoilTEX – 304 Question 229 An object is placed to the left of a convex lens with focal point as illustrated. Several rays are traced from the tip of the object through the lens. Which of the rays is drawn correctly? Object Fb b F 1 2 3 4 – Typeset by FoilTEX – 305 Question 230 An object is placed to the left of a convex lens with focal point as illustrated. Two rays are traced from the tip of the object through the lens and indicate the location of the image. As the object is shifted closer toward the left focal point, which of the following is true? 1. The location and height of the image remain fixed. 2. The image gets closer to the lens and its height decreases. Object 3. The image gets closer to the lens and its height stays constant. Fb Fb 4. The image gets further from the lens and its height increases. 5. The image gets further from the lens and its height decreases. – Typeset by FoilTEX – 306 Question 231 An object is placed between a convex lens and its focal point. Object Fb Provided that the object is somewhere between the lens and its focal point, which of the following is true is regarding the size of the image? 1. Smaller than the object regardless of object position. Fb 2. Same as the object regardless of object position. 3. Larger than the object regardless of object position. 4. Larger than the object for certain object positions, smaller for others. – Typeset by FoilTEX – 307 Question 232 An object is placed to the left of a convex lens with focal point as illustrated. Two rays are traced from the tip of the object through the lens and indicate the location of the image. As the object is shifted closer toward the left focal point, which of the following is true? 1. The magnification stays constant. 2. The magnification decreases. 3. The magnification increases. Object Fb – Typeset by FoilTEX – Fb 308 Question 233 An object is placed to the left of a concave lens with focal point as illustrated. Two rays are traced from the tip of the object through the lens and indicate the location of the image. As the object is shifted closer toward the lens, which of the following is true? 1. The location and height of the image remain fixed. 2. The image is produced at the focal point and its height increases. Object 3. The image gets closer to the lens and its height decreases. Fb Fb 4. The image gets closer to the lens and its height increases. 5. The image gets further from the lens and its height increases. – Typeset by FoilTEX – 309 Question 234 An object is placed to the left of a convex lens with focal point as illustrated. As the object is shifted closer toward the left focal point, which of the following is true? 1. The location and height of the image remain fixed. Object 2. The image gets closer to the lens and its height decreases. Fb Fb 3. The image gets closer to the lens and its height increases. 4. The image gets further from the lens and its height increases. 5. The image gets further from the lens and its height decreases. – Typeset by FoilTEX – 310 Question 235 An object is placed to the left of a convex lens with focal length of 1 m. The distance from the object to the lens is more than 2 m. Which of the following is true of the image location? 1. di is exactly equal to do. 2. di is not equal to do but is more than 2 m. Object 3. di is less than 2 m. F b – Typeset by FoilTEX – F b 311 Question 236 An object is placed to the left of a convex lens with focal point as illustrated. The distance from the object to the lens is less than 2f. Which of the following is true of the size of the magnification? 1. m = 1 2. m > 1 3. m < 1 Object F b – Typeset by FoilTEX – F b 312 Question 237 An object is placed to the left of a convex lens with focal point as illustrated. The distance from the object to the lens is greater than 2f. Which of the following is true of the size of the magnification? 1. m = 1 2. m > 1 Object 3. m < 1 F b – Typeset by FoilTEX – F b 313 Question 238 A simple model of the eye without any lens mechanism is illustrated below. Two tiny light sources are located to the left of the eye opening. Which of the following best illustrates the image produced on the ”retina?” Case 1 b Case 2 b b b b b Case 3 – Typeset by FoilTEX – Case 4 314 Question 239 The eye always produces a clear image on the retina provided that the object is beyond the near point. As the object moves closer to the eye, which of the following is true? 1. The focal length of the lens stays constant; the image size stays constant. Object Retina Fb Fb 2. The focal length of the lens stays constant; the image size stays increases. 3. The focal length of the lens increases; the image size increases. 4. The focal length of the lens decreases; the image size increases. 5. The focal length of the lens decreases; the image size decreases. – Typeset by FoilTEX – 315 Question 240 A person who is nearsighted needs to observe a tree which is beyond that person’s far point. This can be accomplished by placing a lens in front of the eye. The lens must produce an image of the tree which is upright and closer to the lens that the tree. Which arrangement will accomplish this? 1. A concave lens placed so that the tree is beyond the focal point of the lens. 2. A concave lens placed so that the tree is between the lens and its focal point. 3. A convex lens placed so that the tree is beyond the focal point of the lens. 4. A convex lens placed so that the tree is between the lens and its focal point. – Typeset by FoilTEX – 316 Question 241 A person who is farsighted needs to observe an ant which is closer that person’s near point. This can be accomplished by placing a lens in front of the eye. The lens must produce an image of the ant which is upright and further from the lens than the ant. Which arrangement will accomplish this? 1. A concave lens placed so that the ant is beyond the focal point of the lens. 2. A concave lens placed so that the ant is between the lens and its focal point. 3. A convex lens placed so that the ant is beyond the focal point of the lens. 4. A convex lens placed so that the ant is between the lens and its focal point. – Typeset by FoilTEX – 317 Question 242 Two people, Alex and Xela, have different near points; Alex’s near point is twice as far from his eye as Xela’s (25 cm). Their far points are both at infinity. They both use identical magnifying glass to observe identical ants, each of which is 10 cm from their eyes. They situate the magnifying glass so that the ant is at the focal point of the magnifying glass. Which of the following is true? 1. Only Alex can see a clear image of the ant. 2. Only Xela can see a clear image of the ant. 3. Both Alex and Xela can see a clear image of the ant. 4. Neither can see a clear image of the ant. – Typeset by FoilTEX – 318 Question 243 Two people, Alex and Xela, have different near points; Alex’s near point is twice as far from his eye as Xela’s (25 cm). Their far points are both at infinity. They both use identical magnifying glass to observe identical ants, each of which is 10 cm from their eyes. They situate the magnifying glass so that the ant is at the focal point of the magnifying glass. – Typeset by FoilTEX – Which of the following is true regarding the sizes of the images of the ant produced by the magnifier? 1. The image is larger for Alex. 2. The image is larger for Xela 3. The image sizes are the same. 4. The images are infinitely tall. 319 Question 244 Two people, Alex and Xela, have different near points; Alex’s near point is twice as far from his eye as Xela’s (25 cm). Their far points are both at infinity. They both use identical magnifying glass to observe identical ants, each of which is 10 cm from their eyes. They situate the magnifying glass so that the ant is at the focal point of the magnifying glass. – Typeset by FoilTEX – Which of the following is true regarding angular magnifications attained using the magnifier? 1. Larger for Alex. 2. Larger for Xela. 3. The same. 4. Both infinite. 320 Question 245 A person looks toward a full moon and initially holds a quarter out in such a way that the quarter exactly obscures the moon. The person brings the quarter closer to his eye. Which of the following is true after the person has brought the quarter closer to his eye? 1. The angular size of the quarter is larger than that of the moon. 2. The angular size of the quarter is smaller than that of the moon. 3. The angular size of the quarter is the same as that of the moon. – Typeset by FoilTEX – 321 Question 246 Two objects have the indicated heights and distances from an eye: Which of the following is true? 1. Angular size of blue same as angular size of red. Red arrow Blue arrow – Typeset by FoilTEX – Height Distance 10 cm 2.0 m 20 cm 6.0 m 2. Angular size of blue larger than angular size of red. 3. Angular size of blue smaller than angular size of red. 322 Question 247 A microscope is adjusted so that the intermediate image is located at the focal point of the eyepiece. When this is true the total angular magnification is given by M =− dintN dofeyepiece where dint is the distance from the objective to the intermediate image, N the eye’s near point, do the distance from the objective to the object, and feyepiece the focal length of the eyepiece. – Typeset by FoilTEX – Which of the following is true as the object is brought closer to the objective? 1. The eyepiece must be moved closer to the object. Magnification decreases. 2. The eyepiece must be moved closer to the object. Magnification increases. 3. The eyepiece must be moved further from the object. Magnification decreases. 4. The eyepiece must be moved further from the object. Magnification increases. 323 Question 248 A telescope is used to view a star that is infinitely far away. The eyepiece is situated so that its focal point is located at the image produced by the objective. Which of the following represents the distance between the lenses? 1. fobjective 2. fobjective − feyepiece 3. feyepiece 4. fobjective + feyepiece – Typeset by FoilTEX – 324 Warm Up Question 31 Someone states that, “The image formed by a lens is located at the focal point of the lens, regardless of the location of the object” Is this statement true or not? Explain your answer (you can refer to diagrams in the text if necessary). 1. True. Rays entering the lens in a parallel fashion pass through the focal point. This produces an image at the focal point. 2. True for a converging lens. This always bends light rays through the focal point. 3. False. Diagram 18.30 shows an image that is not located at the focal point of the lens. – Typeset by FoilTEX – 325 Warm Up Question 32 An arrow is placed to the left of a concave lens. Are there any locations where the arrow can be placed so that the lens produces a sharp image of the arrow on a piece of paper? If so, describe where these locations are. Explain your answers. 1. No (locations). It’s a diverging lens and the light rays cannot converge on a screen. 2. Yes. At the focal point. 3. Yes. At a point on the opposite side of the lens. 4. Yes. Place the arrow at the center of the lens. 5. Yes. Place the arrow in the image plane. – Typeset by FoilTEX – 326 Warm Up Question 33 A magnifying glass provides a certain angular magnification, when the object is located near to the focal point of the lens. In order to attain a larger angular magnification, would one use a lens with a larger or smaller focal length? Explain your answer. 1. Focal length does not matter. 2. Larger. A bigger focal length implies that the image is produced further away and is larger. 25 cm 3. Smaller. According to M = smaller focal length gives larger f magnification. 4. Smaller. Since the focal point is smaller, the angle from the lens to the focal point is steeper, so this would make a larger angular magnification. – Typeset by FoilTEX – 327 Warm Up Question 34 Consider the image produced by a microscope. Is this image real or virtual? Upright or inverted? Provide reasons for your answers. 1. Real and upright. First produces real and inverted. Second produces real and re-inverts, giving upright. 2. Real and inverted. The first lens produces a real image. The minus sign in M indicates that it is inverted. 3. Real and inverted. Microscopes produce inverted images. Inverted images are always real. 4. Virtual and upright. The eyepiece acts like a magnifying glass which produces a virtual and upright image. 5. Virtual and inverted. Virtual because the image is on the same side of the lens as the object and it appears upside down after ray tracing. – Typeset by FoilTEX – 328 Warm Up Question 35 A telescope contains two lenses. That closer to the eye is called the eyepiece and that closer to the object, the objective. A particular telescope produces an angular magnification of 3. Describe as precisely as possible how the focal length of the objective is related to the focal length of the eyepiece for this telescope. 1. The focal length of the objective is shorter than that of the eyepiece since the magnification is only 3. 2. The focal length depends on the distance to the object, since the object’s location will affect where any images are produced. 3. The focal length of the eyepiece is the same as that of the objective, since the eyepiece focal point is placed at the location of the image produced by the objective. 4. fobjective = 3feyepiece since this is the ratio given by the magnification. – Typeset by FoilTEX – 329 Warm Up Question 36 In many microscopes it is possible to switch between different objective lenses, having different focal lengths. Suppose that one switches to an objective lens with a smaller focal length. How will the position of the eyepiece lens have to be adjusted (no change, closer or further from object) to produce the correct image? Explain your answer. 1. Closer. The image produced by the objective is closer to the object. The eyepiece must be moved closer so that its focal point is at this image. 2. Further. The image produced by the objective lens is further from the object than before. The eyepiece must be moved further so that its focal point is at this image. 3. Further. The magnification equation predicts a larger objective magnification. The eyepiece magnification must be smaller to compensate. 4. No change. When focusing one does not move the eyepiece. – Typeset by FoilTEX – 330 Quantum Physics – Typeset by FoilTEX – 331 Question 249 A Xenon lamp equipped with a filter that transmits light of wavelength 400 nm. The power (total energy per second) emitted by the light is increased. Which of the following is true? 1. The energy of each photon is unchanged and the rate of photon emission is unchanged. 2. The energy of each photon is unchanged and the rate of photon emission increases. 3. The energy of each photon increases and the rate of photon emission is unchanged. 4. The energy of each photon increases and the rate of photon emission increases. – Typeset by FoilTEX – 332 Question 250 A Xenon lamp equipped with a filter that transmits light of wavelength 400 nm. This light is incident upon a metal and electrons are ejected. The filter is adjusted so that the frequency of the emitted light is increased and the power stays constant. Which of the following is true regarding the emitted electrons? 1. The rate of electron emission is unchanged. 2. The rate of electron emission decreases. 3. The rate of electron emission increases. – Typeset by FoilTEX – 333 Question 251 A Xenon lamp equipped with a filter that transmits light of wavelength 400 nm. This light is incident upon a metal and electrons are ejected. The filter is adjusted so that the frequency of the emitted light is increased and the power stays constant. Which of the following is true regarding the emitted electrons? 1. The energy of each electron is unchanged. 2. The energy of each electron increases. 3. The energy of each electron decreases. – Typeset by FoilTEX – 334 Question 252 Two lasers each emit red light of wavelength 632 nm. The power of laser A is 1 mW and that of laser B is 5 mW. Which of the following is/are true? 1. Each photon from laser A has the same energy as that of laser B. 2. Each photon from laser A has smaller energy than that of laser B. 3. Laser B emits more photons per second than laser A. 4. Laser B emits the same number of photons per second as laser A. 5. The frequency of light from laser B is larger than that of laser A. – Typeset by FoilTEX – 335 Question 253 Photons are fired toward a screen. The probability distribution for arrival at various locations is as illustrated. Consider the two illustrated locations. Which of the following is true? 1. Photons will never arrive at A but will sometimes arrive at B. 2. Photons will never arrive at B but will sometimes arrive at A. Screen A B 3. Photons could arrive at either A or B; they are more likely to arrive at A. 4. Photons could arrive at either A or B; they are more likely to arrive at B. 5. Photons will always arrive at B. – Typeset by FoilTEX – 336 Question 254 Photons are fired toward a screen. The probability distribution for arrival at various locations is as illustrated. Consider the two illustrated locations. Which of the following is true? 1. Photons will never arrive at A but will sometimes arrive at B. 2. Photons will never arrive at B but will sometimes arrive at A. Screen A B 3. Photons could arrive at either A or B; they are more likely to arrive at A. 4. Photons could arrive at either A or B; they are more likely to arrive at B. 5. Photons will always arrive at B. – Typeset by FoilTEX – 337 Question 255 Neutrons are fired toward a barrier/slit arrangement and arrive at a screen. The probability distribution for arrival at various locations depends on the barrier/slit arrangement. A double slit produces the solid dark blue probability distribution. A single slit produces the dashed dark red distribution. Screen Which of the following is true? 1. Single slit ⇒ neutron definitely arrives at A. Double slit ⇒ neutron definitely arrives at A. 2. Single slit ⇒ neutron could arrive at A. Double slit ⇒ neutron could arrive at A. 3. Single slit ⇒ neutron never arrives at A. Double slit ⇒ neutron never arrives at A. 4. Single slit ⇒ neutron could arrive at A. Double slit ⇒ neutron never arrives at A. A – Typeset by FoilTEX – 338 Question 256 Many neutrons are fired toward a barrier/slit arrangement and arrive at a screen. The probability distribution for arrival at various locations depends on the barrier/slit arrangement. A double slit produces the solid dark blue probability distribution. A single slit produces the dashed dark red distribution. Which of the following is true? 1. Single slit ⇒ more arrive at A than B. Double slit ⇒ more arrive at A than B. 2. Single slit ⇒ more arrive at B than A. Double slit ⇒ more arrive at A than B. 3. Single slit ⇒ more arrive at B than A. Double slit ⇒ more arrive at B than A. 4. Single slit ⇒ more arrive at A than B. Double slit ⇒ more arrive at B than A. Screen A B – Typeset by FoilTEX – 339 Question 257 A particle of mass m is contained in a box of length L. The energy of the particle is measured. Which of the following is/are a possible outcome of the energy measurement? h2 1. 8mL2 h2 2. 2 8mL2 h2 3. 4 8mL2 h2 4. 6 8mL2 h2 5. 10 8mL2 – Typeset by FoilTEX – 340 Question 258 A partial energy level diagram for a system is as illustrated. The energies are in units of 10−19 J. E3 = 8.0 Which transition results in emission of light with the largest wavelength (based only on the illustrated energy levels)? 1. 1 → 2 2. 2 → 1 3. 3 → 1 E2 = 4.0 E1 = 2.0 – Typeset by FoilTEX – 4. 1 → 3 5. 3 → 2 341 Question 259 Certain manufactured “artificial atoms” have exactly two energy levels. The artificial atoms are initially in the lowest energy state in each case. Atom A Light is incident upon the artificial atoms. Which of the following is true regarding the wavelengths of light required to excite the atoms from the lower to higher energy states? Atom B 5.0 eV 1. Wavelength for A equals wavelength for B. 4.0 eV 2. Wavelength for A is larger than wavelength for B. 2.0 eV 3. Wavelength for A is smaller than wavelength for B. 1.0 eV – Typeset by FoilTEX – 342 Question 260 The Balmer series lines satisfy λ= 91.1 nm . 1 1 − 2 22 n The red line in the hydrogen spectrum has a longer wavelength than the blue line. Which of the following must be true? 1. The value of n for red is the same as that for blue. 2. The value of n for red is larger than that for blue. 3. The value of n for red is smaller than that for blue. – Typeset by FoilTEX – 343 Question 261 The total energy of an electron that orbits a proton at radius r is 1 e2 E=− 8πǫ0 r If the electron emits energy via electromagnetic radiation as it orbits, then as time passes, which of the following is true? 1. The radius of orbit stays constant. 2. The radius of orbit decreases. 3. The radius of orbit increases. – Typeset by FoilTEX – 344 Question 262 In the Bohr model, the energy levels can be labeled with an integer n. Visible light is emitted when the atom undergoes a transition from a level with n > 2 into one with n = 2. −0.85 eV n=4 −1.51 eV n=3 −3.40 eV n=2 The frequency of blue light is larger than the frequency of red light. Which of the following is true? 1. Blue light and red light are each produced from a transition involving the same energy level to the n = 2 level. 2. Blue light is produced from a transition from a level that is closer in energy (than for red light) to the n = 2 level. 3. Red light is produced from a transition from a level that is closer in energy (than for blue light) to the n = 2 level. −13.6 eV – Typeset by FoilTEX – n=1 345 Question 263 In the Bohr model, it turns out that visible light is emitted when an electron makes a transition from an orbital with n > 2 into the orbital with n = 2. The frequency of blue light is larger than the frequency of red light. Which of the following is true? 1. Blue light and red light are each produced from a transition involving the same orbital to the n = 2 orbital. 2. Blue light is produced from a transition from an orbital that is closer in energy (than for red light) to the n = 2 orbital. 3. Red light is produced from a transition from an orbital that is closer in energy (than for blue light) to the n = 2 orbital. – Typeset by FoilTEX – 346 Question 264 The ground state energy of the Bohr model hydrogen atom is −13.6 eV. Which of the following best represents the energy of the n = 3 level? 1. −1.51 eV 2. +1.51 eV 3. −4.53 eV 4. +4.53 eV 5. −10.6 eV – Typeset by FoilTEX – 347 Question 265 For the f states of the hydrogen atom l = 3. Which of the following is the number of f energy states? 1. 3 2. 5 3. 7 4. 10 5. 14 – Typeset by FoilTEX – 348 Question 266 A hydrogen atom is initially in its ground state (n = 1). A free electron is fired toward the hydrogen atom and collides with the atom. The lowest energy levels for hydrogen are as illustrated. What is the minimum energy that the electron must have in order for it to stop after the collision (and all the energy be absorbed by the atom)? 1. 0.85 eV −0.85 eV n=4 −1.51 eV n=3 −3.40 eV n=2 2. 1.0 eV 3. 10.2 eV 4. 12.8 eV 5. 13.6 eV −13.6 eV – Typeset by FoilTEX – n=1 349 Warm Up Question 37 Two beams of electromagnetic radiation (similar to beams of light), one ultraviolet light and the other infrared light, have the same power. Each of these are incident upon the same type of molecule, whose atoms will be separated if the energy supplied by any incident radiation is large enough. Which beam of light (ultraviolet or infrared) is more likely to be able to split the molecule? Explain your answer. 1. Ultraviolet. Infrared light has a longer wavelength and thus a lower frequency so the energy of it is less than the energy of a photon from ultraviolet light. The ultraviolet light beam will be more likely to split the molecule because it has more energy. 2. Ultraviolet. This has a longer wavelength and therefore larger intensity. 3. Infrared. Infrared light has a longer wavelength and a higher frequency. Thus it has a larger energy. 4. Infrared. Infrared has a larger wavelength and this means it is stronger. 5. Infrared. There are more photons per second. They are more likely to split the molecule. – Typeset by FoilTEX – 350 Warm Up Question 38 Electrons and neutrons are each fired, with the same speed, through a barrier with two slits. The particles strike a screen which produces a pattern such as that of Fig 28.14. This pattern is identical to that produced by light passing through a similar barrier and the locations of the bright bands are found by using a equation 17.8 (this works for any kind of wave). For which type of particle are the bright bands spread out more? Explain your answer. 1. Electrons. Wavelength = h/p = h/mv. Neutrons have larger mass than electrons, so the wavelength of the neutron must be shorter than that of the electron. If the wavelength is shorter the spacing should also be shorter for the neutron, and larger for the electron. 2. Electrons. These have a higher energy and will spread out more. 3. Neutrons. Larger mass means a greater effect at the screen and spread out more. 4. Neutrons. These have a larger wavelength and so are more spread out. – Typeset by FoilTEX – 351 Warm Up Question 39 The Bohr model and quantum physics predict the possible energies for a hydrogen atom and these depend on an integer, n. Is the following statement true: ”As n increases, the energy approaches infinity?” Explain your answer. 1. Not true. As n increases the energy increases to the ionization limit where E = 0 eV. 2. Not true. As n increases, the energy decreases. 3. True. Clearly as n increases, the energy increases and so it will approach infinity. – Typeset by FoilTEX – 352 Warm Up Question 40 The total angular momentum, L, of the hydrogen atom can, in various circumstances, be zero. Suppose that L = 0. Does this imply that the energy of the hydrogen atom must also be zero? Explain your answer. 1. Yes. Since L = n~, it follows that n = 0 so the energy is zero. 2. Yes. If angular momentum is zero but radius is not zero then the speed must be zero. So the kinetic energy will be zero. 3. No. Its l = 0 therefore making L zero. l has nothing to do with energy. 4. No. When n = 1 then l (orbital quantum number) is equal to zero. This means the L (angular momentum) is zero. But at n = 1 the energy is not zero. – Typeset by FoilTEX – 353 Question 267 here 1. 2. 3. 4. – Typeset by FoilTEX – 354 Warm Up Question 41 Question 1. Response 2. Response – Typeset by FoilTEX – 355 Title Question 1. Response 2. Response – Typeset by FoilTEX – 356

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