AP Physics B – Practice Workbook – Book 2 Electricity and Magnetism, Waves and Optics, Modern Physics …. The following(© is applicable to this entire document – copies for student distribution for exam preparation explicitly allowed. 1) Copyright © 1973-2009 College Entrance Examination Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Central, AP Vertical Teams, APCD, Pacesetter, Pre-AP, SAT, Student Search Service, and the acorn logo are registered trademarks of the College Entrance Examination Board. PSAT/NMSQT is a registered trademark of the College Entrance Examination Board and National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service. Other products and services may be trademarks of their respective owners. 2) © 1994-2009 AAPT Has a copyright or other licensing restriction. Table of Contents Chapter 10 Electrostatics Electrostatics Multiple Choice .........................................................................................................5 Electrostatics Free Response ..........................................................................................................43 Answers to Electrostatics Questions ..............................................................................................67 Chapter 11 Circuits Circuits Multiple Choice ................................................................................................................93 Circuits Free Response ................................................................................................................127 Answers to Circuits Questions .....................................................................................................147 Chapter 12 Magnetism and Induction Magnetism and Induction Multiple Choice Section A – Magnetostatics .............................................................................................169 Section B – Induction .......................................................................................................181 Magnetism and Induction Free Response Section A – Magnetostatics .............................................................................................189 Section B – Induction .......................................................................................................209 Answers to Magnetism and Induction Questions ........................................................................219 Chapter 13 Waves and Optics Waves and Optics Multiple Choice Section A – Waves and Sound .........................................................................................247 Section B – Physical Optics .............................................................................................255 Section C – Geometric Optics ..........................................................................................258 Waves and Optics Free Response Section A – Waves and Sound .........................................................................................271 Section B – Physical Optics .............................................................................................274 Section C – Geometric Optics ..........................................................................................280 Answers to Waves and Optics Questions ....................................................................................311 Chapter 14 Modern Physics Modern Physics Multiple Choice Section A – Quantum Physics and Atom Models ............................................................353 Section B – Nuclear Physics ............................................................................................359 Modern Physics Free Response Section A – Quantum Physics and Atom Models ............................................................365 Section B – Nuclear Physics ............................................................................................380 Answers to Modern Physics Questions ........................................................................................383 This book is a compilation of all the problems published by College Board in AP Physics B and AP Physics C that are appropriate for the AP B level as well as problems from AAPT’s Physics Bowl and U.S. Physics Team Qualifying Exams organized by topic. The problems vary in level of difficulty and type and this book represents an invaluable resource for practice and review and should be used… often. Whether you are struggling or confident in a topic, you should be doing these problems as a reinforcement of ideas and concepts on a scale that could never be covered in the class time allotted. The answers as presented are not the only method to solving many of these problems and physics teachers may present slightly different methods and/or different symbols and variables in each topic, but the underlying physics concepts are the same and we ask you read the solutions with an open mind and use these differences to expand your problem solving skills. Finally, we are fallible and if you find any typographical errors, formatting errors or anything that strikes you as unclear or unreadable, please let us know so we can make the necessary announcements and corrections. Problems marked with an asterisk (*) are challenging problems that some would consider to be outside the scope of the course, but rely on the concepts taught within the course or they may require information taught in a later part of the course. These are for those students who wish to go beyond the level needed, but are not required for success in the AP B course. Chapter 10 Electrostatics 3 4 AP Physics Multiple Choice Practice – Electrostatics 1. The electron volt is a measure of (A) charge (B) energy (C) impulse (D) momentum (E) velocity 2. A solid conducting sphere is given a positive charge Q. How is the charge Q distributed in or on the sphere? (A) It is concentrated at the center of the sphere. (B) It is uniformly distributed throughout the sphere. (C) Its density decreases radially outward from the center. (D) Its density increases radially outward from the center. (E) It is uniformly distributed on the surface of the sphere only. 3. A parallel–plate capacitor is charged by connection to a battery. If the battery is disconnected and the separation between the plates is increased, what will happen to the charge on the capacitor and the voltage across it? (A) Both remain fixed. (B) Both increase. (C) Both decrease. (D) The charge increases and the voltage decreases. (E) The charge remains fixed and the voltage increases. Questions 4 – 5. A point P is 0.50 meter from a point charge of 5.0 × 10–8 coulomb. 4. The intensity of the electric field at point P is most nearly (A) 2.5 × 10–8 N/C (B) 2.5 × 101 N/C (C) 9.0 × 102 N/C (D) 1.8 × 103 N/C (E) 7.5 × 108 N/C 5. The electric potential at point P is most nearly (A) 2.5 × l0–8 V (B) 2.5 × 101 V (C) 9.0 × 102 V (D) 1.8 × 103 V (E) 7.5 × 103 V 6. One joule of work is needed to move one coulomb of charge from one point to another with no change in velocity. Which of the following is true between the two points? (A) The resistance is one ohm. (B) The current is one ampere. (C) The potential difference is one volt. (D) The electric field strength is one newton per coulomb. (E) The electric field strength is one joule per electron. Questions 7 – 8 Two positive charges of magnitude q are each a distance d from the origin A of a coordinate system as shown above. 7. At which of the following points is the electric field least in magnitude? (A) A (B) B (C) C (D) D (E) E 8. At which of the following points is the electric potential greatest in magnitude? (A) A (B) B (C) C (D) D (E) E 9. A parallel–plate capacitor has a capacitance C . A second parallel–plate capacitor has plates with twice the area o and twice the separation. The capacitance of the second capacitor is most nearly (A) ¼C (B) ½C (C) C (D) 2C (E) 4C o o o o o 5 10. Two identical conducting spheres are charged to +2Q and –Q. respectively, and are separated by a distance d (much greater than the radii of the spheres) as shown above. The magnitude of the force of attraction on the left sphere is F . After the two spheres are made to touch and then are reseparated by distance d, the magnitude of 1 the force on the left sphere is F . Which of the following relationships is correct? 2 (A) 2F = F (B) F = F (C) F = 2F (D) F = 4F (E) F = 8 F 1 2 1 2 1 2 l 2 1 2 11. The capacitance of a parallel–plate capacitor can be increased by increasing which of the following? (A) The distance between the plates (B) The charge on each plate (C) The area of the plates (D) The potential difference across the plates (E) None of the above 12. An electron volt is a measure of (A) energy (B) electric field (C) electric potential due to one electron (D) force per unit electron charge (E) electric charge Questions 13 – 14 An electron is accelerated from rest for a time of 10–9 second by a uniform electric field that exerts a force of 8.0 x 10–15 newton on the electron. 13. What is the magnitude of the electric field? (A) 8.0 × 10–24 N/C (B) 9.1 × 10–22 N/C (C) 8.0 × 10–6 N/C (D) 2.0 × 10–5 N/C (E) 5.0 × 104 N/C 14. The speed of the electron after it has accelerated for the 10–9 second is most nearly (A) 101 m/s (B) 103 m/s (C) 105 m/s (D) 107 m/s (E) 109 m/s 15. A hollow metal sphere of radius R is positively charged. Of the following distances from the center of the sphere, which location will have the greatest electric field strength? (A) 0 (center of the sphere) (B) 3R/2 (C) 5R/4 (D) 2R (E) None of the above because the field is of constant strength 16. Two isolated charges, + q and – 2q, are 2 centimeters apart. If F is the magnitude of the force acting on charge –2Q, what are the magnitude and direction of the force acting on charge +q? Magnitude Direction (A) (1/2) F Toward charge – 2q (B) 2 F Away from charge –2q (C) F Toward charge – 2q (D) F Away from charge – 2q (E) 2F Toward charge – 2q 17. Charges + Q and – 4Q are situated as shown above. The net electric field is zero nearest which point? (A) A (B) B (C) C (D) D (E) E 6 18. A positive charge of 10–6 coulomb is placed on an insulated solid conducting sphere. Which of the following is true? (A) The charge resides uniformly throughout the sphere. (B) The electric field inside the sphere is constant in magnitude, but not zero. (C) The electric field in the region surrounding the sphere increases with increasing distance from the sphere. (D) An insulated metal object acquires a net positive charge when brought near to, but not in contact with, the sphere. (E) When a second conducting sphere is connected by a conducting wire to the first sphere, charge is transferred until the electric potentials of the two spheres are equal. 19. Two large parallel conducting plates P and Q are connected to a battery of emf E, as shown above. A test charge is placed successively at points I, II, and III. If edge effects are negligible, the force on the charge when it is at point III is (A) of equal magnitude and in the same direction as the force on the charge when it is at point I (B) of equal magnitude and in the same direction as the force on the charge when it is at point II (C) equal in magnitude to the force on the charge when it is at point I, but in the opposite direction (D) much greater in magnitude than the force on the charge when it is at point II, but in the same direction (E) much less in magnitude than the force on the charge when it is at point II, but in the same direction 20. Forces between two objects which are inversely proportional to the square of the distance between the objects include which of the following? I. Gravitational force between two celestial bodies II. Electrostatic force between two electrons III. Nuclear force between two neutrons (A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III 21. The diagram above shows an isolated, positive charge Q. Point (B) is twice as far away from Q as point A. The ratio of the electric field strength at point A to the electric field strength at point B is (A) 8 to 1 (B) 4 to 1 (C) 2 to 1 (D) 1 to 1 (E) 1 to 2 22. Which of the following is true about the net force on an uncharged conducting sphere in a uniform electric field? (A) It is zero. (B) It is in the direction of the field. (C) It is in the direction opposite to the field. (D) It produces a torque on the sphere about the direction of the field. (E) It causes the sphere to oscillate about an equilibrium position. 7 23. Two conducting spheres of different radii, as shown above, each have charge –Q. Which of the following occurs when the two spheres are connected with a conducting wire? (A) No charge flows. (B) Negative charge flows from the larger sphere to the smaller sphere until the electric field at the surface of each sphere is the same. (C) Negative charge flows from the larger sphere to the smaller sphere until the electric potential of each sphere is the same. (D) Negative charge flows from the smaller sphere to the larger sphere until the electric field at the surface of each sphere is the same. (E) Negative charge flows from the smaller sphere to the larger sphere until the electric potential of each sphere is the same. 24. Two parallel conducting plates are connected to a constant voltage source. The magnitude of the electric field between the plates is 2,000 N/C. If the voltage is doubled and the distance between the plates is reduced to 1/5 the original distance, the magnitude of the new electric field is (A) 800 N/C (B) 1,600 N/C (C) 2,400 N/C (D) 5,000 N/C (E) 20,000 N/C Questions 25 – 26 The figure above shows two particles, each with a charge of +Q, that are located at the opposite corners of a square of side d. 25. What is the direction of the net electric field at point P ? (A) (B) (C) (D) (E) 26. What is the potential energy of a particle of charge +q that is held at point P ? 2 qQ 1 qQ 2 qQ 2 2 qQ (A) Zero (B) (C) (D) (E) 4πε d 4πε d 4πε d 4πε d 0 0 0 0 27. Two parallel conducting plates, separated by a distance d, are connected to a battery of emf E. Which of the following is correct if the plate separation is doubled while the battery remains connected? (A) The electric charge on the plates is doubled. (B) The electric charge on the plates is halved. (C) The potential difference between the plates is doubled. (D) The potential difference between the plates is halved (E) The capacitance is unchanged. 8