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UW-Madison PHYSICS 208 - Physics 208 Final Exam

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Page 1 Name: ____________________________________________________ Student ID: ___________________________ Section #: _________ Physics 208 Final Exam Dec. 21, 2007 Print your name and section clearly above. If you do not know your section number, write your TA’s name. Your final answer must be placed in the box provided. You must show all your work to receive full credit. If you only provide your final answer (in the box), and do not show your work, you will receive very few points. Problems will be graded on reasoning and intermediate steps as well as on the final answer. Be sure to include units, and also the direction of vectors. You are allowed two double-sided 8½ x 11” sheets of handwritten notes and no other references. The exam lasts exactly 120 minutes. Coulomb constant: ! ke= 9.0 "109 N # m2/C2 Speed of light in vacuum: ! c = 3 "108m / s Permittivity of free space:! "o= 1/ 4#ke= 8.85 $10%12C2/ N & m2 Permeability of free space: ! µo= 4"#10$7T % m / A Planck’s constant: ! h = 6.626 "10#34J $ s ! = 4.1357 "10#15eV $ s , h = h /2% Bohr radius: ! ao= 0.053nm Bohr magneton: ! µB= 5.788 "10#5eV /T Atomic mass unit: ! 1 u = 1.66054 "10#27kg ! = 931.494 MeV /c2 Electron mass: ! me= 9.11"10#31kg ! = 0.00055u = 0.51 MeV /c2 Proton mass: ! mp= 1.67262 "10#27kg ! = 1.00728u = 938.28 MeV /c2 Neutron mass: ! mn= 1.67493 "10#27kg ! = 1.00866u = 939.57 MeV /c2 Fundamental charge: ! e = 1.60 "10#19C ! hc = 1240eV " nm ! 1eV = 1.602 "10#19J Problem 1: _______ / 20 Problem 2: _______ / 25 Problem 3: _______ / 20 Problem 4: _______ / 20 Problem 5: _______ / 25 Problem 6: _______ / 10 TOTAL: _______ / 120Page 2 1) [20 pts, 4 pts each] Multiple choice. Show work/explanation for full credit. a) A parallel-plate 1 µF capacitor is connected to a 2 V battery while the plates are being pulled apart, doubling the separation. The 2V battery stays connected the entire time. How does the charge after compare to the charge before pulling the plates apart? a. two times bigger b. two times smaller c. four times bigger d. four times smaller e. same b) A positively-charged particle is moving as shown parallel to a wire carrying a positive current I in the direction shown. The direction of the force on the particle due to the current in the wire is a. down b. up c. right d. left e. out of page f. into page c) A quantum particle in a box can have only these energies: E1=1 eV, E2=4 eV, and E3=9 eV. Which of these photons could be emitted from the box? a. 310 nm b. 138 nm c. 413 nm d. 572 nm e. both a & b I v Explanation/Work: Explanation/Work Explanation/WorkPage 3 d) Radioactive ! 918F, used in positron emission tomography (PET), is observed to emit a positron from the nucleus. What isotope does it become after the decay? a. ! 714N b. ! 818O c. ! 1018Ne d. ! 919F e. ! 917F e) You are in a room that is 3 meters high. You hold a lens below a light bulb on the ceiling, forming an image of the bulb directly below it on the floor. What focal length lens could form the largest image on the floor? a. 0.2 m b. 0.5 m c. 1.0 m d. 2.0 m e. 3.0 m Explanation/Work: Explanation/Work:Page 4 2) [25 points, 5 pts each] Short-answer questions Explain your answers! a) The binding energy of 235U is 7.3 MeV/nucleon. Suppose that each 235U nucleus in 1 kg breaks apart (fissions) into two smaller nuclei, one with 120 nucleons and the other with 115 nucleons. Each of these smaller nuclei has a binding energy of 8.3 MeV/nucleon. There are about ~2.5x1025 U atoms in 1 kg. Calculate the energy released in the fission of 1 kg of 235U. b) A parallel-plate capacitor has two square plates, each 10cmX10cm, with a separation of 0.1 cm. The top plate has charge density 10µC/m2, and the bottom plate has charge density -10µC/m2. The charge is uniformly distributed over the plates. What is the force on a -0.2 µC point-like particle 0.02 cm above the bottom plate? F= Value Units Direction E = Value Units -10µC/m2 +10µC/m2 -0.2µ C 0.1cm 0.02cmPage 5 c) A hydrogen atom is in the n=4, l=3 state. How many orientations of the orbital angular momentum are possible? d) Experiments have shown that a human eye is sensitive enough to detect 1 milli-second (0.001s) flashes of 50 femto-Watt (50x10-15 W) green (500 nm) light. How many photons are in this flash of light? e) A 2 cm diameter conducting wire is carrying a current of 200 A. The current is uniformly distributed throughout the volume of the wire. Calculate the force on a +10µC charge moving at a speed of 5 m/s in the direction shown. [Hint: Use Ampere’s law] Magnitude Direction Units F = # orientations = Value 2 cm 1 cm +10µC V=5m/s I=200 A x y z # photons = ValuePage 6 3) [20 pts, 4 pts each] A magnet and coil of wire are shaken so that the magnet slides all the way back and forth through the coil, as shown in the drawing below. The ends of the coil are connected to each other, so that current can flow in the coil. a) The graph below shows the magnetic flux through the coils as a function of time as it slides back and forth. Sketch the current in the coil as a function of time. The vertical CURRENT axis and the horizontal TIME axis have arbitrary units. b) Does the magnitude of the maximum current depend on how fast you shake it? Explain. ! " TIME ! +1 mT " m2 ! "1 mT # m2 TIME CURRENT 0 N SPage 7 c) Does the magnitude of the total amount of charge flowing through the coil on each shake (one trip of magnet through coil in one direction) depend on how fast you shake it? Explain. d) If the coil has N=100 turns, and a resistance of R=10Ω, what is the magnitude of the total charge that flows through the coil each time the magnet moves through it? Hint: the flux through the coil changes by ! 2 mT " m2 = 0.002 T "m2( ) each time the magnet passes through the coil. e) Flashlights without batteries use this technique to charge a super-capacitor, which then powers the flashlight. It also has a circuit element so that during shaking the capacitor is charged, but never discharged. Suppose that the charge through the coil is 0.03 C for each shake, and all


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UW-Madison PHYSICS 208 - Physics 208 Final Exam

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