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Final Exam Physics 196 Fall 2010 Name: Write name in upper right corner of this page. Time allowed is 2 hours Answer all questions on the question sheets and turn in the sheets. Total number of points is 15. Each question is worth 0.5 points. Communications with classmate result in no credit given for the exam. 1. Find the force acting on the charge q due to the charges 2Q and Q in the figure shown (k=Coulomb’s law constant) Qq 2r 2 3Qq b. k 2 2r 5Qq c. k 2 2r 7Qq d. k 2 2r a. k 2. Find the magnitude of the electric field at the point P due to the charges 6nC and –6nC in the figure shown (Take Coulomb’s law constant k=9×109 N-m2/C2) a. b. c. d. 1.3 N/C 2.1 N/C 3.6 N/C 4.8 N/C 3. It is desired to put a charge of +8.0nC on an isolated metallic sphere of radius 4.0cm by connecting it to a battery. What should be the voltage of the battery? (Take Coulomb’s law constant k=9×109 N-m2/C2) a. b. c. d. 600 V 1200 V 1800 V 2400 V 1 4. The potential difference between two plates of a parallel plate capacitor is 200 V. A helium ion with twice the charge of a proton and four times the mass of a proton is released at rest on the plate at lower potential. What is its velocity when it reaches the other plate? (mass of proton = 1.67×10-27 kg, charge of proton = 1.6×10-19 C) a. b. c. d. 4.24×105 m/s 3.06×105 m/s 2.22×105 m/s 1.38×105 m/s 5. A solid sphere of radius a carries a total charge q uniformly distributed throughout its volume. Using Gauss’s law, the electric field at a distance r from the center is qr 20 a 3 1 q b. 40 a 2 1 qr c. 40 a 3 1 q d. 20 a 2 a. 1 6. The electric potential in a region of space is given by and V is in volts. Find the electric field at x=1.0m. a. b. c. d. V x 10 8x 6 x 2 where x is in meter 8 V/m 4 V/m –8 V/m –4 V/m 7. A metallic sphere of radius R carrying charge Q is connected by a conducting wire to a distant metallic sphere of radius R/3 initially carrying no charge. Find the charge on the large sphere after the connection. Q 4 3Q b. 4 Q c. 2 2Q d. 3 a. 2 8. Point charges Q and Q occupy adjacent corners of a square of side a . How much work must be done to move a point charge q from the unoccupied corner closer to the charge Q to the other unoccupied corner? kQq a kQq b. 0.59 a kQq c. 1.47 a kQq d. 0.59 a a. 1.47 9. The diagram shows a region where a uniform electric field of 60V/m exists and point to the right. The points A,B, and C form a right angled triangle with sides indicated. The line BC is perpendicular to the electric field lines. The potential difference VA VB is a. b. c. d. 300 V -300 V 240 V -240 V 10. In a DC circuit where a 5-V battery with internal resistance 2Ω is connected to a 8.0Ω resistor, the potential difference between the terminals of the battery is a. b. c. d. 3V 4V 5V 6V 3 11. A potential difference of 12.0V is applied to the combination of resistors as shown. The potential difference across the 3.0 Ω resistor is a. b. c. d. 2V 3V 4V 5V 12. Find the current I indicated in the circuit as shown: a. b. c. d. 1.0 A 2.0 A 3.0 A 4.0 A 13. The emf of a battery is a. b. c. d. the potential difference between the positive and negative terminals of the battery the energy delivered by the battery in unit time the energy delivered by the battery for every unit of charge flowing through it the ratio of the current over resistance 14. A 20-μF capacitor is initially charged to 50V. It is then discharged through a resistance 200Ω. After what time is the charge on it equal to 0.29 mC? a. b. c. d. 2.0 ms 7.0 ms 3.0 ms 5.0 ms 4 15. You charge up a 4μF parallel plate capacitor to 8μC by a battery. With the battery disconnected, you move the plates apart so that the distance between them is doubled. The work you do is a. b. c. d. 4μJ -4μJ 8μJ -8μJ 16. The period of the orbit of a 10 keV proton moving perpendicular to a magnetic field of 0.02T is (mass of proton=1.67×10-27kg, charge of proton=1.60×10-19C) a. b. c. d. 1.1 μs 2.2 μs 3.3 μs 4.4 μs 17. The diagram shows the circular orbits in a magnetic field of four particles with the same kinetic energy which carry charge of the same magnitude but different masses. Two of the charges are negative. The magnetic field points into the paper. Which orbit corresponds to the heaviest particle with a positive charge? a. b. c. d. 1 2 3 4 18. The diagram shows two infinitely long wires carrying 5.0A currents in opposite directions. With distances as indicated, the magnetic field at the point P is a. b. c. d. 0.15 mT 0.25 mT 0.35 mT 0.45 mT 5 19. A very long wire of radius a carries a current I uniformly distributed over its cross-sectional area. The magnetic field at a distance a / 3 from its axis is equal to a. 0 I 4a I b. 0 6a I c. 0 4a I d. 0 6a 20. A horizontal circular loop of radius 10 cm carries a current of 10A running counter clockwise when viewed from the top. An electron happens to be at the center travelling with velocity 8.0×106 m/s due east. The magnitude and direction of the force on the electron are a. b. c. d. 8.0×10-17 N due north 8.0×10-17 N due south 6.0×10-17 N due north 6.0×10-17 N due south 21. A current element has length 3.0mm and carries a 8.0A current in the y-direction of a rectangular coordinate system. The magnetic field it creates at the point (1,2,-3) is (coordinates are measured in meters) a. (1.37iˆ 0.46 ˆj ) 10 10 T b. (0.46iˆ 1.37 ˆj ) 10 10 T c. (0.46iˆ 1.37kˆ) 10 10 T d. (1.37iˆ 0.46kˆ) 10 10 T 22. The diagram shows the orientations of four current carrying rings in a region of uniform magnetic field. The ring that will return to its original position when disturbed is a. b. c. d. 1 2 3 4 6 23. A metal ring 1.0cm in radius and with 2.0Ω electrical resistance lies flat on a table in a region where there is a uniform magnetic field of 2.5T upward. The magnetic field reverses direction in 5.0ms. The magnitude and direction of the electric current induced in the ring are a. b. c. d. 0.16A clockwise 0.16A counter-clockwise 0.25A clockwise 0.25A counter-clockwise 24. The thick arrow indicates the direction of the magnetic moment created when an external field Bapp is applied to a material specimen. Which of the following statements is correct? Bapp a. b. c. d. the material is paramagnetic and the magnetic field inside the specimen is less than Bapp the material is paramagnetic and the magnetic field inside the specimen is greater than Bapp the material is diamagnetic and the magnetic field inside the specimen is less than Bapp the material is diamagnetic and the magnetic field inside the specimen is greater than Bapp 25. You connect a dc battery to a resistor and a switch. When the switch is closed, you find that it takes a little while before the current reaches its final value. You can conclude that a. b. c. d. The switch is not perfect The battery has internal resistance The circuit has inductance The circuit has capacitance 26. A 4-μF capacitor is charged and then connected across a 25-μH inductor. The frequency of oscillations of the current is a. b. c. d. 20 kHz 16 kHz 12 kHz 8 kHz 7 27. An LR circuit has a resistance R=4.0Ω, an inductance L=2.0 H, and a battery of emf=12 V. How much energy is stored in the inductance of this circuit when a steady current is achieved? a. b. c. d. 0J 3J 6J 9J 28. A series RLC circuit is driven by a 2.0-kHz oscillator. The circuit parameters are Vrms=30 V for the oscillator, L=1.0mH, C=12.0μF, and R=10 Ω. Under steady-state conditions, the rms current in the circuit will be a. b. c. d. 1.5 A 2.6 A 3.7 A 4.8 A 29. For the same circuit as question 28, if the voltage from the oscillator has the temporal dependence cos t , the current along the resistor has the behavior a. b. c. d. cost 90 cost 90 cost 31 cost 31 30. A circuit consists of a 600Ω resistor in series with a 5.0μF capacitor and an AC signal generator of frequency 60Hz. The rms voltage across the resistor is found to be 3.0V. The rms voltage of the AC generator is a. b. c. d. 5.0 V 4.0 V 3.0 V 2.0 V 8 Formula Sheet (PHYS 196) F 1 q1q2 4 0 r 2 F qE k E 1 4 0 1 q rˆ 40 r 2 V2 V1 E d 2 Ex 1 1 Q2 U 2 C L R A Q C V V IR q E dA n V x C 0 9.0 109 Nm 2 / C 2 U qV A d P IV 0 V 1 2 0E2 P I 1 q 40 r E E0 R R1 R2 RC F q B F IL B IAn B 0 Id rˆ dB 0 4 10 7 T m / A B d 0 I 2 4 r 0 I I B B 0 B 0 nI 2r 2R B 0 M M m En 0 C C1 C 2 1 1 1 R R1 R2 Bapp M dm d m Bn dA N m B E d dt dt 1 dI N2 1 B2 N m LI U LI 2 V L L 0 A B 2 dt L 2 0 L R 1 Arms A0 2f VR IR VL IX L VC IX C X L L 2 VL I I VC Z R 2 X L X C tan 2 I I 0 cost 0 cos t P I rms rms cos 0 1 LC Q 1 1 1 C C1 C 2 XL XC R I0 Z 2 P I rms R 0 9 XC 1 C