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Final Exam Physics 196 Spring 2011 Name: 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. Some Physics Constants: electronic charge Coulomb constant Permittivity of free space Permeability of free space Mass of electron Mass of proton e = 1.6×10-19 C k = 9.0×109 Nm2/C2 Ξ΅0 = 8.85×10-12 C2/Nm2 m0 = 4p ´107 F / m me = 9.11×10-31 kg mp = 1.67×10-27 kg 1. Two electrically neutral objects A and B are rubbed against each other. Afterwards, the charge on A is found to be +480nC . Assuming that the charging is due to transfer of electrons, how many have been transferred and from which object? (a) (b) (c) (d) 3 × 1012 ππππ π΅ 3 × 1012 ππππ π΄ 6 × 1012 ππππ π΅ 6 × 1012 ππππ π΄ 2. The electrostatic force between two identical point charges π a distance π apart is πΉ. If the charges are doubled, and the distance is tripled, the force is (a) (b) (c) (d) 2πΉ β3 2πΉ β9 4πΉ β9 4πΉ β27 3. If it is desired to push a point charge of ο 8nC toward the SW direction with a force of 320µN from an electric field, the magnitude and direction of the electric field should be (a) (b) (c) (d) 40ππ/π, NE 40ππ/π, SW 30ππ/π, NE 30ππ/π, SW 1 4. Find the magnitude and direction of the electric field produced by the two point charges at the point P as shown: (a) (b) (c) (d) 31 π βπ, left 31 π βπ, right 23 π βπ, left 23 π βπ, right 5. A solid sphere of radius π is uniformly filled with electric charge throughout its volume. The total charge is π. Find the electric field at a point in its interior that is at a distance of πβ3 from its center. (a) (b) (c) (d) π β(3ππ0 π2 ) 3π β(4ππ0 π2 ) 3π β(8ππ0 π2 ) π β(12ππ0 π2 ) 2 ο² 6. On the x-y plane, the electric field is uniform and is given by E ο½ 300iΛ( N / C ) . Find the potential difference VB -VA between the point A , which has coordinates ( 2,-1) and B , which has coordinates ο¨ο 5,4ο© where coordinates are measured in meters (a) (b) (c) (d) 1900π β1900π 2100π β2100π 7. The electric potential measured in volts in a region of space is given by V ( x) ο½ 4 ο 7 x 2 ο« x 4 where x is in meters. The electric field at the point x ο½ 2 is (a) (b) (c) (d) 2 π βπ β4 π βπ 6 π βπ β8 π βπ 8. The diagram shows two identical point charges π at adjacent corners of a square of side π. How much work is required to move another point charge π from A to B where A and B are the unoccupied corners as shown. (a) (b) (c) (d) β0.59 ππ 2 βπ +0.59 ππ 2 βπ β0.26 ππ 2 βπ +0.26 ππ 2 βπ 3 9. A metallic spherical shell of radius 3.0ππ is charged by connecting it to a power supply so that its electric potential is 60ππ assuming the potential is zero at infinity. Given that the breakdown electric field in air is 3.0ππ/π, will the charge stay on the sphere? Give reason for your answer. (a) Yes (b) No (c) Not enough information 10. Which of the following statement(s) regarding the capacitance of a capacitor are correct? (a) (b) (c) (d) It increases with the charge on the capacitor It increases when the potential difference is reduced It decreases when dielectric is introduced None of the above is correct. 11. A bare nucleus of helium atom 2 He 4 at rest is placed at a distance 5.0×10-10m from a carbon nucleus that contains 12 protons. Pushed away from the carbon nucleus by electrostatic repulsion, what is the highest kinetic energy of the helium nucleus? (a) (b) (c) (d) 310ππ 240ππ 138ππ 69ππ 4 12. When a parallel plate capacitor is charged to the voltage 20π and then discharged through a resistor, it takes 30ms for the voltage to fall to 12π. If the distance between the plates is doubled and the resistance is also doubled, the time for the same change of voltage is (a) (b) (c) (d) 7.5ππ 15ππ 30ππ 120ππ 13. Find the equivalent electrical resistance between the points A and B in the network shown where the resistance of each resistor is 1.0Ξ© (a) (b) (c) (d) 4.5Ξ© 3.0Ξ© 2.75Ξ© 1.25Ξ© 14. When a load of resistance 20W is connected with a battery, the observed current is 2.0A . When the load is replaced by one with resistance 15W , the current is 3.0A. Find the emf of the battery. (a) (b) (c) (d) 20π 30π 40π 50π 5 15. Determine the current πΌ1 indicated in the circuit: (a) (b) (c) (d) 1.0π΄ 2.0π΄ 3.0π΄ 4.0π΄ 16. Which of the following statements concerning the emf of a battery is correct? (a) It is the force that pushes electric charge inside the battery. (b) It has the unit of work per unit charge (c) It is a quantity occurring in Ohmβs law. (d) It is equal to the terminal voltage of the battery in an open circuit. 17. In which of the following diagram(s) for the magnetic field, particle velocity, and magnetic force, does the charged particle carry negative charge? 6 18. In a region where the magnetic field is 25ππ due north, a proton with kinetic energy 200MeV travels in the direction 60 S of W. Find the magnitude of the acceleration experienced by the proton. (a) (b) (c) (d) 4.17 × 1012 πβπ 2 3.46 × 1012 πβπ 2 2.35 × 1011 πβπ 2 1.29 × 1011 πβπ 2 19. A proton with velocity 6 ´10 7 m / s enters a region where the magnetic field is 2.5T perpendicular to the paper from the point A and exits at the point B as shown. Find the distance AB and the direction of the magnetic field (a) (b) (c) (d) 0.25π 0.25π 0.50π 0.50π ππ’π‘ ππ π‘βπ πππππ πππ‘π π‘βπ πππππ ππ’π‘ ππ π‘βπ πππππ πππ‘π π‘βπ πππππ 20. A very long solenoid is formed by winding tightly a wire of diameter 0.15ππ. Find the magnetic field inside when a 5.0A current runs through the wire. (a) (b) (c) (d) 0.027π 0.042π 0.066π 0.075π 7 21. The diagram shows two very long wires parallel to each other and at a distance of 2.4m apart. They carry anti-parallel currents of 18.0A each. The magnetic field at a point P midway between the two wires is (a) (b) (c) (d) 0.0ππ 2.0ππ 3.0ππ 6.0ππ 22. A very long wire of radius a carries a current I uniformly distributed over its cross-sectional area. The magnetic field at a distance 2a / 3 from its axis is equal to (a) (b) (c) (d) π0 πΌ β(2ππ) 3 π0 πΌ β(2ππ) 2π0 πΌ β(3ππ) π0 πΌ β(3ππ) 23. Faradayβs law can explain the operation of (more than one answer is possible) (a) A transformer (b) A mass spectrometer (c) A cyclotron (d) An AC generator 24. The diagram shows a planar wire loop of electrical resistance 40W. The area inside the loop is 0.03m2 . A uniform magnetic field exists in pointing into the paper. It is observed that a clockwise current of 15m A runs in the wire while the magnetic field is changing. The magnetic field is (a) (b) (c) (d) increasing at 0.02 π/π decreasing at 0.02 π/π increasing at 0.04 π/π decreasing at 0.04 π/π 8 25. In the circuit shown, what is the energy stored in the inductor a long time after the switch is closed? (a) (b) (c) (d) 12ππ½ 24ππ½ 36ππ½ 48ππ½ 26. A capacitor is charged and then connected across a 25-ΞΌH inductor. The frequency of oscillations of the current is found to be 12kHz. Find the capacitance. (a) (b) (c) (d) 6.0ππΉ 7.0ππΉ 8.0ππΉ 9.0ππΉ 27. In the AC circuit shown, the emf measured in volt is β = 150πππ 300ππ‘ where π‘ is in seconds. The current is (a) (b) (c) (d) πΌ πΌ πΌ πΌ = 30πππ (300ππ‘ β 0.64) = 30πππ (300ππ‘ + 0.64) = 60πππ (300ππ‘ β 0.32) = 60πππ (300ππ‘ + 0.32) 9 28. In a series RLC circuit with an AC power source of frequency π, denoting by πΏ the phase difference between the emf and the current, maximum power will be delivered to the resistor if (multiple answer possible) (a) (b) (c) (d) π =0 πΏ=0 4π 2 π 2 πΏπΆ = 1 π = 1ββπΏπΆ 29. In the AC circuit shown, where the frequency of the generator is 60Hz, the peak voltage of the capacitor is 10.0V. What is the peak emf of the generator? (a) (b) (c) (d) 13.5π 12.9π 11.7π 10.3π 30. Which of the following circuits can be used as a high-pass filter? 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