# FINAL EXAM - Physics Patel SPRING 1998 FORM CODE - A

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1 FINAL EXAM - Physics Patel SPRING 1998 FORM CODE - A Be sure to fill in your student number and FORM letter (A, B, C, D, E) on your answer sheet. If you forget to include this information, your Exam will not be counted towards your grade. Each question may have one answer, which is more correct than the others. Be sure to read all five answers so than you will not miss the best one. The last page has a list of equations you may find useful and may be detached for use during the exam. 1. Extra Credit: What is your form code? (a) A (b) B (c) C (d) D (e) E

2 2. The diagrams below depict four different charge distributions. The charges are all the same distance from the origin. Rank the situations according to the magnitude of the electric field at the origins, least to greatest. A) 4, 3, 2, 1 B) 4, 3, 1, 2 C) 1, 2, then 3 and 4 tie D) 1, 2, 3, 4 E) 2, 1, then 3 and 4 tie 3. Two point charges are arranged as shown. In which region could a third charge +1 C be placed so that the net electrostatic force on it is zero? A) I only B) I and II only C) lii only D) I and III only E) II only

3 4. A charged oil drop with a mass of 2x10-4 kg is held suspended by a downward electric field of 300 N/C in earth gravity. The charge on the drop is: A) +1.5x10-6 C B) -1.5x10-6 C C) +6.5x10-6 C D) -6.5x10-6 C E) 0 5. Choose the INCORRECT statement: A) Gauss' law can be derived from Coulomb's law B) Gauss' law states that the net number of electric field lines crossing any closed surface in an outward direction is proportional to the net charge enclosed within the surface C) Coulomb's law can be derived from Gauss' law and symmetry D) Gauss' law applies to a closed surface of any shape E) According to Gauss' law, if a closed surface encloses no charge, then the electric field must vanish everywhere on the surface

4 6. An electron goes from one equipotential surface to another along one of the four paths shown below. Rank the paths according to the work done by the electric field, from least to greatest. A) 4 and 2 tie, then 3, then 1 B) 1, 2, 3, 4 C) 4, 3, 1, 2 D) 1, 3, 4 and 2 tie E) 4, 3, 2, 1 7. Two parallel-plate capacitors with different capacitance but the same plate separation are connected in series to a battery. Both capacitors are filled with air. The quantity that is the same for both capacitors when they are fully charged is: A) potential difference B) stored energy C) energy density D) electric field between the plates E) charge on the positive plate

5 8. Which of the following graphs best represents the current-voltage relationship for a device that obey Ohm's law? A) IV B) III C) I D) V E) II 9. The current in the 5.0-Ω resistor in the circuit shown is: A) 0.42 A B) 0.67 A C) 1.5 A D) 2.4 A E) 3.0 A

6 10. An electron is launched with velocity v in a uniform magnetic field B. The angle θ between v and B is 90 o. It returns to its initial position in a time interval of: A) 2πm/eB B) 2πmv /eb C) πm/eb D) none of these E) πmv/eb 11. The current is from left to right in the conductor shown. The magnetic field is into the page and point S is at a higher potential than point T. The charge carriers are: A) positive B) negative C) neutral D) absent E) none of the above

7 12. The four wire loops shown have edge lengths of either L, 2L, or 3L. They will move with the same speed into a region of uniform magnetic field B, directed out of the page. Rank them according to the maximum magnitude of the induced emf, greatest to least. L 2L 2L 3L A) 4, 2, 3, 1 B) 3 and 4 tie, then 1 and 2 tie C) 1, 2, 3, 4 D) 1 and 2 tie, then 3 and 4 tie E) 4, 2 and 3 tie, then 1

8 13. A square loop of wire moves with a constant speed v from a field-free region into a region of uniform B field, as shown. Which of the five graphs correctly shows the induced current i in the loop as a function of time t? v B I II i i i III t t t i IV i V t t A) I. B) II. C) III. D) IV. E) V.

9 14. The figure shows a bar moving to the right on two conducting rails. To make an induced current i in the direction indicated, a constant magnetic field in region "A" should be in what direction? i i A i v i A) right B) left C) into the page D) out of the page E) impossible, cannot be done with a constant magnetic field 15. A rectangular loop of wire has area A. It is placed perpendicular to a uniform magnetic field B and then spun around one of its sides at frequency f. The maximum induced emf is: A) 4BAf B) BAf C) 2BAf D) 2πBAf E) 4πBAf

10 16. A 0.20-cm radius cylinder, 3.0 cm long, is wrapped with wire to form an inductor. At the instant the magnetic field in the interior is 5.0 mt the energy stored in the field is: A) 0 B) 3.8x10-6 J C) 7.5x10-6 J D) 7.5x10-4 J E) 9.9 J 17. The B field lines due to an ordinary bar magnet: A) form closed curves B) leave the S pole, loop around the outside of the magnet, and enter the N pole C) cross one another near the poles D) are more numerous near the N pole than near the S pole E) none of the above

11 18. The diagram shows two small diamagnetic spheres, one near each end of a bar magnet. Which of the following statements is true? A) The forces on 1 and 2 are both toward the magnet B) The forces on 1 and 2 are both away from the magnet C) the force on 1 is toward the magnet and the force on 2 is away from the magnet D) The magnet does not exert a force on either sphere E) The force on 1 is away from the magnet and the force on 2 is toward the magnet 19. An electric field exists in the cylindrical region shown and is parallel to the cylinder axis. The magnitude of the field might vary with time according to any of the four graphs shown. Rank the four variations according to the magnitudes of the magnetic field induced at the edge of the region, least to greatest. E 1 A) 3 and 4 tie, then 1,2 B) 2, 1, 3, 4 C) 4, 3, 2, 1 D) 4, 3, 1, 2 E) 2, 4, 3, t

12 20. A 0.70-m radius cylindrical region contains a uniform electric field that is parallel to the axis and is increasing at the rate 5.0x10 12 V/m s. The magnetic field at a point 0.25 m from the axis has a magnitude of: A) 0 B) 7.0x10-6 T C) 2.8x10-5 T D) 5.4x10-5 T E) 7.0x10-5 T 21. We desire to make an LC circuit that oscillates at 100 Hz using an inductance of 2.5 H. We also need a capacitance of: A) 1 F B) 1 mf C) 1 µf D) 100 µf E) 1 pf

13 22. An LC series circuit with an inductance L and a capacitance C has an oscillation frequency f. Two inductors, each with inductance L, and two capacitors, each with capacitance C, are all wired in series and the circuit is completed. The oscillation frequency is: A) f/4 B) f/2 C) f D) 2f E) 4f 23. In an oscillating LC circuit, the total stored energy is U. When q = Q/2, U B is: A) U/2 B) U/4 C) D) 3 2 U / E) 3U/4 U 2

14 24. In a purely capacitive circuit the current: A) leads the voltage by π/2 B) leads the voltage by π C) lags the voltage by π/2 D) lags the voltage by π E) is in phase with the voltage 25. If the amplitude of the electric field in a plane electromagnetic wave is 100 V/m then the amplitude of the magnetic field is: A) 3.3x10-7 T B) 6.7x10-7 T C) 0.27 T D) 8.0x10 7 T E) 3.0x10 9 T 26. In an RLC series circuit, which is connected to a source of emf ε m sin(ωt), the current lags the voltage by 45 if: A) R = 1/ωC - ωl B) R = 1/ωL - ωc C) R = ωl - 1/ωC D) R = ωc - 1/ωL E) ωl = 1/ωC

15 Answer Key 1. A 4, 3, 2, 1 2. A I only 3. D -6.5x10-6 C 4. E According to Gauss' law, if a closed surface encloses no charge, then the electric field must vanish everywhere on the surface 5. A 4 and 2 tie, then 3, then 1 6. E charge on the positive plate 7. E II 8. C 1.5 A 9. A 2πm/eB 10. A positive 11. E 4, 2 and 3 tie, then C III. 13. C into the page 14. D 2πBAf 15. B 3.8x10-6 J 16. A form closed curves 17. B The forces on 1 and 2 are both away from the magnet 18. E 2, 4, 3, B 7.0x10-6 T 20. C 1 µf 21. C f 22. E 3U/4 23. A leads the voltage by 1/4 cycle 24. A 3.3x10-7 T 25. C R = ωl - 1/ωC

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