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1 Mark Reeves - Physics 22, Fall A point charge of mass kg and charge q = µc is suspended by a thread between the vertical parallel plates of a parallel-plate capacitor, as shown in the figure below. d An electron beam is deflected upward through 3.22 mm while traveling in a vacuum between two deflection plates 12.0 mm apart (the figure below ). The potential difference between the deflecting plates is 123 kv and the kinetic energy of each electron as it enters the space between the plates is J. What is the kinetic energy of each electron when it leaves the space between the plates? + Electron beam _ Deflection q (in J) 3.A C E B D If the angle of deflection is θ = 24.6, and the separation between the plates is d = m, what is the potential difference between the plates? (in V) 1.A B C D E Two identical conducting spheres carry charges of µc and µc respectively. They are initially a large distance L apart. The spheres are brought together, touched together, and then returned to their original separation L. What is the ratio of the magnitude of the force on either sphere after they are touched to that before they were touched? 2.A B C D E 1.28 Find the electric potential energy for the following array of charges: charge q 1 = µc is located at (x, y) = (0.0, 0.0) m; charge q 2 = µc is located at (3.92, 3.07) m; and charge q 3 = µc is located at (0.0, 3.07) m. (in J) 4.A B C D E Two uniformely charged spheres are suspended by strings of length L from vertically adjustable supports. The spheres are in static equilibrium and at the same height, as shown below. Q T W Z

2 Mark Reeves - Physics 22, Fall Which statements regarding a plate capacitor are true? The angles with respect to the vertical are Q=11.1, and T=21.3. The amount of charge on Z can be equal to that on W. 5. A True B False C Cannot tell The charge on W can be positive and that on Z negative. 6. A True B False C Cannot tell The amount of charge on Z can be greater than that on W. 7. A True B False C Cannot tell The charge on W can be positive and that on Z positive. 8. A True B False C Cannot tell The mass of W can be less than that of Z. 9. A True B False C Cannot tell The tension in the string supporting sphere W is 2.75E- 5 N. Calculate the tension in the other string. (in N) 10.A B C D E Three arrangements of capacitors with capacities indicated (in µf) are shown in the figure below Rank their equivalent capacitances in order of INCREASING value. (smallest has rank 1) Capacitance of configuration X. 11. A Rank 1 B Rank 2 C Rank 3 Capacitance of configuration Y. 12. A Rank 1 B Rank 2 C Rank 3 Capacitance of configuration Z. 13. A Rank 1 B Rank 2 C Rank The charge of a disconnected charged plate capacitor increases when the plates are pulled apart 14. A True B False The capacitance is proportional to the area 15. A True B False The capacitance is proportional to the gap width 16. A True B False The voltage across a disconnected charged plate capacitor increases when the plates are pulled apart 17. A True B False The capacitance depends on the material between the plates. 18. A True B False A capacitor is completely charged with 680 nc by a voltage source that had 225 V. What is its capacitance? (in F) 19.A B C D E Now the plates of the charged capacitor are pushed together with the voltage source already disconnected. 20. A The energy stored in the capacitor remains the same. B The capacitance increases. C The charge on the plates increases. D The voltage drop between the plates increases. E None of the above. The initial air gap of the capacitor above was 8 mm. What is the stored energy if the air gap is now 2 mm? (in J) 21.A 0.00 B C D E

3 Mark Reeves - Physics 22, Fall The figure shows the equipotential lines of a charge distribution and labelled locations. D C E A 5-year old has nothing better to do than to connect three capacitors to a voltage source as shown. The capacitors have C 1 =58 mf, C 2 =70 mf, and C 3 =18 mf, respectively, and the voltage source has 4 Volts. B A What is the total capacitance? (in mf) 22.A 26.5 B 31.0 C 36.3 D 42.5 E 49.7 What is the total energy stored in the capacitors? (in mj) 23.A 398 B 465 C 544 D 637 E 745 Where do you expect the strongest electric field? 26. A A B B C C D D E E What is the direction of the electric field at A? P Q + O - R 27. A Approximately parallel to the x-axis. B Approximately parallel to the y-axis. C No field. S Two charges of equal magnitude are located on the horizontal axis at equal distances from the vertical axis. At what location does the electric field point due west? 24. A P B S C O D None of the locations What is the direction of the electric field at E? 28. A Approximately parallel to the x-axis. B Approximately parallel to the y-axis. C No field. The following figure shows the electric field lines of two point charges: A D Where does the electric field point at location R? 25. A West B South C East D North E No field C B

4 Mark Reeves - Physics 22, Fall Closest to which one of the locations would you expect no electric field? 29. A A B B C C D D E Nowhere. How much work by an external force does it take to move the charge Q = 11µC from x 1 = 0.07 m to x 2 = 0.32 m? (in J) 32.A B C D E d The electric field at location A is A... stronger than at location C B... about the same strength as at location C, and neither is zero. C... weaker than at location C, but not zero. D... zero. a b c e Consider the arrangement of two fixed point charges, equal in magnitude, shown in the figure. Which of the following statements are correct for the initial motion of a third charge if it is released from rest in the vicinity of the two charges shown? A negative charge at point e will accelerate up. 33. A True B False A negative charge at point d will accelerate down. 34. A True B False A positive charge at point c will accelerate toward the lowerleft. 35. A True B False A constant electric field of magnitude E = 306 V/m points in the positive x-direction. A charge Q is moved in positive x-direction within the field by an external force. A positive charge at point a will accelerate toward the lowerleft. 36. A True B False A negative charge at point b will accelerate down. 37. A True B False 31. A The work required is inversely proportional to the distance travelled. B The work required is directly proportional to the distance travelled. C Without an external force, a free negative charge would accelerate perpendicular to the depicted path. D Without an external force, a free negative charge would accelerate in the direction of the depicted path. E The work required is proportional to the square of the charge.

5 Mark Reeves - Physics 22, Fall Three charges, Q 1, Q 2, and Q 3 are located in a straight line. The position of Q 2 is m to the right of Q 1. Q 3 is located m to the right of Q 2. The force on Q 2 due to its interaction with Q 3 is directed to the... Left if the two charges are positive. 38. A True B False Left if the two charges are negative. 39. A True B False Left if the two charges have opposite signs. 40. A True B False Right if the two charges have opposite signs. 41. A True B False Right if the two charges are negative. 42. A True B False In the above problem, Q 1 = C, Q 2 = C, and Q 3 = C. Calculate the total force on Q 2. Give with the plus sign for a force directed to the right. (in N) 43.A 1.30 B 1.47 C 1.67 D 1.88 E 2.13 Now the charges Q 1 = C and Q 2 = C are fixed at their positions, distance m apart, and the charge Q 3 = C is moved along the straight line. For what position of Q 3 relative to Q 1 is the net force on Q 3 due to Q 1 and Q 2 zero? Use the plus sign for Q 3 to the right of Q 1. (in m) 44.A B C D E c a b Consider two uniformly charged parallel plates as shown in the figure. The magnitudes of the charges are equal. Select True or False for the following statements. If the plates are oppositely charged, there is no electric field at c. 45. A True B False If both plates are positively charged, there is no electric field at b. 46. A True B False If both plates are negatively charged, the electric field at a points towards the top of the page 47. A True B False If the plates are 1.0 cm by 1.0 cm squares, and the charges on the plates are +/- 2.2 µc respectively, what is the magnitude of the electric field at b? Assume that the spacing between the plates is much less than 1 cm. (in V/m) 48.A B C D E Consider a sphere of radius R = 7.16 m where a charge of Q = 12.7 µc is uniformly distributed through the volume of the sphere. What is the magnitude of the electric field at a point halfway between the center of the sphere and its surface? (in V/m) 49.A B C D E

6 Mark Reeves - Physics 22, Fall A solid metal sphere of radius a = 1.30 cm is surrounded by a concentric spherical metal shell of inner radius b = 1.80 cm and outer radius c = 2.30 cm. The inner sphere has a net charge of Q 1 = 4.10 µc, and the outer spherical shell has a net charge of Q 2 = µc. +q Figure 1 L -q -q Figure 2 -q c b a * c * a -q b +q * +q d * +q What is the radial component of the electric field E r at a point located at radius r = 1.50 cm, i.e. between the two conductors? E r is positive if it points outward, negative if it points inward. (in N/C) 50.A B C D E What is E r at a point located at radius r = 2.70 cm, i.e. outside the outer shell? (in N/C) 51.A B C D E What is the surface charge density, σ b, on the inner surface of the outer spherical conductor? (in C/m^2) 52.A B C D E What is the surface charge density, σ c, on the outer surface of the outer spherical conductor? (in C/m^2) 53.A B C D E Consider two separate systems, each with four charges of magnitude q arranged in a square of length L as shown above. Points a and c are in the center of their squares while points b and d are half way between the lower two charges. Complete the following statements. The electric potential at a is A Positive B Negative C Zero The electric potential at c is A Positive B Negative C Zero The electric potential at d is A Positive B Negative C Zero The electric potential at b is A Positive B Negative C Zero Voltage (volts) x (meters) 5 10 What is the electric field at the point x=6.5 m? E-fields point to the right. (in V/m) Positive 58.A B C D E -1.96

7 Mark Reeves - Physics 22, Fall The figure below shows identical light bulbs connected to a battery. All the bulbs are glowing. Rank the brightness of the bulbs, from brightest (rank 1) to dimmest (rank 5). In the circuit below, a constant current of i = 2.37 A flows from b to c through the 8 Ω resistor bulb E 59. A Rank 1 B Rank 2 C Rank 3 Calculate the potential difference between points a and d. (in V) 65.A B C D E bulb D 60. A Rank 1 B Rank 2 C Rank 3 bulb A 61. A Rank 1 B Rank 2 C Rank 3 Consider the circuit shown in the figure. Calculate the potential difference across R 4. Use the following data: R 1 = 27.0 Ω, R 2 = 18.5 Ω, R 3 = 19.0 Ω, R 4 = 25.5 Ω, ε = 25.0 V. bulb B 62. A Rank 1 B Rank 2 C Rank 3 bulb F 63. A Rank 1 B Rank 2 C Rank 3 (in V) 66.A 4.71 B 5.88 C 7.35 D 9.19 E In the circuit above, the magnitudes of the currents through R 1,R 2,R 3 are I 1,I 2,I 3, respectively. Which one of the following equations is always true? Calculate the current in R 2. (in A) 67.A B C D E A I 2 = I 3 R 2 /R 3 B I 2 = I 1 R 2 /R 3 C I 1 = I 2 = I 3 D I 1 I 3 E I 2 = I 3

8 Mark Reeves - Physics 22, Fall Two batteries (V 1 = 15 V and V 2 = 12 V) are in a circuit with three identical resistors (R 1 = R 2 = R 3 = 5.7 Ω). What is the current in the R 3 resistor? Note that all resistor values are equal, which greatly simplifies your loop equations. (in A) 68.A B C D E Consider the circuit shown below, with a battery and three identical light bulbs, and a switch connecting the third bulb to the circuit. Initially, the switch is open. Now, we are going to close the switch. Which of the following statements are true when the switch is closed (compared to the initial state, when the switch was open)? Bulb #3, which was initially on, now goes out completely. 69. A True B False The total power dissipated in the circuit increases. 70. A True B False The voltage across bulb #2 does not change. 71. A True B False Bulb #2 gets dimmer than before, but does not go out. 72. A True B False The current through the battery decreases. 73. A True B False Printed from LON-CAPA MSU Licensed under GNU General Public License

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