51. A certain capacitor has a capacitance of 5 μF. After it is charged to 5 μC and isolated, the plates are brought closer together so its capacitance becomes 10 μF. The work done by the agent is about ______.
(A) −1.25 × 10^–6J
(B) 8.3 × 10^–7J
(C) −8.3 × 10^–7J
(D) 1.25 × 10^–6J
(E) −3.75 × 10^–6J

47. A tuning fork is known to vibrate with frequency 262 Hz. When it is sounded along with a mandolin string, four beats are heard every second. Next, a bit of tape is put onto each tine of the tuning fork, and the tuning fork now produces five beats per second with the same mandolin string. What is the frequency of the string? (A) 257 Hz (B) 258 Hz (C) 262 Hz (D) 266 Hz (E) 268 Hz

48. Determine the energy stored in C2 when C1 = 15 μF,C2 = 10 μF, C3 = 20 μF, and V0 = 18 V.(A) 1.60 mJ (B) 0.72 mJ (C) 0.50 mJ (D) 0.32 mJ (E) 0.18 mJ

49. A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge Q. Concentric with this sphere is an uncharged, conducting, hollow sphere whose inner and outer radii are b and c as shown in the figure. Find the magnitude of the electric field for r ＜ a. (A) (B) (C)(D) (E) E = 0

50. Two long straight current-carrying parallel wires cross the x axis and carry currents I and 3I in the same direction, as shown in the figure. At what value of x is the net magnetic field zero?(A) 1 (B) 3 (C) 4 (D) 5 (E) 7

52. A plane with a wing length of 50 m is flying westward where the downward component of the earth’s magnetic field is 6 ✖ 10-5 T. What is the difference in potential between the wingtips when the speed of the plane is 720 km/hr, and which wingtip is positive? (A) 2.16 V, south (B) 2.16 V, north (C) 0.96 V, south (D) 0.96 V, north (E) 0.60 V, south 

53. Implanted medical devices are often charged by transcutaneous energy transfer (TET), which uses a pair of coils in close proximity for wireless charging. The change of current in the coil outside the body causes the magnetic flux of the coil inside the body to change, thus generating an induced electromotive force. There are 10 coils with a radius of 1 cm, and the current of the outer coil drops from 10 A to 0, within 6 × 10-6 s, what is the average induced electromotive force of the inner coil? (Magnetic constant μ0 is 4π ✖ 10-7 T●m/A.) (A) 2.58 V (B) 2.79 V (C) 3.05 V (D) 3.29 V (E) 3.54 V

54. A beam of unpolarized light of intensity I0 passes through four successive ideal polarizing filters, each of whose polarizing axis makes a 30° angle with the previous one. What is the intensity of the transmitted beam? (A) 1 (B) 81/256 (C) 27/128 (D) 9/16 (E) 0

55. When sitting in an airplane at an altitude of 10 km, you look down on the ground. Assuming that your pupil is about 1.5 mm in radius and considering the effect of diffraction only, what is the minimum separation s between objects on the ground that you can distinguish? (The wavelength of visible light is around 500 nm.) (A) 0.5 m (B) 2 m (C) 8 m (D) 20 m (E) 50 m

56. A spaceship S1 is moving away from us at a speed of 0.8 c. Another spaceship S2 is moving away from us in the opposite direction at a speed of 0.5 c. What is the speed of S1 measured by an observer on S2? (A) 1.3 c (B) 1.0 c (C) 0.97 c (D) 0.93 c (E) 0.89 c

57. Silicon (Si) is a semiconductor material whose properties fit perfectly in solar cells to convert the light energy into electrical energy. Based on this evidence, what the value of energy gap of Si probably is? (A) several tenths of eV (B) 1.1 eV (C) 3.1 eV (D) 5.1 eV (E) 7.1 eV