54. The voltage across a parallel-plate capacitor is measured to be 92.5 V. When a dielectric is inserted between the plates, the voltage drops to 23.4 V. What is the dielectric constant of the inserted material? Assume that the vacuum electric permittivity is
(A) 0.26
(B) 2.64
(C) 0.62
(D) 3.95
(E) 1.82

50. Halley's comet moves about the Sun in an elliptical orbit with its closest approach to the Sun being 0.59 A.U. and its farthest distance being 35 A.U. If the comet's speed at closest approach is 54 km/s, what is its speed when it is farthest from the Sun? [1 Astronomical Unit (A.U.) is the Earth-Sun distance.] (A) 3203 m/s (B) 910 m/s (C) 15 m/s (D) 13 m/s (E) 7011 m/s

複選題51. A rod of 0.3 m carries a current of I = 48.0 A in the direction shown in the figure and rolls along the rails with a constant speed. A uniform magnetic field of magnitude 0.25 T is directed perpendicular to the rod and the rails. What is the force acting on the rod? (A) 3.6 N (→) (B) 2.4 N (←) (C) 1.2 N (←) (D) 3.6 N (←) (E) 1.2 N (→)

52. Three point charges align along the x-axis as shown in the figure. What is the equilibrium position x of the charge q2. (The electrical constant is ke). (A) 0.45 m (B) 0.62 m (C) 0.36 m (D) 0.78 m (E) 0.59 m

53. Two parallel thin planes of charge electrical charge density 2.5✖108 C/m2 . What is the electric field in the region between the two planes? Assume that the vacuum electric permittivity is (A) (B) (C) (D) (E)

55. An AC generator consists of 6 turns of a wire. Each turn has an area of 0.040 m2 . The loop rotates in a uniform field (B = 0.20 T) at a constant frequency of 50 Hz. What is the maximum induced emf? (A) 2.4 V (B) 3.0 V (C) 4.8 V (D) 13 V (E) 15 V

56. It is known that the magnetic field of 0.17 T can cause an ion to move in a circular orbit of radius 2 m. Find the radius of circular orbit of a ion with identical velocity in the same magnetic field. (Ion moves in direction perpendicular to the magnetic field.) (A) 0.12 m (B) 0.25 m (C) 0.34 m (D) 0.52 m (E) 0.72 m

57. What is the electric flux through a surface in between two parallel planes shown in the figure if w = 2 cm, l = 5 cm, E = 500 N/C and θ = 30°? (A) 0.52 N⋅m2 /C (B) 0.26 N⋅m2 /C (C) 0.81 N⋅m2 /C (D) 0.43 N⋅m2 /C (E) 0.36 N⋅m2 /C

58. A solenoid with 200 turns of copper wires is operated by a 1000 V power supply and must be 25 cm long. What is the magnitude of magnetic field that is created in the solenoid? (The resistance of Cu wire is 0.2 Ω and the permeability T⋅m/A) (A) 5.03 T (B) 3.21 T (C) 7.84 T (D) 4.58 T (E) 4.36 T

59. For a convex mirror with radius of curvature R = 10 cm, if an object is placed 15 cm in front the mirror, what is the magnification of the image and is it a real or virtual? Upright or inverted? (mirror’s equation: 1/p+1/q = 2/R) (A) 3.75 cm (virtual behind mirror) and M = 0.25, inverted (B) 7.50 cm (virtual behind mirror) and M = 0.5, upright (C) 3.75 cm (real in front mirror) and M = 0.5, inverted (D) 7.50 cm (real in front mirror) and M = 0.25, inverted (E) 3.75 cm (virtual behind mirror) and M = 0.25, upright

複選題60. For a bi-concave thin lens, the radii of curvature are 10 and 20 cm. If an object is placed 15 cm in front of the mirror, what is the magnification of the image and is it a real or virtual? Upright or inverted? (thin lens’ equation: 1/p+1/q = (n−1)(1/R1−1/R2), the refractive index of glass is 1.5). (AB) 9.72 cm (virtual behind mirror) and M = 0.64, inverted (AC) 11.64 cm (virtual behind mirror) and M = 0.58, inverted (AD) 10.91 cm (virtual in front mirror) and M = 0.73, upright (AE) 8.69 cm (real in front mirror) and M = 0.25, inverted (BC) 12.45 cm (virtual behind mirror) and M = 0.53, upright (BD)一律送分