51. An infinite long wire is charged uniformly with line charge density λ. What is the electric field at a point with a distance y from the stick? (Electric constant is ε₀)
(A)
(B)
(C)
(D)
(E)

47. An ideal parallel-plate capacitor connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. The plates are pulled apart to a separation from d to 2d while the capacitor remains connected to the battery. After the plates are 2d apart, what are the magnitude of the charge on the plates and the potential difference between them? (A) 0.5Q0, 0.5V0 (B) 0.5Q0, V0 (C) Q0, V0 (D) 2Q0, V0 (E) 2Q0, 2V0

48. A group of identical capacitors is connected first in series and then in parallel. The combined capacitance in parallel is 100 times larger than for the series connection. How many capacitors are in the group? (A) 5 (B) 10 (C) 50 (D) 100 (E) 200

49. A cylinder contains n mol of helium gas (ideal monatomic gas) at a temperature of 300 K. The universal gas constant is R ( ) , where is Avogadro’ number and is Boltzmann’s constant. If the gas is heated at constant pressure, how much energy must be transferred by heat to the gas after it is heated to 500 K? (A) 200n? (B) 300n? (C) 500n? (D) 800n? (E) 1000n?

50. The switch is connected to position a for a long time interval as shown in the figure. At t = 0, the switch is thrown to position b. After this time, what are the frequency of oscillation of the LC circuit? (A) 159 Hz (B) 359 Hz (C) 559 Hz (D) 759 Hz (E) 959 Hz

52. A charge +q is at the position a and a second charge – q is placed at – a as shown in the figure. What is the limiting form of the electric field for x ≫ a? (Coulomb’s constant is )  (A) (B) (C) (D) (E)

53. A 30-turn circular coil of radius 1 m and resistance 1 Ω is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = 0.1 t + 0.04 t2 , where B is in tesla and t is in second. Calculate the induced emf in the coil at t = 5 s. (A) 27 V (B) 37 V (C) 47 V (D) 57 V (E) 67 V

54. Electric currents I1 and I2 are flowing through two parallel electric wires which are separated apart by a distance ?. What is the force per unit length between the two parallel wires? (Magnetic constant is μ0) (A) (B) (C) (D) (E)

55. While you are under water in a pool, you look up and see objects above water in a circle of light with a radius ?. The rest of your vision is the color of the sides of the pool. Assume that the index of refraction of air is 1 and that of water is n. How deep are you in the pool? (A) (B)(C) (D) Rn (E)

56. The pupil of a cat’s eye narrows to a vertical slit of width 0.5 mm in daylight. Assume the average wavelength of the light is 500 nm. What is the angular resolution for horizontally separated mice? (A)(B)(C)(D) (E)

57. The focal length of a spherical, concave mirror is 8 cm. An object is placed at a distance of 24 cm in front of the mirror. How fast does the image move if the object starts to move at speed toward the concave mirror? (A) (B)(C) (D) (E)