41. What is the magnitude of the magnetic ficld at point P if a = R and b = 2R?  
(A)
(B)
(C)
(D)
(E)

37. When a cube is inscribed in a sphere of radius r, the length L of a side of the cube is L = . If a positive point charge Q is placed at the center of the spherical surface, the ratio of the electric flux Qsphere at the spherical surface to the flux Qcbe at the surface of the cube is(A)(B)(C) 1(D)(E)

38. For the potential Y = 3x2z - 2yz3, what is the corresponding electric field at the point (2,2,2)?(A)(B) (C) (D)  

39. A square loop (L = 0.20 m) consists of 50 closely wrapped turns, each carrying a current of 0.50 A. The loop is oriented as shown in a uniform magnetic field of 0.40 T directed in the positive y  direction. What is the magnitude of the torque on the loop?(A) 0.21 Nㆍm(B) 0.20 N ㆍm (C) 0.35Nㆍm(D) 0.12 N ㆍm(E) 1.73 N ㆍm

40. A bar magnet is dropped from above and falls through the loop of wire shown below. The north pole of the bar magnet points downward towards the page as it falls. Which statement is correct?  (A) The current in the loop always flows in a clockwise direction. (B) The current in the loop always flows in a counterclockwise direction. (C) The current in the loop flows first in a clockwise, then in a counterclockwise. direction. (D) The current in the loop flows first in a counterclock wise, then in a clockwise. direction. (E) No current flows in the loop because both ends of the magnet move through the. loop

42. A long wire carries a current of 3.0 A along the axis of a long solenoid (radius = 3.0 cm, n = 900 turns/m, current = 30 mA). What is the magnitude of the magnetic field at a point 2.0 cm from the axis of the solenoid? Neglect any end effects. (A)34 μT (B)64 μT (C)30 μT (D)45 μT (E)4.0 μT

43. A uniform magnetic field is applied perpendicular to the plane of a 60-turn circular coil with a radius of 6.0 cm and a resistance of 0.60 Q. If the magnetic field increases uniformly from 0.20 T to 1.8 T in 0.20 s, what is the magnitude of the emf induced in the coil? (A)7.2 V (B)5.4 V (C)9.2 V (D)12 V (E)16 V

44. A loop of wire (resistance = 2.0 mΩ) is positioned as shown with respect to a long wire which carries a current. If d = 1.0 cm, D = 6.0 cm, and L = 1.5 m, what current(I) is induced in the loop at an instant when the current in the wire is increasing at a rate of 100 A/s? (A)34 mA(B)30 mA(C)27 mA(D)38 mA(E)0.50 mA

45. A conducting rectangular loop of mass M, resistance R, and dimensions a x b is allowed to fall from rest through a uniform magnetic field which is perpendicular to the plane of the loop. The loop accelerates until it reaches a terminal speed (before the upper end enters the magnetic field). If a = 2.0 m, B = 6.0 T, R= 40 2, and M = 0.60 kg, what is the terminal speed? (A) 1.6 m/s (B) 20 m/s (C) 2.2 m/s (D) 26 m/s (E) 5.3 m/s

46. A conducting sphere of radius R carries an excess positive charge and is very far from any other charges. Which one of the following graphs best illustrates the potential (relative to infinity) produced by this sphere as a function of the distance r from the center of the sphere? (A)(B)(C)(D)(E)

47. A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity). if the sphere's radius were twice as large, but the charge on the sphere were the same, what would be the potential on the surface relative to infinity? (A) 50 V (B) 25 V (C) 100 V (D) 200 V (E) 150 V