14. The wave function for a particle must be normalizable because
(A) the particle must be somewhere.
(B) the particle's angular momentum must be conserved.
(C) the particle's charge must be conserved.
(D) the particle's momentum must be conserved.
(E) the particle cannot be in two places at the same time.

15. In the circuit shown in the figure, the capacitors are initially uncharged. The switch is first thrown to position A and kept there for a long time. It is then thrown to position B. Let the charges on the capacitors be Q1, Q2, and Q3 and the potential differences across them be V1, V2, and V3. Which of the following conditions must be true with the switch in position B?(A) Q1=Q2=Q3,(B) V2=V2=V3,(C)V1+V2=V3,(D) Q1+Q2 =Q3, (E) V3 =V0

16. Two long conducting cylindrical shells are coaxial and have radii of 20 mm and 80 mm. The electric potential of the inner conductor, with respect to the outer conductor, is +600 V. What is the maximum electric field magnitude between the cylinders? (k = 1/4πεo = 8.99 x 109Nㆍm2/C2) (A) 22,000 V/m, (B) 18,000 V/m, (C) 10,000 V/m, (D) 14,000 V/m, (E) 26,000 VIm.

17. In a certain region, the electric potential due to a charge distribution is given by the equation V(x.y) = 2xy - x2 - y, where x and y are measured in meters and V is in volts. At which point is the electric field equal to zero? (A) x=0.5 m,y=0.5 m (B) x=0m,y=0m (C) x=1m,y=1m (D) x=0.5 m,y=1 m (E) x=1m,y=0.5m

18. A long straight very thin wire on the y-axis carries a 10-A current in the positive y-direction. A circular loop 0.50 m in radius, also of very thin wire and lying in the yz-plane, carries a 9.0-A current, as shown. Point P is on the positive x-axis, at a distance of 0.50 m from the center of the loop. What is the magnetic field vector at point P due to these two currents? (μ0 =4πx 10-7 T m/A) (A) zero (B) -8.0 x10-6Tk (C)(+4.0x10-6T)i- (4.0 x10-6T)k (D) (-8.0x10-6T)i - (8.0 x 10-6T)k (E)(-4.0x10-6T)i-(4.0 x10-6T)k

19. Wire is wound on a square frame, 30 cm by 30 cm, to form a coil of 7 turns. The frame is mounted on a horizontal shaft through its center (perpendicular to the plane of the diagram), as shown in the figure. The coil is in clockwise rotation, with a period of 0.060 s. A uniform, horizontal, magnetic field of magnitude 0.40 T is present. At a given instant, the plane of the coil forms a 60° angle with the horizontal, as shown. At that instant, what is the magnitude of the emf induced in the coil? (A) 2.1 V,(B) 23 V, (C) 26 V, (D) 3.6 V, (E) 13 V.

20. An LRC series circuit has R = 15.0 Ω, L = 25.0 mH, and C = 30.0 μF. The circuit is connected to a 120-V (rms) ac source with frequency 200 Hz. (A) The impedance of the circuit is 163 Ω, (B) The rms current in the circuit is 7.16 A, (C) The rms voltage across the resistor is 110V, (D) The rms voltage across the inductor is 239 V, (E) The rms voltage across the capacitor is 123 V

21.Some properties of glass are listed here.   glass window pane is 2.7 m high, 2.4 m wide, and 2.0 mm thick. The temperature at the inner surface of the glass is 22℃ and at the outer surface 4.0℃. How much heat is lost each hour through the window under steady state conditions? (A)1.7x108J,(B)4.7x104J,(C)1.7x106J,(D) 1.7 x 105 J,(E)4.7 x 101 J.

22. When an electromagnetic wave falls on a white, perfectly reflecting surface, it exerts a force F on that surface. If the surface is now painted a perfectly absorbing black, what will be the force that the same wave will exert on the surface? (A) F/2,(B) F, (C) F/4, (D)4F,(E) 2F.

23. A microwave oven operates with sinusoidal microwaves at a frequency of 2400 MHz. The height of the oven cavity is 25 cm and the base measures 30 cm by 30 cm. Assume that microwave energy is generated uniformly on the upper surface of the cavity and propagates directly downward toward the base. The base is lined with a material that completely absorbs microwave energy. The total microwave energy content of the cavity is 0.50 μJ. What is the amplitude of the electric field? (c = 3.00 x 108m/s, μ0 = 4πx 10-7 T m/A, ε0 = 8.85 x 10-12 C2/N m2)(A)  2500 V/m, (B) 1900 V/m, (C) 2200 V/m, (D) 2800 V/m, (E) 1600 V/m.

24. A 1.0-kg block and a 2.0-kg block are pressed together on a horizontal frictionless surface with a compressed very light spring between them. They are not attached to the spring. After they are released and have both moved free of the spring (A) both blocks will have equal speeds. (B) the magnitude of the momentum of the heavier block will be greater than the magnitude of the momentum of the lighter block. (C) the lighter block will have more kinetic energy than the heavier block. (D) the heavier block will have more kinetic energy than the lighter block. (E) both blocks will both have the same amount of kinetic energy.

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