12. 10C (Coulomb) of charge are placed on a spherical conducting shell. A particle with a charge of -3C is placed at the center of the cavity. The net charge on the outer surface of the shell is:

(A)-7C

(B)-3C

(C)0C

(D)+3C

(E)+7C

13. In the circuit shown, both resistors have the same value R. Suppose switch S is initially closed. When it is then opened, the circuit has a time constant \( \tau_a \). Conversely, suppose S is initially open. When it is then closed, the circuit has a time constant \( \tau_b \). The ratio \( \tau_a / \tau_b \) is(A)1(B)2(C)0.5(D)0.667(E)1.5

14. The field just outside the surface of a long conducting cylinder which has a 2.0-cm radius points radially outward and has a magnitude of 200 N/C. What is the charge density on the surface of the cylinder?(A)2.7 nC/m²(B)1.8 nC/m²(C)3.5 nC/m²(D)4.4 nC/m²(E)0.90 nC/m²

15. Positive charge Q is placed on a conducting spherical shell with inner radius \( R_1 \) and outer radius \( R_2 \). A point charge q is placed at the center of the cavity. The magnitude of the electric field at a point outside the shell, a distance r from the center, is(A)\( Q / 4\pi\varepsilon_0 R_2^2 \)(B)\( Q / 4\pi\varepsilon_0 (R_2^2 - r^2) \)(C)\( q / 4\pi\varepsilon_0 r^2 \)(D)\( (q+Q) / 4\pi\varepsilon_0 r^2 \)(E)\( (q+Q) / 4\pi\varepsilon_0 (R_2^2 - r^2) \)

16. A fisherman starts his outboard motor by applying a steady tangential force of 100 N by means of a starter rope. The flywheel has a moment of inertia of 0.05 kg·m² and a diameter of 0.2 m. Ignoring the effects of friction and the opposing torque due to the compression of the motor, what is the angular speed of the flywheel after it has turned through half a revolution starting from rest?(A)35.4 rad/s(B)50.1 rad/s(C)1256.0 rad/s(D)125.6 rad/s(E)24.5 rad/s

17. A magnetic field CANNOT:(A)exert a force on a charge(B)accelerate a charge(C)change the momentum of a charge(D)change the kinetic energy of a charge(E)change the velocity of a charge

18. A charged particle (m = 2.0 g, q = -50 μC) moves in a region of uniform field along a helical path (radius = 4.0 cm, pitch = 8.0 cm) as shown. What is the angle between the velocity of the particle and the magnetic field?(A)27°(B)72°(C)63°(D)18°(E)58°

19. A conductor of radius r, length ℓ and resistivity ρ has resistance R. It is melted down and formed into a new conductor, also cylindrical, with one fourth the length of the original conductor. The resistance of the new conductor is(A)\( \frac{1}{16} \)R(B)\( \frac{1}{4} \)R(C)R(D)4R(E)16R

20. A square loop of wire moves with a constant speed v from a field-free region, through a region of uniform B field as shown. Which of the five graphs correctly shows the induced current I in the loop as a function of time t?(A)(B)(C)(D)(E)

21. The coulomb is the same as (A : ampere, s : second, M : mass, T : temperature)(A)A·s(B)A/s(C)T·A/M(D)T/M(E)none of the above

22. A 2-μF capacitor in series with a 2-k resistor is connected to a 60-Hz ac source. Calculate the impedance of the circuit.(A)1500 ohms(B)1800 ohms(C)2100 ohms(D)2400 ohms(E)8600 ohms

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