13. Positive charge Q is distributed uniformly throughout an insulating sphere of radius R, centered at the origin. A positive point charge Q is place at x = 2R on the x axis. The magnitude of the electric field at x = R/2 on the x axis is:
(A) Q/(4πε₀R²)
(B) Q/(8πε₀R²)
(C) 17Q/(72πε₀R²)
(D) Q/(72πε₀R²)
(E) none of these.

9. The displacement of a string carrying a traveling sinusoidal wave is given by y(x,t) = (kx – wt – φ). At time t = 0 the point at x = 0 has velocity v0 and displacement y0. The phase constant φ is given by tan (A) ν0/ωγ0 (B)ων0/γ0 (C) wy0/v0 (D) y0/ων0 (E) 0.

10. Consider the following processes: The temperature of two identical gases are increased from the same initial temperature to the same final temperature. Reversible processes are used. For gas A the process is carried out at constant volume while for gas B it is carried out at constant pressure. The change in entropy: (A) is greater for A only if the initial pressure of gas A is higher than gas B (B) is the same for A and B (C) is greater for A (D) is greater for B (E) can't be compared without more information.

11. Two identical conducting spheres, "1" and "2", carry equal charge. They are separated by a distance much larger than their diameters. A third identical conducting sphere, "3", is uncharged. Sphere "3" is first touched to "1", then to "2", and finally removed. As a result, the electrostatic force between "1" and "2", which was originally F, becomes: (A) F/2 (B) F/4 (C) F/18 (D) 3F/8 (E) 0.

複選題12. The diagram shows the electric field lines due to two charged parallel metal plates. Then:  (A) the upper plate is positive and the lower plate is negative (B) a positive charge placed at X would experience a greater force than if it were placed at Z (C) a positive charge placed at X would experience the same force if it were placed at Y (D) a positive charge placed at X would experience less force than if it were placed at Z (E) a negative charge at X could have its weight balanced by the electrical force.

14. An electron has charge - e and mass m. A proton has charge e and mass 1840 m. A "proton volt” is equal to: (A) 1840 eV (B) 1 eV (C) (1/1840) eV (D) √1840 eV (E) (1/√1840) eV.

15. A certain x-ray tube requires a current of 7 mA at a voltage of 80 kV. The power (in watts) dissipated is: (A) 5600 (B) 560 (C) 26 (D) 11.4 (Ε) 87.5.

16. A charged capacitor is being discharged through a resistor. At the end of one time constant the charge has been reduced by (1 – 1/e) = 63% of its initial value. At the end of two-time constants the charge has been reduced by what percent of its initial value? (A) 82% (B) 100% (C) 86% (D) between 90% and 100% (E) 40%

17. A proton, traveling perpendicular to a magnetic field, follows a circular path with the same radius as an alpha particle which is also traveling perpendicular to the same field. The ratio of their speeds, v proton/v alpha is: (A) 0.5 (B) 4 (C) 1 (D) 2 (Ε) 8.

18. 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) g(E)

19. An unmagnetized steel bar is placed inside a solenoid. As the current in the solenoid is slowly increased from zero to some large value, the magnetization of the bar: (A) increases proportionally with the current (B) remains zero for a while and then increases linearly with any further increase in current (C) is unaffected by the current (D) increases with increasing current at first but later is much less affected by it (E) increases quadratically with the current.