12. Which statement below is correct? (In the following, log denotes natural log.)
(A)
(B)
(C)
(D)
(E)

8. What is the minimum coefficient of friction necessary for the cylinder to roll without slipping down the ramp? (A)(B) (C) (D) (E)

9. What is the oscillating amplitude of ratioof m₂ (Δx₂) over m₁ (Δx₁)?(A) (B)(C) (D) (E)

10. What is the natural angular frequency of the system?(A)(B)(C)(D)(E)

11. Two infinite planes of constant surface charge densities σ1and σ2  are located at z = -1 and z = 1, respectively, both parallel to the x-y plane. What is the electric field in the range 1 ＞ z ＞ -1?(A)(B)(C)(D)(E) E = 0.

13. What is the electric potential for R1 ＞ r ＞ 0?(A) (B)(C)(D)(E)

14. What is the potential difference VC on the capacitor and the current IL on the inductor at t = 0+, instantaneously after the circuit is closed?(A)VC = 0, IL = 0.(B) VC = 0, IL = V0/R2. (C)VC = V0/R1, IL = 0. (D) VC = V0, IL = 0. (E) VC = V0, IL = V0/R2.

15. What happens in the limit t → ∞?(A)VC = 0, IL = 0. (B) VC = 0, IL = V0/R2. (C) VC = V0/R1, IL = 0.(D) VC = V0, IL = 0.(E)VC = V0, IL = V0/R2.

16. Which statement below is correct?(A) Two capacitors C1, C2 in parallel is equivalent to the capacitance of (C1-1+ C2-1), (B)The potential energy of a capacitorC at potential difference V equals CV2, (C) Maxwell’s equations imply charge conservation,(D) Maxwell’s equations imply the Lorentz force law. (E) The (volume) energy density for a magnetic field B in vacuum is

17. A background of magnetic field B(x, y) =(a + by)x is prepared on the x-y plane for given constants a and b. A rectangular loop (see figure) moves at a constant velocity v. The bottom of the loop coincides with the x axis, and its left side is at x = 0 when t = 0. What is the induced emf on the loop at time t? (z direction points out of plane.)(A) (a + bh)Lv clockwise. (B) (a + bh)Lv counter-clockwise. (C) (ah + bh2/2)Lv clockwise. (D) (ah + bh2/2)Lv counter-clockwise. (E) 0.

18. Which statement below is correct? (A) A point charge at constant velocity radiates due to Lorentz contraction. (B) A point charge in free fall in a gravitational field feels no back-reaction force. (C) A point charge in free fall does not radiate. (D) A radiation in an inertial frame may appear like vacuum in another inertial frame. (E) The energy radiated from an accelerating point charge per unit time is the same in every inertial frame.