25. Ion channels are narrow pores that allow ions to pass through cell membranes. A particular channel has a circular across section 0.15 nm in radius; it opens for 1 ms and passes 1.0 × 10⁴ singly ionized potassium ions. What is the current density in the channel? Note that one elementary charge is about 1.6 × 10⁻¹⁹ C.
(A) 5.0 × 10⁶ A/m²
(B) 2.5 × 10⁷ A/m²
(C) 5.0 × 10⁷ A/m²
(D) 7.5 × 10⁷ A/m²
(E) 1.0 × 10⁸ A/m²

26. Because the magnetic force depends on velocity but the electric force doesn’t, it’s possible to use perpendicular electric and magnetic fields to select charged particles with a particular velocity. A such velocity selector uses a 20-mT magnetic field perpendicular to a 2-kN/C electric field. At what speed will charged particles pass through the selector undeflected? (A) 20 km/s (B) 40 km/s (C) 80 km/s (D) 100 km/s (E) 200 km/s

27. The design of an airplane wing causes the speed of the airflow above the wing to be greater than that below it. If both the upper and lower surface areas of the wing are A, the air density is ρ, the flow speed above is v₁, and the flow speed below is v₂ (v₁ ＞ v₂), what is the approximate magnitude of the lift force experienced by the wing? (A) (1/2)ρA(v₁ - v₂)² (B) (1/2)ρA(v₁² - v₂²) (C) ρA(v₁ - v₂) (D) ρA(v₁² - v₂²)

28. An air bubble rises from the bottom of a lake to the surface. Assuming the lake water temperature is uniform and treating the air inside the bubble as an ideal gas, the volume of the bubble at the surface becomes 3 times its volume at the bottom. Given that atmospheric pressure is equivalent to the pressure of a 10-meter column of water, what is the approximate depth of the lake in meters? (A) 10 m (B) 20 m (C) 30 m (D) 40 m

29. Coronal streamers in the Sun’s atmosphere contain magnetic fields in the opposite directions. The figure shows a model calculation of the magnetic field in a single streamer. The long dimension of the rectangular loop in the figure is400 Mm, and the magnetic field strength near the loop has a constant magnitude of 2 mT. What is the total current encircled by the rectangle? Note that the magnetic constant ?0 is 1.26 × 10−6 N/A2 .(A) 0 A (B) 103 A (C) 106 A (D) 109 A (E) 1012 A

30. In the emission spectrum of mercury, there is a spectral line at 404.66 nm produced by mercury atoms undergoing electronic transitions from n=7 to n=6, where n is the principal quantum number. Since the upper level is threefold degenerate, in an external magnetic field the symmetry is broken and the degeneracy disappears, and thus the spectral line splits into three, as shown in the figure. This spectroscopic phenomenon is ascribed to (A) Meissner effect (B) Stark effect (C) Raman effect (D) Hall effect (E) Zeeman effect. 。

31. With sufficient energy, it’s possible to eject an electron from an inner atomic orbital. A higher-energy electron will then drop into the unoccupied state, emitting a photon with energy equal to the difference between the two levels. For inner-shell electrons, photon energies are in the keV range, putting them in the X-ray region of the spectrum. These characteristic X-rays are labeled with the letter indicating the shell to which the electron drops, followed by a Greek letter indicating the higher level from which it drops; thus ?? designates a transition from the L shell to the K shell. Molybdenum’s X-ray spectrum has its ?? peak at17.4 keV. Note that Plank’s constant is 6.626 × 10−34 m2 ∙ kg/s, speed of light is 3 × 108 m/s, and one electron charge is 1.6 × 10−19 C. The corresponding X-ray wavelength is closest to (A) 10 pm (B) 30 pm (C) 70 pm (D) 150 pm (E) 200 pm.

32. A long ladder leans against a smooth vertical wall, with its base resting on a rough horizontal floor. Let the length of the ladder be L, its weight be W, and the angle it makes with the floor be θ (less than 90°). If the ladder is on the verge of sliding, what is the coefficient of static friction between the floor and the base of the ladder? (A) (1/2) tan θ (B) (1/2) cot θ (C) 2 tan θ (D) 2 cot θ

33. The circuit in the figure extends forever to the right, and all the resistors have the same value ?. What is the equivalent resistance measured across the two terminals at left? Note that ≈ 1.414, ≈ 1.732, ≈ 2.236, and≈ 2.646. (A) 1.57 ? (B) 1.62 ? (C) 1.67 ? (D) 1.72 ? (E) 1.77 ?

34. What is the function of the circuit in the figure if we focus on the voltage change across the resistor? Assume the RC time constant is large enough in the case. (A) As a step-up transformer (B) As a step-down transformer (C) As a DC power supply (D) As an AC power supply (E) As a photodiode

35. Phasor diagrams summarize phase and amplitude relations among passive components in AC circuits. A phasor is an arrow whose length represents the amplitude of an AC voltage or current, rotating counterclockwise with the angular frequency ω of the AC quantity. The phasor’s component on either axis represents the sinusoidally varying AC quantity. The figure shows the phasor diagram for an RLC circuit. Note that VRp is the peak value of the voltage across the resistor, VCp is the peak value of the voltage across the capacitor, and VLp is the peak value of the voltage across the inductor. About this RLC circuit, which of the following statement is correct? (A) The driving frequency is above resonance. (B) The driving frequency is about resonance. (C) The driving frequency is below resonance. (D) The driving frequency varies. (E) The driving frequency is dominantly determined by V?p.

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