9. A standing light wave is composed by two counter-propagating plane waves. The electric field is written as E_standing(r, t) = E₁(r, t) + E₂(r, t), where E₁(r, t) = E₀ cos(kz − ωt) e_x and E₂(r, t) = E₀ cos(−kz − ωt) e_x. Find the magnetic field of the standing wave.
(A) B(r, t) = (2E₀/c) cos(kz) cos(ωt) e_z
(B) B(r, t) = (2E₀/c) cos(kz) cos(ωt) e_y
(C) B(r, t) = (2E₀/c) sin(kz) cos(ωt) e_y
(D) B(r, t) = (2E₀/c) cos(kz) sin(ωt) e_y

(E) B(r, t) = (2E₀/c) sin(kz) sin(ωt) e_y

1. Consider a cylindrical tank filled with water with 2.5-m depth. The water emerges from a small hole at the center of the bottom. The diameter of the hole is 1 mm. The cross-section area of the vertical water stream decreases as it falls. Find the diameter of the water stream at the position 7.5 m from the hole. (A) 0.23 mm(B) 0.36 mm(C) 0.50 mm(D) 0.58 mm(E) 0.71 mm

2. Three identical cylinders are stacked on a table as shown in the figure. Find the minimum value of the coefficient of static friction between the cylinder and the table surface. (A)(B)(C)(D)(E)

3. A cube rotates around one of its edges as shown in the figure. The mass of the cube is M and the side length is L. Find the moment of inertia of the cube about that axis. (A) (1/6)ML²(B) (1/3)ML²(C) (1/2)ML²(D) (2/3)ML²(E) (5/6)ML²

4. A man plays a Yo-Yo ball as shown in the figure. The mass of the ball is m, and the length of the string is L. The ball moves in a circle along a vertical plane. What is the difference of the string tension at the lowest point (T₂) and the highest point (T₁)? (A) T₂ − T₁ = 2mg(B) T₂ − T₁ = 3mg(C) T₂ − T₁ = 4mg(D) T₂ − T₁ = 5mg(E) T₂ − T₁ = 6mg

5. A parallel plate capacitor is composed of two circular plates of radius r = 40 mm separate by a distance d = 1 mm. The capacitor is charged that the potential difference between the plates changes at 10⁴ volt/sec. Find the displacement current in the capacitor?(A) 3.0 × 10⁻⁷ A(B) 3.5 × 10⁻⁷ A(C) 4.0 × 10⁻⁷ A(D) 4.5 × 10⁻⁷ A(E) 5.0 × 10⁻⁷ A

6. Consider a thermodynamic engine based on ideal gas. The operating cycle is shown in the pressure(P)-volume(V) diagram. The a→b and c→d are isochoric (constant volume) processes, and the b→c and d→a are adiabatic processes. Which one of the following statements is wrong? (A) During a→b, the heat flows from the engine to the surrounding.(B) During b→c, the temperature of the gas decreases.(C) During c→d, the internal energy of the gas decreases.(D) During d→a, the internal energy of the gas increases.(E) During d→a, the engine does negative work on the surrounding.

7. Continued from the last question, find the efficiency of this engine.  (Note: adiabatic process of ideal gas: PVᵞ= constant, γ = Cp/Cv, Cv: molar specific heat at constant volume, Cp: molar specific heat at constant pressure.)(A)(B)(C)(D)(E)

8. As shown in the right figure, a circuit is composed of a DC voltage source (V), two resistors (R₁ and R₂), one inductor (L), and a switch (S). Initially S is closed and the circuit is at steady condition, then S is opened at time t = 0. Find the current through the inductor as a function of time at t ＞ 0. (A)(B)(C)(D)(E)

10. The setup of photoelectric effect experiment is shown in the following figure. The anode is irradiated by light with intensity I and frequency f. The electric potential between the anode and cathode is controlled by a variable power supply with voltage V. The resulted current A is measured by an ampere meter. If we use two difference light sources with the same intensity I and different frequencies f₁ and f₂, where f₁ ＜ f₂, which one of the following current-voltage (A-V) diagrams is correct?(A)(B)(C)(D)(E)

11. Consider the following optical phenomena, which ones of them can be deduced from Fermat's principle of least time?(A) single slit diffraction(B) double slit interference(C) reflection law (The angle of incidence is equal to the angle of reflection.)(D) refraction law (Snell's law)(E) zero reflection at Brewster's angle

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