12.Consider a particle traveling in the potential step shown in the figure. What is the correct wavefunction for the particle at x ＜ 0?

(A) Ae^ikx + Be^-ikx
(B) Ae^ikx
(C) Ae^-ikx
(D) Ae^-ikx
(E) Ae^-ikx + Be^-ikx

1.In the figure shown on the right, a wire is extended from y = -(a+L) to y = a+L and is bent as a semicircle in the xy plane. If the wire carries a current I flowing along the direction indicated by the arrows and the magnetic flux density B in the region is along the +z direction, determine the magnetic force acting on the semicircular arc with the following parameters: I = 2 A, B = 5 T, a = 1 m, L = 2 m. (A) 10 Nt (B) 20 Nt (C) 30 Nt (D) 40 Nt (E) 5 Nt

2.In free space with the permittivity of ε₀, there are two point charges of Q₁ = q and Q₂ = 6q located at (0, 2r, r) and (r, 0, 3r) in rectangular (Cartesian) coordinate system. what is the magnitude of the force experienced by Q₂?(A) (B) (C) (D) (E)

3.On the right is the cross-sectional view of a hollow and infinitely long conductor. The conductor is placed along the z axis and carries a current of 6 A in the +z direction. If the inner and the outer radii are respectively 2 cm and 4 cm (i.e. a=2 cm and b=4 cm), what is the magnitude of the magnetic field intensity at r = 3 cm? (A) 5/12π T/cm (B) 2/5π T/cm (C) 0 T/cm (D) 3/5π T/cm (E) 5/12π T/cm

4.A uniform plane wave is traveling in free space with the electric field intensity: = 12 cos(ωt + 5z) , where ω is the frequency, k is a constant, and is the unit vector in x direction. What is the propagation velocity of the wave?(A) 3×10⁸ m/s (B) 1.8×10⁹ m/s (C) -3×10⁸ m/s (D) -1.8×10⁹ ẑ m/s (E) -1.8×10⁹ m/s

5.In a perfect dielectric medium with the permeability of μ, there exists an electric field given as: = E₀ cos(ωt + kz) . What is the magnetic field (H) in the region?(A) (B) (C) (D) (E)

6.A long core-shell structure is made to transmit an optical wave through total internal reflection within the core region. If the refractive indices for the core and the shell are respectively n₁ = 1 and n₂ = 2 as depicted in the figure, what is the maximum value of the angle θ for a successful transmission? (A) 30° (B) 60° (C) 45° (D) 90° (E) None of the above

7.An object is placed at the position being 12 cm from a convex lens with the focal length of 10 cm. What is the possible distance between the image and the lens?(A) 5 cm (B) 10 cm (C) 15 cm (D) 20 cm (E) 25 cm

8.The spherical waves of wavelength λ emitted from a single point source are passing through two small holes, S₁ and S₂, which are separated by the distance of a, as shown in the figure. If a ＞＞ s, what is the approximated condition for destructive interference at a point P on the screen? (A) b tanθ = 1.5λ (B) a sinθ = 1.5λ (C) a sinθ = λ (D) b tanθ = λ (E) a sinθ = λ

9.A particle is strictly confined in a region of length L, but moving freely in the region. The wavefunction of the particle is shown on the right. If the total energy of the particle is 4 eV, what is its total energy when the length of the region is shrunk to be 0.5L? (A) 2 eV (B) 8 eV (C) 16 eV (D) 12 eV (E) 20 eV

10.An electron is trapped in a quantum well with the width of 10 nm, in which the first three energy states are E₁ = 3.7 meV, E₂ = 14.8 meV, and E₃ = 33.3 meV. A photon is emitted when the electron is transferred from energy level E₃ to E₂. what is the wavelength of the photon?(A) 98.12 μm (B) 111.71 μm (C) 41.89 μm (D) 27.98 μm (E) 67.03 μm

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