12. The Fig. 6 shows the cross section of a long cylindrical conductor with radius a, which contains a long cylindrical hole of radius b. The central axes of the cylinder and the hole are parallel and are distance d apart. Current density j is uniformly distributed in the conductor with its direction along the z-axis. What is the magnetic field B in the hole?

where j = |j| is the magnitude of the current density, and eₓ, eᵧ, and eₓ are the unit vectors along x, y, and z-axes.

(A)
(B)
(C)
(D)
(E)

13. A parallel plate capacitor has rectangular plates of area A = 5 (cm²) separate by distance d = 0.5 (mm). If the potential difference between the plates changes at a rate of 10⁴ (volt/sec), what is the displacement current? (permittivity of vacuum ε₀ = 8.854 × 10⁻¹² (F/m)) (A) 8.854 × 10⁻⁴ (amp) (B) 4.427 × 10⁻⁸ (amp) (C) 1.771 × 10⁻⁷ (amp) (D) 4.427 × 10⁻⁷ (amp) (E) 8.854 × 10⁻⁸ (amp)

14. Consider a spherical capacitor which consists of two concentric conducting spheres. The radii of the inner and outer spheres are R₁ and R₂, respectively. What is its capacitance? (A) (B) (C)(D)(E)

15. A 10-kW radio antenna transmits at 100 MHz. Assume it radiates as a point source. Find the radiation pressure at a distance of 20 km. (A) 1.5 × 10⁻¹⁶ (Nt/m²) (B) 4.8 × 10⁻¹⁶ (Nt/m²) (C) 1.5 × 10⁻¹⁵ (Nt/m²) (D) 3.3 × 10⁻¹⁵ (Nt/m²) (E) 6.6 × 10⁻¹⁵ (Nt/m²)

16. An observer A stands on the ground with clock CA and an observer B sits on an airplane with clock CB. The airplane moves with a velocity v with respect to the ground. Consider the relativistic time dilation effect, which one of the following descriptions is correct? (A) The observer A finds that Cₐ counts faster than CB, but the observer B finds that CB counts faster than CA. (B) The observer A finds that CA counts slower than CB, but the observer B finds that CB counts slower than CA. (C) Both A and B find that CA counts faster than CB. (D) Both A and B find that CA counts slower than CB. (E) Both A and B find that CA counts as fast as CB.

17. Which one of the following physical quantities is associated with the electron spin? (A) kinetic energy (B) angular momentum (C) electric charge (D) temperature (E) magnetic moment

18. Which one of the following descriptions of the matter wave Ψ(x, t) is correct? (A) The mass distribution of a particle at position x and time t is proportional to the value of Ψ(x, t). (B) The mass distribution of a particle at position x and time t is proportional to the value of |Ψ(x, t)|. (C) The mass distribution of a particle at position x and time t is proportional to the value of |Ψ(x, t)|². (D) The probability of finding the particle at position x and time t is proportional to the value of |Ψ(x, t)|. (E) The probability of finding the particle at position x and time t is proportional to the value of |Ψ(x, t)|².

19. Which one of the following reactions is nuclear fusion? (A) (B) (C) (D) (E)

20. Which one of the following reactions is β-decay? (A) (B) (C) 2 H₂O + O₂ → 2 H₂O (D) (E)

1. The Planck constant has the same SI unit as: (A) energy (B) momentum (C) power (D) angular momentum (E) torque

2. The ratio of the centripedal acceleration to the gravitational acceleration of a person standing on the earth surface around equator is about: (A) 0.003% (B) 0.03% (C) 0.3% (D) 3% (E) 30%

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