計算題（每題二十五分）
An electric field is directed out of the page within a circular region of radius R=3.00 cm. The magnitude of the electric field is given by E = (0.500 V/m·s)(1-r/R)t, where t is in seconds and r is the radial distance (r ≤ R). What is the magnitude of the induced magnetic field at radial distance (a) 2.00 cm and (b) 5.00 cm?

二. 計算題 (每題二十五分)A block of mass M is connected to a spring of mass m and oscillates in simple harmonic motion on a horizontal, frictionless track. The force constant of the spring is k, and the equilibrium length is L. Find (a)(10%) the kinetic energy of the system when the block has a speed v, and (b)(10%) the period of oscillation. (Hint: Assume that all portions of the spring oscillate in phase and that the velocity of a segment dx is proportional to the distance x from the fixed end)

D. Quantum Physics: [10%] Solve Schrodinger's equation for an electron trapped in a one-dimensional infinite potential well of width L and impose the boundary condition that the solutions be zero at the infinite walls.

C. Electromagnetism: [10%] Describe the physical significance of the Maxwell's equations, and describe the physical meaning of 'Displacement current'.

2. An ideal gas undergoes a path from A (P1, V1) to B (P2, V2) adiabatically, B (P2, V2) to C (P2, V1) isobarically, and C to A at constant volume V1. Plot the P-V figure (2%) and calculate the efficiency of the cycle (8%).

1. One mole ideal gas is changed from temperature T1 and molar volume V1 to T2 and V2. Write down the change in entropy.

二、計算題:(A. Damped Simple Harmonic Oscillation: [6%] A car's suspension system acts like a damped simple harmonic oscillating system. The damped mass-spring system is with mass m=100 kg and the spring constant k=50 N/m. A car's shock absorber system provides a damping constant b=200 kg/s. If the car hits an accident, how many oscillations will it make before the amplitude drops to half its initial value?

14. An LED is constructed from a p-n junction based on a certain Ga-As-P semiconducting material whose energy gap is Eg. What is the wavelength of the emitted light?Ans：___(18)____

13. A plane wave of monochromatic light with wavelength A in vacuum is incident on two slits of equal width w, as shown schematically blow. A pattern is observed on a screen a large distance away. The intensity of the light at the central (θ = 0) is initially I. If one slit is blocked, the intensity is ___(17)____.

12. Place a DVD on a flat surface. A laser, with a wavelength of λ, points to the DVD and the ray is perpendicular to the DVD. First-order maxima appeared on a wall at a distance of x cm from the DVD and at a height of d cm. What is the distance between two adjacent recording tracks on the DVD?Ans：___(16)____

11. The current density in a cylinder of radius R is given by J = Kr, where K is a constant. What is the magnetic field within the cylinder?Ans：___(15)____

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