108年 - 108 國立臺灣大學_碩士班招生考試試題：普通物理學#139136

(a).Suppose that the cylinder is sliding without rolling down the smooth inclined face of the wedge, and the wedge is free to move on a horizontal plane with friction. How far has the wedge moved by the time the cylinder has descended from a rest a vertical distance h?Ans：___(1)____

(b). Now suppose that the cylinder is free to roll down the wedge without slipping. The horizontal plane is still without friction. How far does the wedge move in this case?Ans：___(2)____

2. A particle of mass m with a velocity of v collides elastically with the end of a uniform thin rod of mass M. (The other end of the rod is fixed.) The length of M is L. After the collision, m is stationary. In the case, determine the mass of M.Ans：___(3)____

3. A girl holds a tuning fork vibrating at 400 Hz and walks at 10 m/s away from a wall. What beat frequency does he hear between the fork and the echo? The speed of sound is 330 m/s.Ans：___(4)____

4. Calculate the minimum coefficient of friction necessary to keep a thin circular ring from sliding as it rolls down a plane inclined at an angle θ with respect to the horizontal plane.Ans：___(5)____

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6. An electric dipole consists of two equal and opposite charges (+q) separated by a distance d. Find the approximate electric potential at point P. (d ＜＜ r)Ans：___(9)____

7. The total energy of a uniformly charged spherical shell of total charge q and radius R.Ans：___(10)____

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9. A long, straight coaxial cable has an inner wire of radius a with a surface charge density σ₁ and an outer cylindrical shell of radius b with σ₂. Find the relationship between σ₁ and σ₂ for the field strength to be zero outside the cable.Ans：___(13)____

10.The space between the plates of a parallel-plate capacitor is filled with two dielectrics K₁, к₂ of equal size, as shown in figure. What is the resulting capacitance in terms of k₁, K₂, and Co, the capacitance with a vacuum between the plates? (K₁, к₂ are dielectric constants) Ans：___(14)____

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)____

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)____

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)____.

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)____

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?

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

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%).

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

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.