※ [本文转录自 NTU-Exam 看板] 作者: yaujack (大头) 看板: NTU-Exam 标题: [试题] 94下 苏德润 普通物理甲下 期末考 时间: Fri Jun 23 20:46:34 2006 课程名称︰普通物理学甲下 课程性质︰机械系必修 课程教师︰苏德润 开课系所︰物理系 考试时间︰94-06-23 是否需发放奖励金： 是 （如未明确表示，则不予发放） 试题 : 1. (a) The energy function of a free particle is E = K + V = p^2/2m + V(x) What is the momentum p of a matter wave in terms of the wavelength λ? In turn, what is p as a function of the angular wave number k = 2π/λ? What is the angular frequency ω of this E so that the wave function is ψ is proportional to exp(-iωt). Thus the energy function or the Hami- ltonian function is in form of E = E (k,x) = (h^2 k^2 / 8 π^2 m) + V (x) = H (k,x) (b) What is then the Schrodinger equation Hψ = Eψ when we replace k^2 = -d^2 / dx^2. The Schrodinger equation is a differential equation. 2. For a long solenoid of cross-sectional area A, length l, carryling a current i, the energy stored per unit volume is u = U / Al Since U = 1/2 Li^2 for inductance L. What is (a) u in terms of n,i? (b) u in terms of B at any point where the magnetic field is B. Hint: for a solenoid L = (μ_o)Aln^2. 3. In Figure (in the problem of 28-7 in the textbook), an electron accelerated from rest through potential difference V_1 = 1.00kV enters the gap between two parallel plates having separation d = 20.0mm and potential difference V_2 = 100V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap? 4. In Figure (in the problem 68 of Ch33), two light rays pass from air through five layers of transparent plastic and then back into air. The layers have parallel interfaces and unknown thicknesses; their indexes of refraction are n_1 = 1.7, n_2 = 1.6, n_3 = 1.5, n_4 = 1.4, and n_5 = 1.6. Ray b is in- cident at angle θ=20 defrees. Relative to a normal at the last interface, at what angle do (a) ray a and (b) ray b emerge? Hint: Solving the problem algebraically can save time.) If the air at the left and right sides in the figure were, instead, glass with index of refraction 1.5, at what angle would (c) ray a and (d) ray b emerge? (Use sin A = A, A～20 degrees in radian, 1 radian～57 degrees) 5. Figure 29-16a (in the textbook) shows the cross section of a long conduction cylinder with inner radius a = 2.0cm and outer radius b = 4.0cm. The cylinder carries a current out of the page, and the magnitude of the current density in the cross section is given by J = cr^2, with c = 3.0×10^6 A/m^4 and r in meters. What is the magnetic field B at a point that is 3.0cm from the central axis of the cylinder? μ_o = 4π×10^-7 Tm/A --

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