課程名稱︰普通物理學甲下 課程性質︰必帶 課程教師︰林敏聰教授 開課學院：理學院 開課系所︰ 考試日期（年月日）︰100.06.24 考試時限（分鐘）：10:00 ~ 17:00 是否需發放獎勵金：是 （如未明確表示，則不予發放） 編按 : * 下標以底線作區隔, 如 Xo 會寫成 x_0 * 一些特殊的符號採用如下的記法 圓周率 = /pi, 真空磁導率 = /mu_0, 真空電容率 = /eps_0 試題 : 1. Please derive the relation of c = (/mu_0 * /eps_0)^(-1/2) and E/B = c in a traveling electromagnetic wave in application of Maxwell's equations. (10%) 2. A square loop of wire of edge length a carries current i. Show that, at the center of the loop, the magnitude of the magnetic field produced by the current is 2√2*/mu_0*i B = --------------. (10%) /pi*a 3. Derive the differential equation of a RLC in series circuit and find q(t) at the following conditions: (a) There is no damping, i.e., R = 0. (5%) (b) Under damping: /alpha < /omega_0 (/omega_0 = 1/√(LC), /alpha = R/2L is called damping factor) (5%) (c) Set q(0) = Q. Calculate the energy-loss per second of the above two cases at the steady-state. (5%) (Hint: let q(t) = q_0 * e^(/lamda * t) feed into the differential equation and then solve /lamda) 4. Consider an arbitrary charge distribution /rho(r) within a volume V. Please express the electric potential /phi(r) with terms of monopole charge, dipole moment, and quadrupole moment. (10%) (Hints: using binomial expansion). 5. A wire with mass m, length L is suspended by a pair of flexible leads in a uniform magnetic field of magnitude B. What are the magnitude and direction (left or right) of the current required to remove the tension in the supporting leads? (10%) ----+------------------+---- | | # = flexy lead (spring) # x x x x # D = wire # # x = magnetic field L__DDDDDDDDDDDDDD__J x x x x 6. Please try to use the concept of band structure to explain the different conductivity behavior and their temperature dependence for conducting metal and semiconductor. Please also compare the different pictures for describing electric transport in classic and modern physics. (10%) 7. Explain the concept of duality, and give two examples (described in details, please) for the "wave" behaving as "particle" and "particle" as "wave", respectively. Finally, if someone asks: "'Is' the light or the electron 'particle' or 'wave'?" What would your answer be? (10%) 8. Please use the Bragg relation in a low energy electron diffraction experiment to express the vertical interlayer distance d by the primary energy of the electron E_p, electron mass m, and the incident angle /theta with respect to the sample surface. (10%) 9. (a) Please write down the Schrodinger equation with a one-dimensional potential well with infinite height and width d for a particle of energy E (5%) (b) Find out the solution of the wave function and energy. (We call the solution of wave function and energy eigenfunction and eigenenergy, respectively.) (10%) (c) What is the minimal energy of the particle existing in this quantum well (called ground state)? (5%) (d) Please estimate the minimal temperature at which the particle may stay at higher energy state than ground state. (10%) (e) Give a brief interpretation of your solution with comparison of classic physics.(10%) 10. Good luck and Have a nice summer vacation !!! (Total 125%) -- 如有錯誤 還煩請告知或站內信 感激不盡 --

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