※ [本文转录自 NTU-Exam 看板] 作者: Danceaway (瑶小五) 看板: NTU-Exam 标题: [试题] 94下 梁启德 普通物理学 期末考 时间: Fri Jun 23 22:54:00 2006 课程名称︰普通物理学甲 课程性质︰ 课程教师︰梁启德 开课系所︰材料系 考试时间︰2 hr 是否需发放奖励金：是，谢谢 （如未明确表示，则不予发放） Final examination (21/6/2006) 1. Please write down Maxwell;s equations. [Hint: There are four of them in total.] (20%) 2.A nonconducting sphere has mass 80.0g and radius 20.0 cm. A flat compact coil of wire with 5 turns is wrapped tightly aroundit, with each turn concentric with the sphere. As shown in Fig.1, the sphere is placed on an inclined plane that slopes downward to the left, making an angleθ with the horizontal, so that the coil is parrallel the the inclined plane. A uniform magnetic field of 0.350 T vertically upward exists in the region fo the spere. What current in the coil will enable the sphere to rest in equilibrium on the inclined plane? (10 %) Fig.1 一斜面上有一球，斜面角度θ，球上有线圈平行斜面，磁场B垂直向上。 3. The voltage source in Fig2 has an output of ΔVrms= 100 V at ω = 1,000 rad/s. Determine (a) the current(rms) in the circuit and (10%) (b) the power supplied by the source. (10%) (c) Show that the power delivered to theresistor is equal to the power supplied by the source. (10%) Fig.2 一回路，顺时钟依序为交流电电源，50.0μF电容，40.0Ω电阻，50.0mH电感。 4. A beam of 580-nm light passes throught two closely space glass plates, as shown if Fig.3. For what minimum onozero value of the plate separation d is the transmitted light btight? (10%) Fig.3 二玻璃板，光穿越第一片，在第二片一分为二，一直接穿过，一反射碰到第 一片，再反射，穿越第二片。 5. Michael Jordan is 198 cm tall. How tall must a vertical mirror be if he is to be able to see his entire length in it? (10%) 6.(a) Light traveling in a medium of refractive index n1 is incident at an angleθ on the surface of a medium of index n2. The angle between reflected and refracted rays isβ. Show that (10%) tanθ= n2*sinβ/(n1-n2*cosβ) (Syggestion: Use the identity sin(A+B) = sinAcosB + cosAsinB.) (b) Show that this expression for tanθ reduces to Brewster's law when β=90°, n1=1, nad n2=n The permittivity ε0=8.85*10^-12 C^2/Nm^2 The permeability constant μ0=4π*10^-7 Tm/A 4. --

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