课程名称︰普通物理甲下 课程性质︰必 课程教师︰赵治宇 开课学院：理学院 开课系所︰物理系 考试日期（年月日）︰4/28/100 考试时限（分钟）： 3hr 是否需发放奖励金：yes （如未明确表示，则不予发放） 试题 : 满分120 1. (a) Using the concept of energy band to describe the insulator, semiconductor, and metal. (b) Describe the n-type and p-type semiconductors. (6,4 points) 2. How to design the voltmeter and ammeter, and how they are connected with the circuits for application? (10 points) 3. Design an experimental setup that can measure thermal signal down to 10^-9 joule. (10 points) 4. Describe tje microscopic milecular model of dielectrics in capacitor, and briefly state why the capacitance of a capacitor should increase when a dielectric is inserted between the capacitor plates. (10 points) 5. A copper wire, which is 3.2 mm in diameter carries a current of 5 (A). Determone (a) drift velocity of the free electrons. (b) Estimate the root mean squre speed of electrons assuming they behave like ab ideal gas at 20 degree C. Assume that one electron per Cu atom is free to tmove. The mass density of copper is 8.8g/cm^3, and the atomic of Cu is 63.5g/mol. (7,3 ponts) 6. Describe the Hall effect and what important physics were found in the Hall's experiments? (10 points) 7. Two charged beads are on the plastic ring in Fig.1(a). Bead 2, which is not shown, is fixed in the place on the ring, which has radius R = 60 cm. Bead 1 is initially on the x axis at angle of 0. Tis is the moved to the opposite side, angle of pi, through the first and second quardrants of the xy coordinate ststem. Figure 1(b) gives the x component of the net electric field produced at the origin by the two beads as a function of the angle, and Figure 1(c) gives the y component. The vertical axis scales are set by Exs = -5.0 E4 N/C and Eys = -9.0 E4 N/C. (a) At what angle is bead 2 located? What are charges of (b) Bead 1 and (c) Bead 2? (4,3,3 points) Figure (a): 一个圆 R = 60 cm, 上标有 Bead 1 以及 the angle. Figure (b): at the angle = 0, Ex=-Exs; at the angle = pi/2, Ex=0; at the angle = pi, Ex=Exs. Figure (c): at the angle = 0 Ey = 4/9 Eys; at the angle = pi/2, Ey=Eys at the angle = pi, Ey=4/9 Eys (都是用图形表示，可是BBS话不出来，因此用文字表示图形重点所在 by 我) 8. A non-conducting solid sphere has a uniform volume charge density d. Let -> r be the vectir frin tge cebter if the sphere to a generak oiubt p within the sphere. (a) Determine the electric field E at P. (b) A psherical cavity is hollowed out of the sphere, as shown in Figure 2. Show that the electric field at all poonts within the cavity is uniform and equal to da/3*epson, where a is the position vector from the center of the sphere to the center of the cavity. (5,5 points) Figure 2: 一个球挖掉一部份 (同7. 说明，同理，epson的那个符号我打不出来。 9. Capaitor3 in Figure 3(a) is a varible capacitor. Figure 3(b) gives the electric potential V1 across capacitor 1 versus C3. The horizontal scale is set by C3s = 12.0 uF. Electric potential V1 approaches an asymptote of 8.0 V as C3 approaches infinity. What are (a) the electirc potential V across the battery, (b) C1, and (c) C2? (4,3,3 points) Figure 3(a): --- -------------| | | | === | === C1 | | | | | ------ ====== | | ==== V | | | C2 === === C3 | === === | | | | | | --------------------- (-, | 都表是导线) Figure 3(b): when C3 = 0, V1 = 2 V; when C3 = 5 uF, V1 = 5 V when C3 =10, V1 = 6 V; (说明同7.，图形非线性) 10. In Figure 4, the resitances are R1 = 1.0 ohm and R2 = 2.0 ohm, and the ideal batteries have emfs E1 = 2.0 V and E2 = E3 = 4.0 V. What are the (a) size and (b) direction (up or down) of the current in battery 1, (c) size and (d) direction (up or down) of the current in battery 2, (e) size and (f) direction (up or down) of the current in battery 3.? (g) What is the potential fifference Va - Vb? (10 points) (p.s. 未说明各小题分配) Figure 4: --------R1----a--------R1-----| | | | | R | | 2 | | | | | | ======= ======= ======= ===== E3 ===== E1 ===== E2 | | | R | | 1 |------R1-----b---------------| (说明同9.) 11. Figure 5 shows a wood cylinder of mass m and length L, with N turns of wire wrapped around it longitudinally, so that the plane of the wure coild contains the long central axis of the cylinder. The cylinder is released on a plane inclined at an angle theta (希腊符号) to the horizontal, with the plane of the coil parallel to the plane. If there is a vertical uniform magnetic field of magnitude B (T), that is the least current i through the coil that keeps the cylinder from rolling down the plane? Describe it in terms of m, L, N, B, theta, g (gravity). (10 points) Figure 5: |\ | \ | \ | \ | \ | \ --------theta (非原图，原图是立体的，不好画，不过叙述很清楚了。) 12. In unit-vetor notation, what is the magnetic field at point P in Figure 6? Please describe it in terms of a, i, mu0 (磁场的常数), and pi. (10 points) Figure 6: --------------- | | | p | | | ^ y | | | ^ i | | | | |----> x | | | | --------------- (说明: 边长为a的正方形，上带有电流i, p距离上与左导线均为a/4。) Exam ends here. -- 花退残红青杏小，燕子飞时，绿水人家绕。枝上柳棉吹又少，天涯何处无芳草。 墙里秋千墙外道，墙外行人，墙里佳人笑。笑渐不闻声渐悄，多情却被无情恼。 --

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