课程名称︰普通物理学甲下 课程性质︰系定必修 课程教师︰赵治宇 开课学院：工学院 开课系所︰化工系 考试日期（年月日）︰2008/04/24 考试时限（分钟）：170分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1. Fig. 1 shows electrons 1 and 2 on an x axis and charged ions 3 and 4 of identical charged charge -q and at identical angles Θ. Electron 2 is free to move; the other three paticles are fixed in place at horizontal distances R form electron 2 and are intened to hold electron 2 in place. For physical possible values of q≦5e what are the (a) smallest, (b) second smallest, and (c) third smallest values of Θ for which electron 2 is held in place? (3％, 3％ ,4％) (P577 习题21-34 Fig.21-35) 2. Fig. 2 shows an electric quadrupole. It consists of two dipoles with dipole moments that are equal in magnitude but opposite in direction. Calaulate the value of the electric field on the axis of the quadrupole for a point P a distance z form its center. (Assume z＞＞d) (10％) (P600 习题22-21 Fig.22-42) 3. A nonconducting soild sphere has a uniform volume charge density ρ. Let r be the vector from the center of the sphere to a general point P within the sphere. (a) Show that the electric field at P. (b) A spherical cavity is hollowed out of the sphere, as shown in Fig. 3. Show that the electric field at all points within the cavity is uniform and equal to E = ρa/3εo, where a is the position vector form the center of the sphere to the center of the cavity. (5％, 5％) (P627 习题23-77 Fig.23-57) 4. Fig. 4 shows a flat ring with outer radius R,inner radius r, ane uniform charge density σ. (a) Find the electric field at point P. (b) Derive the electric potential at point P directly form (a). (Assume the electric potential V=0 at infinity) (5％, 5％) (P652 习题24-70 Fig.24-56) 5. (a) Derive the capacitance of a parallel-plate capacitor of plate area A, plate separation d. (b) A slab of copper of thickness b=2.00 mm is thrust into a parallel-plate capacitor of plate area A=2.40 cm2 and plate separation d=5.00 mm, as shown in Fig. 5; the slab is exactly halfway between the plates. What is the capacitance after the slab is introduced? (c) If a charge q=3.40 μc is maintained on the plates, how much work is done on the slab as it inserted? (3％, 3％, 4％) (P681 习题25-74 Fig.25-59) 6. Capacitor 3 in Fig. 6(a) is a variable capacitor. Figure 6(b) gives the electric potential V1 across capacitor 1 versus C3. The horizontal scale is set by C3s=12.0 μF. Electric potential V1 approaches an asymptote of 10V as C3→∞. (a) What is the electric potential V across the battery? (b) What are C1 and C2? (5％, 5％) (P678 习题25-28 Fig.25-44) 7. In Fig. 7, current is set up through a truncated right circular cone of resistivity 731Ω*m, left radius a=2.00 mm, right radius b=2.30 mm, and length L=1.94 cm. Assume that the current density is uniform across any cross section taken perpendicular to the length. What is the resistance of the cone? (10％) (P702 习题26-35 Fig.26-30) 8. (a) In Fig. 8, when switch S is closed on a, the capacitor is charged through the resistor. Write down the charging equation and solve the function q(t) which satisfies the intial condition q(0)=0. (b) Assume now that the capacitor is fully charged to a potential V0 equal to the emf ε of the battery. At a new time t=0, switch S is thrown from a to b. Write down the discharging equation and solve q(t). (5％, 5％) 9. In Fig. 9,a conducting rectangular solid of dimensions dx=5.00 m, dy=3.00 m and dz=2.00 m moves at constant velocity v=(20.0 m/s)i through a uniform magnetic field B=(30.0 mT)j. What are the resulting (a) electric field within the soild, in unit-vector notation, and (b) potential difference across the solid? (5％, 5％) (P758 习题28-15 Fig.28-38) 10. A wire of length 25.0 cm carrying a current of 4.51 mA is to be formed into a circular coil and placed in a uniform magnetic field B of magnitude 5.71 mT. If the torque on the coil form the field is maximized, what are (a) the angle between B and the coil`s magnetic dipole moment and (b) the number of turns in the coil? (c) What is the magnitude of that maximum torque? (3％, 3％, 4％) (P762 习题28-63 无图) 11. In Fig. 10, part of a long insulated wire carrying current i=5.78 mA is bent into a circular section of radius R=1.89 cm. In unit-vector notation, what is the magnetic field at the center of curvature C if the circular section (a) lies in the plane of the page as shown and (b) is perpendicular to the plane of the page after being rotated 90。 counterclockwise as indicated? (5％, 5％) (P785 习题29-28 Fig.29-56) 12. In Fig.11, a long circular pipe with outside radius R=2.6 cm carries a (uniformly distributed) current i=8.00 mA into the page. A wire runs parallel to the pipe at a distance of 3.00R from center to center. Find the (a) magnitude and (b) direction (into or out of the page) of the current in the wire such that the net magnetic field at point P has the same magnitude as the net magnetic field at the center of the pipe but is in the opposite direction. (5％, 5％) (P787 习题29-48 Fig.29-71) 绿色字是向量 --

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