(word完整版)年泛珠三角及名校物理奥林匹克邀请赛.docx

Pan Pearl River Delta Physics Olympiad 2007年泛珠三角及中华名校物理竞赛Pan Pearl River Delta Physics Olympiad 20072007年泛珠三角及中华名校物理奥林匹克邀请赛Part-1 (Total 7 Problems) 卷-1（共7题）(9:30 am – 12:30 pm, 02-26-2007)Q.1 (3 points) 题1（3分）An airplane is initially rising up at speed v0 at an angle q to the horizon. Find the trajectory of the plane such that weightless condition can be achieved in the plane.一架飞机以与水平面成q 角的初速度v0上升求飞机以什么样的轨迹飞行，能使飞机里的物体处于失重状态Q.2 (6 points) 题2（6分）As shown, two identical weights are fixed on the two ends of a uniform rigid rod of length L. The upper weight is restricted to move on a smooth horizontal rail and the rod is free to swing along the rail. The masses of the weights and the rod are equal. Find the small angle vibration frequency of the system. 如图所示，两个质量为m的重块分别固定在一根长度为L质量为m的均匀杆两端。

上面的重块可以沿光滑的水平轨道滑行，杆可沿轨道方向自由摆动求整个系统的小角度振动频率Q.3 (6 points) 题3（6分）(a) A disc shaped medium block of radius R and thickness d (<< R) is uniformly magnetized with magnetization perpendicular to the disc plane. Find the magnetic field at point-O on the central axis of the disk and at a distance h from the cavity center.一半径为R，厚度为d (<< R)的圆盘形均匀磁化介质，磁化强度为盘的表面垂直于求圆盘中心轴上到圆盘中心距离为h的点O的磁场b) A long and thin cylindrical medium is uniformly magnetized with magnetization along the cylinder long axis. Find the magnetic field inside and outside the medium. 一细长圆柱型介质沿柱轴方向均匀磁化，磁化强度为。

求介质里、外的磁场Q.4 (5 points) 题4（5分）A large flat dielectric slab of thickness d and dielectric constant e is moving along the x-direction at speed v. Its large surface plane is perpendicular to the y-axis. A magnetic field of strength B is applied along the z-direction. Find the surface bound charge density on the two large surfaces of the slab, and the electric field in the slab.一个厚度为d，介电常数为e 的大平板以速度v 沿X-方向运动它的表面与Y-轴垂直Z-方向加有磁场B求平板两表面上的束缚电荷密度，以及平板中的电场Q.5 (10 points) 题5（10分）The space between two concentric conductor spherical shells of radii R1 and R3 is filled with two types of media. The dielectric constant and the conductivity of medium-1 and medium-2 are e1, s1 and e2, s2, respectively. The voltage difference between the two shells is V0. (a) In case-A, the media form two concentric shells with the conductor shells, and the radius of the boundary between the two media is R2. Find the following: (i) total current from the inner shell to the outer shell; (ii) total free charge on the two conductor shells and on the boundary between the two media. (b) In case-B, medium-1 fills the upper hemisphere and medium-2 fills the other half. Find the following: (i) total current from the inner shell to the outer shell; (ii) total free charge on the upper and lower halves of the two conductor shells. Case-A Case-B如图所示，两个半径分别为R1和R3的同心导电球壳之间充满了两种介质。

球壳之间电势差为V0介质1和2的介电常数和导电率分别为 e1, s1 和 e2, s2a) 两种介质为与导电球壳同心的球壳，其界面为半径为R2的球面i) 求两导电球壳间的总电流；(ii) 求两导电球壳以及两介质之间界面上的电荷b) 介质-1填充上半部分，介质-2填充下半部分i) 求两导电球壳间的总电流；(ii) 求两导电球壳上、下部分的电荷Q.6 (12 points) 题6（12分）(a) Assume that atmosphere is made of diatom ideal gas in adiabatic equilibrium. Determine air pressure P, temperature T and density r as a function of altitude h, provided that their values at h = 0 are known. (Hint: Set up a differential equation for a thin layer of air at some altitude. , where is a constant.) (6 points)(a) 大气可看成绝热平衡下的双原子理想气体。

求空气压强P、温度T和密度r作为高度h的函数，假定它们在h = 0处的值为已知提示：对某高度的一薄层气体建立微分方程6 分)(b) When the partial pressure of water vapor in air exceeds the saturated water vapor pressure (Ps) at a given temperature, the water vapor will condense into droplets which fall down as rain. Ps = 55.35 mmHg at 40°C, and Ps = 6.50 mmHg at 5 °C. The air/vapor mixture can be considered as diatom ideal gas and the mass of a water molecule is approximately the same as an ‘air’ molecule. In the humid air at sea level at 40°C the water vapor partial pressure is 90 % of Ps. The density of air is ρ0 = 1.18 kg m-3 at 20 °C and 1.0 atm. The humid air then rises adiabatically to an altitude where the temperature is 5 °C. Ignore air pressure change due to the reduction of water vapor.(b1) How much rain can one cubic meter of the humid air at sea level generate? (5 points)(b2) Use the results in (a), find the altitude where the temperature is 5 °C. (1 point)(b) 当空气中水蒸汽的分压强超过该温度下的饱和水蒸汽压(Ps)时，水蒸汽将凝聚成滴导致下雨。

已知40°C时Ps = 55.35 mmHg，5 °C时 Ps = 6.50 mmHg空气/水蒸汽的混合物可当作是双原子理想气体，水分子的质量近似等于‘空气’分子的质量40°C时海平面上的潮湿空气中，水蒸汽分压是Ps的90 %已知20 °C时，1个大气压下的空气密度 ρ0 = 1.18 kg m-3忽略由于水蒸汽的减少导致的气压改变该潮湿空气绝热上升到某一高度，该处温度为5 °Cb1）一立方米海平面上的潮湿空气能够产生多少雨？(5 分)（b2）用（a）的结果，求温度为5 °C处的高度1 分)Q7 (8 points) 题7（8分）(i) Find the torque on an electric dipole in a uniform electric field. (1 point)(ii) A medium is uniformed polarized with polarizationby an electric field. Find the torque per volume on the medium exerted by the electric field. (1 point)(iii) An 。