※ [本文转录自 NTU-Exam 看板] 作者: ultimatePTT (终极俊) 看板: NTU-Exam 标题: [试题] 94下 蔡尔成 普通物理学甲 期中考 时间: Sat Apr 22 08:06:38 2006 课程名称︰普通物理学甲 课程性质︰系定必修 课程教师︰蔡尔成 开课系所︰大气科学系 考试时间︰95/04/17 试题 : 2 2 1.The electric potencial is given by ψ(x,y,z)=x -y +xz, what is the eletric → field E at the point (x,y,z)? 2.At what distance along the central perpendicular axis of a uniformly charged plastic disk of radius R is the magnitude of the eletric field equal to one-half the magnitude of the field at the center of the surface of the disk? 3.Charge is distributed uniformly with the density ρ throughout the volume of an infinitely long solid cylinder of radius R. At the distance (a) r < R, → (b) r > R, give the expression for the magnitude E of the eletric field E. 4.Show that, according to the free-electron model of electrical conduction in metals and classical physics, the resistivity of metals should be proportional to √T, where T is the temperature in kelvins. 5.Two capacitors C and C are connected in series and are separated by a large 1 2 distance so that the electric field of one cannot affect the other. What is the equivalent capacitance of the combination? 6.A wire of arbitrary shape carrying a current i between points a and b in a uniform magnetic field. Prove that the force on the wire is the same as that on a straight wire carrying current i directly from a to b. 7.In a certain cyclotron a charged particle with charge q, mass m, moves in a circle of radius R. The magnitude of the magnetic field is B. (a) What is the oscillator frequency? (b) What is the kinetic energy of the charged particle? → 8.Show that the charge density is zero in a region where the eletric field E is uniform. 9.An initially uncharged capacitor C is fully charged by a device of constant emf ξ, in series with a resistor R. Show that the final energy stored in the capacitor is half the energy supplied by the emf device. 10.A single isolated spherical conductor of radius a may be considered as a capacitor with the other conductor being a sphere at infinity. (a) What is the capacitance? (b) Suppose charge Q is uniformly distributed on the sphere. What is the electrostatic energy? --

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