课程名称︰电磁学上 课程性质︰系必修 课程教师︰陈政维 开课学院：理学院 开课系所︰物理学系 考试日期（年月日）︰2008/11/10 考试时限（分钟）：120 是否需发放奖励金：是！ 试题 : 1.(a) Please find the electric field a distance z above one end of a straight line segment of length L, which carries a uniform line charge density λ. (b) A hollow spherical shell carries charge density in the region a≦r≦b, please find the electric field as a function of r. 2.Find (a) the electric potential as a function of r for a uniformly charged solid sphere, and (b) the net force of the southern hemisphere of a uniformly charged solid sphere exerts on the northern hemisphere. (express your answer in terms of the radius R and the total charge Q of the sphere) 3.(a) Two infinitely long wires running parallel to the x axis carry uniform charge densities +λ and -λ, find the potential at any point (x, y, z), using the origin as your reference. (b) Find the potential of a point charge q situated a distance a from the center of a grounded conducting sphere of radius R. 4.(a) Charge density σ(θ) = kcosθ (k is a constant) is glued over the surface of a spherical shell of radius R. Find the resulting potential inside and outside the sphere. (b) Charge density σ(ψ) = 5sin5ψ is glued over the surface of an infinite cylinder of radius R. Find the potential inside and outside the cylinder. 5.(a) Find the capacitance per unit length of two coaxial metal tubes, of radii a and b. (b) A rectangular pipe, running parallel to the z-axis (from -∞ to +∞), has three grounded metal sides, at y = 0, y = a, and x = 0. The fourth side, at x = b, is maintained at a potential V0. Find the potential within the pipe. --

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