课程名称︰电磁学上 课程性质︰必修 课程教师︰陈政维 开课学院：理学院 开课系所︰物理系 考试日期（年月日）︰ 考试时限（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. Please calculuate th electric field for a sphere of radius R that carries a polarization P(r)=kr, where k is a constan and r is the vextor from the enter.(10%) 2. Please find the force on a slab of linear dielectric material (with electric susceptibility Xe) that is partially inserted between the plates of a parallel-plate capacitor (the distance between the plates is d and the width of plate is w, and the potential between the plates is V) (15%) ╴╴╴╴╴╴╴╴╴╴╴╴╴╴ ╱ ╱ w ╱ ╱ ╱╴╴╴╴╴╴╴╴╴╴╴╴╴╱ ╱ ▕///////////////////////////︳ d ╱ ▕///////////////////////////︳ ╱ ▕///////////////////////////︳ ╱ ▕///////////////////////////︳ ￣￣￣￣￣￣￣￣￣￣￣￣￣￣ 3. A steady current I flows down a long cylindrical wire of radius a, with the current density proportional to s (s is the from the center axis). Please find the magnetic field, both inside and outside the wire. (10%) 4. Please find the vector potential A of an infinite solenoid with n turns per unit length, radius R, and current I. (10%) 5. A current I folws down a long straight wire of radius a. If the wire is made of linear material with susceptibility Xm and the current is distributed uniformly. Please find the magnetic field a distance s from the axis and all the bound currents. (15%) 6. Starting from the Lorentz force law (dF=dI╳V), please show that the torque on any steady current distribution in a unoform field B is m ╳ B. (10%) 7. Please calculate the ratio ofdisplacement current to conduction current for a long coaxial cable that carries an alternationg current I at frequency f = 10^10 Hz (the current flows in the center wire with negligible radius, and back along the outer cylinder, of radius a = 0.10cm). (15%) 8. A superconductor is a perfect conductor with the additional property that the B inside it is zeor. (a) Please show that the current in a superconductor is confined to the surface. (b) Suppose you cool a superconducting sphere (with radius R) to the temperature below its ^ superconducting transtition temperatrue in a uniform magnetic field B0z, please find the induced surface current density K, as a function of the polar angle θ. (15%) --

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