课程名称︰电磁学 课程性质︰电机系必修 课程教师︰江衍伟 开课学院：电机资讯学院 开课系所︰电机系 考试日期（年月日）︰99.4.23 考试时限（分钟）：100 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : (以下以黄色字体表示单位向量,亮字表示向量) 1.(6%) Consider two points P(r,θ,ψ) and Q(r+dr,θ+dθ,ψ+dψ) at differential distance in the spherical coordinate system. Please write the expressions for three side lengths that would define the differential volume formed by incrementing the coordinates from point P to point Q. 2.(8%) For the current element Idx(ax+ay)(A-m) situated at the point (1,-2,2), find the magnetic flux density at the point (2,-1,3). 3.(8%) Prove that for any vector field A the vloume integral ∫ (▽‧▽ X A )dv = 0 v Please state clearly the theorems you use. 4.(8%) At time t=0 a rigid straight line section of metallic wire of length L(m) is situated on the y-axis with its tips located at (0,L/2,0) and (0,-L/2,0), respectively, and in the whole free space there exists a uniform magnetic field, B = √3B0ax + B0az (Wb/m^2) , where Bo is a positive constant. Now the line section is moved with constant velocity, v(m/s), along the z-direction. What is the open-circuit voltage induced between the tips of the line section? Also explain which tip has higher potential. 5.(15%) Find the unit vector normal to the surface 2x^2+y^2=6 at the point (√2,√2,0). 6.(20%) A circular ring of radius a lies in the xy-plane and has its center at the origin. The ring is coated with charge such that the charge density is given by ρL=ρL0 sinψ(C/m), where ψ is the angle variable as in the cylindrical or polar coordinate system. Find the electric field intensity vector at a point on the z-axis. 7.(20%) For the electric field E = E0^(-kx)cos((3*10^8)t-y)az in free space (J=0), find the value(s) of k for which the field satisfies both of Maxwell's curl equations. 8.(15%) Current I flows along a straight wire from a point charge Q1(t) located at (1,1,2) to a point charge Q2(t) located at (0,0,1). Find the line integral of the magnetic field intensity vector H along the square closed path having the vertices at (1,1,0), (-1,1,0), (-1,-1,0), and (1,-1,0) and traversed in that order. --

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