課程名稱︰電磁學 課程性質︰電磁學 課程教師︰陳政維 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰2009/11/09 考試時限（分鐘）：110 mins(am 8:10-10:00) 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : (1) Please find the electic field E a distance z above one end of a straight line sement of length L, which carries a uniform line charge λ. (2) Please find the potential V of a hollow spherical shell carries charge density ρ=k/r^2 in the region a≦r≦b. (3) Please find the fource of repulsion between the "northern" hemisphere and the "southern" semisphere of radius R and carries a total charge Q. (4) The enerage of the following configuration: two concentric spherical shall , of radii a and b (a<b), the inner one carries a charge q, and the outer one carries a charge -q (both of them uniformly distributed over the surfaces) (5) Please prove the uniqueness theorem: Let V1 and V2 be the solutions to the Laplace's (or Poisson's) equation with the boundary condition specified, then V1=V2. (6) Please find the force on the charge +q for the following configuration: 3 charges +q, +2q, +3q fixed at distances d, 2d, 3d above the grounded conducting xy plane. (7) An infinitely long 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 constant potential V0. Find the potential within the pipe. (8) A hollow sphere with radius R, and specified potential V0(θ)=ksin^2(θ/2) on the surface, find the potentia; inside and outside the sphere. (9) Charge density σ(ψ)=a sin 5ψ(a is a constant) is glued over the surface of an infinite cylinderof radius R. Find the potential inside and outside the cylinder. (10) A point charge q is situates a large distance r from a neutral atom of polarizability α.. Find the force of attraction between them 教授有畫出(2)(6)題的圖，而且(5)Laplce's equation 和Pisson's equation 都要寫出來 --

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