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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