推 PSOUL :推一個 11/12 23:18
課程名稱︰電磁學上
課程性質︰系必修
課程教師︰陳政維
開課學院：理學院
開課系所︰物理學系
考試日期（年月日）︰2008/11/10
考試時限（分鐘）：120
是否需發放獎勵金：是！
試題 :
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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