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）︰2009/01/12
考試時限（分鐘）：125
是否需發放獎勵金：是！
試題 :
1.(a) A dipole ｐ is a distance r from a point charge q, and oriented so that
ｐ makes an angle θ with the vector r from q to ｐ. What is the force on
ｐ?
(b) A point charge q is situated a large distance r from a neutral atom of
polarizability α. Find the force of attraction between them.
2.(a) Suppose the entire region below the plane z = 0 is filled with uniform
linear dielectric material of susceptibility χe. Calculate the force on a
point charge q situated a distance d above the origin.
(b) A point charge q is imbedded at the center of a sphere of linear
dielectric material (with susceptibility χe and radius R). Find the
electric field, the polarization, the bound charge densities ρb and σb,
and the total bound charge on the surface.
3.(a) Find the magnetic field a ditance z above the center of a square of
widths a, which carries a steady current I.
︿
(b) An infinite uniform surface current Ｋ = Kｙ flows over the xy plane at
z = 0. Please find the magnetic field Ｂ.
4.(a) Find the vector potential of an infinite solenoid with n turns per unit
length, radius R, and current I.
︿
(b) A long circular cylinder of radius R carries a magnetization Ｍ= ks^2ψ,
︿
where k is a constant, s is the distance from the axis, and ψ is the
azimuthal unit vector. Find the magnetic field due to Ｍ, for points inside
and outside the cylinder.
5.(a) Starting from the Lorentz force law, Ｆmag = I∫(dｌ×Ｂ), show that the
torque on any steady current distribution in a uniform field Ｂ is ｍ×Ｂ.
(b) A current Iflows down a long straight wire of radius a. If the wire is
made of linear material of susceptibility χm, and the current is
distributed uniformly, what is the magnetic field a distance s from the
axis? Also please find all the bound currents.
1
Note: ａ = ∫dａ = ／ ∮ｒ×dｌ.
s 2
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