課程名稱︰電磁學下
課程性質︰物理系必修
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）︰98.6.15
考試時限（分鐘）：08:10~10:20
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.
(a)If we stay away from the resonances, the damping can usually be ignored,
and the index of refraction can be written as:
n=1+(Nq^2/2mε0)Σfj/(ωj^2-ω^2).Show that for transparent materials,
j
because the nearest significant resonances typically lie in the ultra-
violet, n can be expressed in terms of the wavelength in the vacuum as
n=1+A(1+B/λ^2) in the optical region, with A and B being constant.
(b)Find the width of the anomalous dispersion region for the case of a single
resonance at frequency ω0 (assuming that γ<<ω0).
(c)Suppose we have a rectangular wave guide with height a=3.00 cm, and width
b=1.00 cm, and the driving frequency is 1.70x10^10 Hz, what TE modes will
propagate in this wave guide? (30pts)
2.Please fin the resulting electric and magnetic fields of an infinite straight
wirethat carries the current I(t)=0 for t<=0 and I(t)=Io for t>0. The wire is
electrically neutral and Io is a constant. (15 pts)
3.A partical of charge q moves in a circle of radius a at a constant angular
velocity ω.(Assume the circle lies in the xy plane, centered at the origin,
and at time t=0 the charge is at (a,0), on the positive x axis). Please find
the electric and magnetic fields at the center. (15 pts)
4.A charged particle with mass m and charge q approaches an infinite conducting
surface(lying in the xy plane at z=0) along the -z direction. Please find the
total radiated power, as a function of its height z above the plane. (10 pts)
→
5.An electric dipole p lies in the xy plane at z=0, rotates about the z-axis at
→ ^
a constant angular velocity ω. Assuming that p=p0 x at t=0, please find the
electric and magnetic fields, and the intensity of radiation of this dipole.
(15 pts)
6.With the inclusion of the radiation force, Newton's second law of a chared
particle becomes a=τ(da/dt)+F/m, where F is the external force acting on
the particle and τ=(μ0)q^2/6πmc. If a particle is subjected to a constant
force F, beginning at time t=0 and last until time T. Exclude the runaway
solution, calculate the work done by the external force. (15 pts)
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◆ From: 115.30.80.137
※ 編輯: alan7872 來自: 115.30.80.137 (06/17 12:37)
※ 編輯: alan7872 來自: 115.30.80.137 (06/17 12:38)
※ 編輯: alan7872 來自: 115.30.80.137 (06/17 12:41)