[試題] 105-1 朱國瑞 古典電力學(一) 期末考
課程名稱︰古典電力學（一） Classical Electrodynamics (I)
課程性質︰物理學系選修、物理所碩士班必修、應用物理所碩士班選修
課程教師︰朱國瑞
開課學院：理學院
開課系所︰物理學研究所
考試日期（年月日）︰2017/01/13
考試時限（分鐘）：120 min.
試題 :
Electrodynamics (I), Final Exam (6 problems) 1/13/2017
┌─Note──────────────────────────────────┐
│(1) You may use Jackson, a dictionary, and a calculator. Any other │
│ materials (including the lecture notes or insertions of any kind) are │
│ NOT allowed. │
│(2) You may use any equations in Jackson without derivation unless you are│
│ asked to derive it. │
│(3) Notations are follow Jackson. │
└─────────────────────────────────────┘
1. Consider an insulated, hollow conductor of outer radius a and inner radius
b. The total charge on the conductor is zero. There is only a point charge
q (at rest) in the hollow region of the conductor.
(a) What is the total charge on the inner surface of the conductor? Why?(5%)
(b) What is the total charge on the outer surface of the conductor? Why?(5%)
(c) What is the surface charge density σ on the outer surface of the
conductor? Why?(5%)
(d) Use the proper theorem (or law) to calculate E in the region r > a.(5%)
2. Explain why the method of expansion in orthogonal functions (as in Sec.2.9)
is a general method, but the method of images is not a general method.(5%)
3.
(a) Can the magnetization current Jm in Jackson Eq. (5.79) be formed of
moving charges? (No explaination is required. Just answer :yes" or "no".)
(5%)
(b) Prove mathematically that Jm can never produce a charge density.(5%)
4. A conducting surface has a static charge density σ. For simplicity, assume
that the surface is flat. Use Maxwell stress tensor [Jackson Eqs. (6.120)
and (6.122)] to show that the force per unit area on the conductiong surface
is σ^2 / 2(ε_0).(20%)
5. Answer "yes" or "no" to the following statements (no explaination is
required.).
(a) Poynting's theorem applies to static as well as time-dependent fields.
(b) All 4 Maxwell equations have been used in the derivation of Eqs. (6.15)
and (6.16).
(c) At any given point point in space, the Poynting vector of a linearly
polarized plane wave varies with time.
(d) The retarded Green function G^(+) in Jackson Eq. (6.44) is applicable to
both moving charges and antennas,
(e) The retarded Green function G^(+) in Jackson Eq. (6.44) is not applicable
to a dispersive medium.
(f) The dispersive property of a medium as exhibited in Jackson Eq. (7.51) is
due to an inertial effect.
6. Consider a plane wave in a medium which satisfies the good conductor
criterion.
(a) Show the displacement current in the medium can be neglected.(9%)
(b) Assume the wave frequency is ω and the medium has a conductivity of σ
and permeability of μ_0. Derive the skin depth and the wavelength of the
wave.(9%)
(c) If the wavw has a frequency of 10 Hz and the medium is sea water (σ = 10
/Ωm). Calculate the skin depth and the wavelength.(9%)
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※ 編輯: ycldingo (61.224.170.38), 01/20/2017 10:31:40