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%) --

※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 61.224.170.38 ※ 文章網址: https://webptt.com/m.aspx?n=bbs/NTU-Exam/M.1484845532.A.212.html ※ 編輯: ycldingo (61.224.170.38), 01/20/2017 10:31:40