课程名称︰古典电力学（一） Classical Electrodynamics (I) 课程性质︰物理学系选修、物理研究所硕士班必修、应用物理研究所硕士班选修 课程教师︰朱国瑞 开课学院：理学院 开课系所︰物理学研究所 考试日期（年月日）︰2016/12/09 考试时限（分钟）：120 min. 试题 : Electrodynamics (I), Mid-term Exam (6 problems) 12/9/2016 ┌─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, equation no, and page no follow Jackson. │ └─────────────────────────────────────┘ 1 ρ(x')(x-x') 1. Coulomd's law states E(x)＝──── ∫─────── dV'. Assume ρ(x') 4πε_0 │x-x'│^3 is a finite function of x'. Use Gauss' law and order-of-magnitude considerations to explain why E(x)≠∞ as x→x' [x' is any point in ρ(x')]. (15%) 2. A hollow cube has six square sides. There are no charges inside. Five sides are grounded. The sixth side, insulated from the others, is held at a constant potential φ_0. Shoe that φ at the center of the cube is φ_0/6 by using the physical argument in lecture notes, Sec.2.9[Do not use Eq.(1.44)]. (15%) 3. A spherical surface of radius a has a (static) surface charge density σ(x)＝3 ε_0 E_0 cosθ (in spherical coordinates), which corresponds to a volume charge density: ρ(x)＝3 ε_0 cosθδ(r－a). (a) Calculate the dipole moment p [＝∫xρ(x)dV].(10%) Hint: Express x in spherical coordinates; dV＝r^2 dr dcosθ dφ. (b) Calculate the potential φ (due to σ) at r＜a and r＞a (ε＝ε_0 in both regions).(20%) Hint: Use (1.17), (3.70), (3.53), (3.21), and P_1(x)＝x. 4. A point chsrge q is located in an infinite, uniform medium of permittivity ε. Put the charge at the origin of coordinates. Calculate (a) The potentialφ(x) everywhere.(5%) (b) The polarization charge density ρ_pol(x)[＝－▽‧P(x)].(10%) 5. Explain why the derivation of the magnetic field energy in Jackson Sec.5.16 is valid only if the current J is established at an infinitesimally small rate.(10%) 6. The two rails of a railroad track, insulated from each other and from the ground, are connected by a voltmeter. What is the reading on the voltmeter when a train is approaching at the speed of 180 km/hr, assuming that the vertical component of the earth's magnetic field is 0.2 gauss and that tha tracks are separated by one meter?(15%) --

※ 发信站: 批踢踢实业坊(ptt.cc), 来自: 61.224.170.38 ※ 文章网址: https://webptt.com/cn.aspx?n=bbs/NTU-Exam/M.1484879271.A.C76.html ※ 编辑: ycldingo (61.224.170.38), 01/20/2017 10:30:25