課程名稱︰古典電力學（一） Classical Electrodynamics (I) 課程性質︰物理學系選修、物理研究所碩士班必修、應用物理研究所碩士班選修 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）︰2016/12/09 考試時限（分鐘）：120 min. 試題 : 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%) --

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