课程名称︰古典电力学一 课程性质︰物理系系定选修 课程教师︰朱国瑞 开课学院：理学院 开课系所︰物理学系 考试日期（年月日）︰2019年11月22日 考试时限（分钟）：110分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : Electrodynamics (I), Mid-term Exam (6 problems) 11/22/2019 Note:(1) You may use Hackson. Any other materials (such as lecture notes, dic- tionary, calculator, cell phonem and insertions of any kind) are not allowed. (2) You may use any equation in Jackson without derivation unless you are asked to derive it. (3) Notations, equation no, and page no follow Jackson. 1. Prove the following: (a) There cannot be any static electric field in the interior (the hollow region) of a closed, hollow conductor if there is no charge in the int- erior. (10%) (b) A closed, hollow conductor cannnot shield its exterior from the electr- ic fields due to charges placed in its interior. (10%) 2. Based on information given for the problem on pp.71-72, can wa find σ on the wall at z=c (see figure)? If so, outline the method to find it. If not, explain why not. You will get 0 points if your answer is just "yes" or "no" . (10%) 3. p.114 states "√ρJ_ν(k_{νn}ρ), for fixed ν≧0, n=1,2,..., form an ort- hogonal set on the interval 0≦ρ≦a. Eq.(3.96) implies J_ν(k_{νn}ρ) (n= 1,2,...) are a complete set on the same interval". In the context of the eigenvalue problem discussed in Appendix A of Ch.3, explain why these two statements are inconsistent and which one is right (no algebra is needed). (10%) 4. A surface charge density σ(θ)=σ_0cosθ is glued to the surface of a sph- erical shell of radius R (σ_0 is a constant and θ is the polar angle in the spherical coordinate system.) There is a vacuum, with no charges, both inside and outside of the shell. Calculate the electrostatic potential inside and outside of the spherical shell. 5. Show that, in Eq.(4.30), the second term on the RHS does not diverge as \vec{x}→\vec{x}'. (10%) 6. (a)In Eq.(4.28), the magnitude of <\vec{p}_i> can be much smaller than that of \vec{p}_i. Use an example to explain why. (10%) (b)In Eq.(4.29), the magnitude of <e_i> can be much smaller than that of e_i. Use an example to explain why. (10%) --

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