課程名稱︰古典電力學一
課程性質︰物理系系定選修
課程教師︰朱國瑞
開課學院：理學院
開課系所︰物理學系
考試日期（年月日）︰2019年11月22日
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
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%)