課程名稱︰電磁學上
課程性質︰必修
課程教師︰陳政維
開課學院：理學院
開課系所︰物理系
考試日期（年月日）︰
考試時限（分鐘）：
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. Please calculuate th electric field for a sphere of radius R that carries a
polarization P(r)=kr, where k is a constan and r is the vextor from the
enter.(10%)
2. Please find the force on a slab of linear dielectric material (with electric
susceptibility Xe) that is partially inserted between the plates of a
parallel-plate capacitor (the distance between the plates is d and the width
of plate is w, and the potential between the plates is V) (15%)
╴╴╴╴╴╴╴╴╴╴╴╴╴╴
╱ ╱
w ╱ ╱
╱╴╴╴╴╴╴╴╴╴╴╴╴╴╱
╱ ▕///////////////////////////︳
d ╱ ▕///////////////////////////︳
╱ ▕///////////////////////////︳
╱ ▕///////////////////////////︳
￣￣￣￣￣￣￣￣￣￣￣￣￣￣
3. A steady current I flows down a long cylindrical wire of radius a, with the
current density proportional to s (s is the from the center axis). Please
find the magnetic field, both inside and outside the wire. (10%)
4. Please find the vector potential A of an infinite solenoid with n turns per
unit length, radius R, and current I. (10%)
5. A current I folws down a long straight wire of radius a. If the wire is made
of linear material with susceptibility Xm and the current is distributed
uniformly. Please find the magnetic field a distance s from the axis and all
the bound currents. (15%)
6. Starting from the Lorentz force law (dF=dI╳V), please show that the torque
on any steady current distribution in a unoform field B is m ╳ B. (10%)
7. Please calculate the ratio ofdisplacement current to conduction current for
a long coaxial cable that carries an alternationg current I at frequency
f = 10^10 Hz (the current flows in the center wire with negligible radius,
and back along the outer cylinder, of radius a = 0.10cm). (15%)
8. A superconductor is a perfect conductor with the additional property that
the B inside it is zeor. (a) Please show that the current in a
superconductor is confined to the surface. (b) Suppose you cool a
superconducting sphere (with radius R) to the temperature below its
^
superconducting transtition temperatrue in a uniform magnetic field B0z,
please find the induced surface current density K, as a function of the
polar angle θ. (15%)
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◆ From: 140.112.4.187
※ 編輯: def2864 來自: 140.112.4.187 (01/11 17:36)