[試題] 99下 蔡爾成 普通物理學甲下 期中考
課程名稱︰普通物理學
課程性質︰必帶
課程教師︰蔡爾成
開課學院：工學院
開課系所︰機械工程學系
考試日期（年月日）︰2011/04/22
考試時限（分鐘）：120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.(10%)(23-55)A charge of distribution that is spherically symmetric but not
uniform radially produces an electric field of magnitude E=Kr^4, directed
radially outward from the center of the sphere. Here r is the radial distance
from that center, and K is a constant. What is the volume density p of the
charge distribution?
2.(10%)(23-65)What is the excess charge on a conducting sphere of radius r if
the potential V=Vo at the sphere and the potential V=0 at infinity?
3.(10%)(25-50)Figure 25-49 show a parallel-plate capacitor of plate area A
and plate separation 2d. The left half of the gap is filled with material of
dielectric constant K1; the top of the right half is filled with material of
dielectric constant K2; the bottom of the right half is filled with material
of dielectric constant K3. What is the capacitance?
4.(10%)(26-37)Show that, according to the free-electron model of electrical
conduction in metals and classical physics, the resistivity of metals should
be proportional to T^1/2 ,where T is the temperature in kelvins.
(此題附圖 請看課本對照)
5.(10%)(29-04)A straight conductor carrying current i=5.0A splits into
identical semicircular arcs as shown in Fig.29-35. What is the magnetic field
at the center C of the resulting circular loop?
(此題附圖 請看課本對照)
6.(10%)Show that the electric field E(→) is perpendicular to the surface of
a conductor is E(→)=0 inside the conductor.
7.(10%)A nonconducting solid sphere of radius a has a uniform charge density
p. A spherical cavity of radius b is hollowed out of the sphere, as shown in
the figure below. The center of the solid sphere and the spherical cavity are
distance d apart. Show that the electric field in the hole is uniform.
(此題附圖 一個半徑為a的球 中間挖一個半徑為b的球 a b球圓心距d)
8.(10%)A single isolated spherical conductor of radius a may be considered as
a capacitor with the other conductor being a sphere at infinity (a)(5%)What
is the capacitance? (b)(5%)Suppose charge Q is uniformly distributed on the
sphere. What is the electrostatic energy?
9.(10%)Let B(→) be the magnetic field produced by a current loop of finite
size carrying a steady current I, show that according the law of Biot and
Savart ,at a distance r far away from the current loop, r^2B→0 as r→oo
10.(10%)In a certain cyclotron, a particle of charge q and mass m moves in a
circle of radius R. The magnitude of the magnetic field is B. What is the
kinetic energy of the particle?
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