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課程名稱︰普通物理學甲下
課程性質︰系定必修
課程教師︰趙治宇
開課學院：工學院
開課系所︰化工系
考試日期（年月日）︰2008/04/24
考試時限（分鐘）：170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. Fig. 1 shows electrons 1 and 2 on an x axis and charged ions 3 and 4 of
identical charged charge -q and at identical angles Θ. Electron 2 is free
to move; the other three paticles are fixed in place at horizontal
distances R form electron 2 and are intened to hold electron 2 in place.
For physical possible values of q≦5e what are the (a) smallest, (b) second
smallest, and (c) third smallest values of Θ for which electron 2 is
held in place? (3％, 3％ ,4％)
(P577 習題21-34 Fig.21-35)
2. Fig. 2 shows an electric quadrupole. It consists of two dipoles with dipole
moments that are equal in magnitude but opposite in direction. Calaulate
the value of the electric field on the axis of the quadrupole for a point
P a distance z form its center. (Assume z＞＞d) (10％)
(P600 習題22-21 Fig.22-42)
3. A nonconducting soild sphere has a uniform volume charge density ρ. Let r
be the vector from the center of the sphere to a general point P within
the sphere. (a) Show that the electric field at P. (b) A spherical cavity
is hollowed out of the sphere, as shown in Fig. 3. Show that the electric
field at all points within the cavity is uniform and equal to E = ρa/3εo,
where a is the position vector form the center of the sphere to the center
of the cavity. (5％, 5％)
(P627 習題23-77 Fig.23-57)
4. Fig. 4 shows a flat ring with outer radius R,inner radius r, ane uniform
charge density σ. (a) Find the electric field at point P. (b) Derive the
electric potential at point P directly form (a). (Assume the electric
potential V=0 at infinity) (5％, 5％)
(P652 習題24-70 Fig.24-56)
5. (a) Derive the capacitance of a parallel-plate capacitor of plate area A,
plate separation d.
(b) A slab of copper of thickness b=2.00 mm is thrust into a parallel-plate
capacitor of plate area A=2.40 cm2 and plate separation d=5.00 mm, as shown
in Fig. 5; the slab is exactly halfway between the plates. What is the
capacitance after the slab is introduced?
(c) If a charge q=3.40 μc is maintained on the plates, how much work is
done on the slab as it inserted? (3％, 3％, 4％)
(P681 習題25-74 Fig.25-59)
6. Capacitor 3 in Fig. 6(a) is a variable capacitor. Figure 6(b) gives the
electric potential V1 across capacitor 1 versus C3. The horizontal scale
is set by C3s=12.0 μF. Electric potential V1 approaches an asymptote of
10V as C3→∞. (a) What is the electric potential V across the battery?
(b) What are C1 and C2? (5％, 5％)
(P678 習題25-28 Fig.25-44)
7. In Fig. 7, current is set up through a truncated right circular cone of
resistivity 731Ω*m, left radius a=2.00 mm, right radius b=2.30 mm,
and length L=1.94 cm. Assume that the current density is uniform across
any cross section taken perpendicular to the length. What is the resistance
of the cone? (10％)
(P702 習題26-35 Fig.26-30)
8. (a) In Fig. 8, when switch S is closed on a, the capacitor is charged
through the resistor. Write down the charging equation and solve the
function q(t) which satisfies the intial condition q(0)=0.
(b) Assume now that the capacitor is fully charged to a potential V0
equal to the emf ε of the battery. At a new time t=0, switch S is thrown
from a to b. Write down the discharging equation and solve q(t). (5％, 5％)
9. In Fig. 9,a conducting rectangular solid of dimensions dx=5.00 m, dy=3.00 m
and dz=2.00 m moves at constant velocity v=(20.0 m/s)i through a uniform
magnetic field B=(30.0 mT)j. What are the resulting (a) electric field
within the soild, in unit-vector notation, and (b) potential difference
across the solid? (5％, 5％)
(P758 習題28-15 Fig.28-38)
10. A wire of length 25.0 cm carrying a current of 4.51 mA is to be formed into
a circular coil and placed in a uniform magnetic field B of magnitude 5.71
mT. If the torque on the coil form the field is maximized, what are (a) the
angle between B and the coil`s magnetic dipole moment and (b) the number of
turns in the coil? (c) What is the magnitude of that maximum torque?
(3％, 3％, 4％)
(P762 習題28-63 無圖)
11. In Fig. 10, part of a long insulated wire carrying current i=5.78 mA is
bent into a circular section of radius R=1.89 cm. In unit-vector notation,
what is the magnetic field at the center of curvature C if the circular
section (a) lies in the plane of the page as shown and (b) is
perpendicular to the plane of the page after being rotated 90。
counterclockwise as indicated? (5％, 5％)
(P785 習題29-28 Fig.29-56)
12. In Fig.11, a long circular pipe with outside radius R=2.6 cm carries a
(uniformly distributed) current i=8.00 mA into the page. A wire runs
parallel to the pipe at a distance of 3.00R from center to center. Find
the (a) magnitude and (b) direction (into or out of the page) of the
current in the wire such that the net magnetic field at point P has the
same magnitude as the net magnetic field at the center of the pipe but is
in the opposite direction. (5％, 5％)
(P787 習題29-48 Fig.29-71)
綠色字是向量
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