課程名稱︰普通物理學甲下
課程性質︰化學系必帶,地質系選修
課程教師︰蔡政達
開課學院：理學院
開課系所︰物理系
考試日期（年月日）︰2010.04.20
考試時限（分鐘）：120 mins
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.
Fig A shows, in cross section, two solid spheres with uniformly
distributed charge throughout their volumes. Each has radius R.
(1)Point P1 lies on a line connecting the centers of the spheres,
at radial distance 2R/3 from the center of sphere 1. If the net
electric field at point P1 os zero, what is the ratio q2/q1 of
the total charge q2 in sphere 2 to the total charge q1 in sphere 1?
(10 points)
(2)
In another case, point P2 lies on the same line at radial distance
5R/4 from the center of sphere 2. If the net electric field at point
P2 is zero, what is the ratio q2/q1 ?(10 points)
___ ___
╱ ╲ ╱ ╲ 好難畫囧
∕ ﹨∕ ﹨ 兩球有接觸 半徑都是R
∣ ●○│∣ ● ∣○ 實心圈是球心 右邊空心是P2 左邊是P1
﹨ ∕﹨ ∕ (相對位置 沒有照比例)
╲___╱ ╲___╱
2.
Fig B shows a wood cylinder of mass m=0.4kg and length L=0.2m, with
N=20 turns of wire wrapped around it longitudinally, so that the plane
of the wire coil contants the long central axis of the cylinder. the
cylinder is released on a plane inclined at an angle θ to the horizontal,
with the plane of the coil parallel to the incline plane. If there is a
vertical uniform magnetic field of magnitude 0.5T. what is the least
current i through the coil that keep the cylinder from rolling down
the plane?(20 points)
↑↑ ↑ ↑↑
↑ ╱╲↑↑ ↑B
↑↑╱ ↗╲↑ ↑
╱ L ╱○
╱↑↙ ╱ ╱╲↑
│╲ ↑╱ ╱↗i ↑
│↑╲ Θ╱ ↑ ╱
│ ↑ ╲ ↑ ╱
│ ↑↑ ╲ ╱
│ θ╲╱
└─────
3.
In Fig C, R1=5.00Ω, R2=10.0Ω, R3=15.0Ω,C1=5.00uF,C2=10.0uF,and the
ideal battery has emfε=20.0V. Assuming that the circuit is in the
steady state, what is the total energy stored in the two capacitors?
(20 points)
C1
R2
┌││──┬─﹏─┐
│ │ │
│ │ │
│ │ C2 │
├─﹏──┴─││┤
│+ │
==-ε │
│ R3 │
└───﹏────┘
4.
A pIatic disk of radius R=60.0cm is charged on one side with a uniform
surface charge densuty σ=8.00fC/m^2, and then three quadrants of the
disk are removed. The remaining quadrant is shown in Fig D. With electric
potential V=0 at infinity, then
(I) What is the potential due to the remaining quadrant at point P,
which is on the central axis of the original disk at distancc D=0.26cm
from the origin center? (14 points)
(2) What is the electric field at point P? (6 points)
●P
│↑
│ D （圓形側視圖）囧
＿＿＿
／ │ ＼
／ │↓ ＼
( ● )
╲ ↙R ╱
╲_____ ╱
5.
Fig E shows a cross section of a long cylindrical conductor of radius
a=4.00 cm containing a long cylindrical hole of radius b=1.50 cm. The
central axes of the cylinder and hole are parallel and are distance
d=2.00cm apart; current i=5.25 A is uniformly distributed over the
tinted area.
(a) What is the magnitude of th magnetic field the at the center of
the hole? (10 points)
(b) Discussthe two special cases b=0 and d=0(10 points)
__
╱ ╲
∕ ﹨ 大圓圓心到小圓圓心距離＝d 大圓半徑a
∣ ○∣
﹨ ∕
╲__╱
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