Download 國立彰化師範大學八十八學年度碩士班招生考試試題

國立彰化師範大學九十一學年度碩士班招生考試試題
系所：物理學系碩士班
☆☆請在答案紙上作答☆☆
科目：普通物理
共 2 頁，第 1 頁
注意：
1. The unified atomic mass unit 1u=1.66 10-27 kg.
2. The mass of the electron is me =9.110-31 kg.
一、 填 充 題: (每格 6 分, 共 60 分)
【 Note: You could make an estimate of the number s in the following problems without
using a calculator 】
1. A skier has just begun descending a 45 slope. Assuming the coefficient of kinetic friction is 0.10, the
skier’s acceleration is a=______ g.
2. (a) A geosynchronous satellite of the Earth is the one that stays above the same point on the equator of
the Earth. The height above the Earth’s surface needed for a geosynchronous weather satellite is
hs=_____ [In terms of rE]. [The Earth’s radius rE=6380 km].
(b) Assume the Earth is a perfect sphere, the difference between the values of g at the equator and at
the poles due to the Earth’s rotation is g=_________ m/s2.
3. (a) A proton of mass 1.0 u traveling with a speed of 2104 m/s has an elastic head-on collision with a
helium nucleus of mass 4.0 u initially at rest. The velocity of the proton after the collision is
vP=_________ m/s.
(b) If these two particles are observed to move off at 45, proton above the x-axis and helium below
the x-axis. The velocity of the helium after the collision is vHe= _________ m/s.
4. A uniform thin rod of length L and mass M with its linear mass density  varies linearly from =0 at
the left end to =30 at the right end. Find the center of mass XCM=_________ L.
5. A non-uniform 1.0-kg stick can be balanced at a point 80 cm from one end. If it is pivoted about that
end, it oscillates with a period of 3.14 s. The moment of inertia about an axis perpendicular to the stick
through its center of mass is I=__________ kg-m2.
6. A copper wire 2 mm in diameter carries a 3.14-A current. The drift velocity of the free electrons is
vd = ________ m/s. [The atomic mass of Cu is 63.5 u, so 63.5g of Cu contains 61023 free electrons.
The mass density of Cu is 8.9103 kg/m3].
7. An electron travels at 0.1c (c= speed of light) in a plane perpendicular to a 0.01-T uniform magnetic
field. The cyclotron frequency is f=__________ Hz.
8. An optical coating of MgF2, whose index of refraction is n=1.4, is designed to eliminate reflected light
at wavelengths centered at 560 nm when incident normally on glass for which n=1.5. The minimum
thickness of this non-reflective coating is t=_______ nm.
國立彰化師範大學九十一學年度碩士班招生考試試題
系所：物理學系碩士班
☆☆請在答案紙上作答☆☆
科目：普通物理
共 2 頁，第 2 頁
二、 計算題: (每題 10 分, 共 40 分)
1. A projectile is launched at angle /4 from a cliff of height H above sea level. If it falls into the sea at a
distance equal to 3H from the base of the cliff, then
(a) what is the maximum height above the sea level?
(b) what is the time of flight?
2. (a) A non-conducting thin circular disk of radius R has a uniform surface charge density  (C/m2).
Determine the potential V along the axis of the disk at a distance x from its center.
(b) Using the result of (a), obtain the electric field E for an infinite plate with surface charge density 
(C/m2).
3. (a) Show that, for an ideal gas, CP-CV=R.
(b) Show that, for an adiabatic quasi-static process of an ideal gas, PV is a constant, where =CP/CV.
4. Figure 1 shows the plane Cartesian coordinate system, the axes are labeled x and y, with the origin O
and two points A(0,a),B(0,-a) along the y-axis.
(a) If we put a charge q at point A, and a charge –q at point B, we have an electric dipole. Show that, in
the far-field approximation, the resultant electric field falls off as the inverse cube of the distance
along either the perpendicular bisector (x-axis) or the axis of the dipole (y-axis).
(b) Figure 2 shows an electric dipole in the plane polar coordinate system (r,).
Find the potential V(r,) at point C(r,) in the far-field approximation (i.e. r>>a).
Then, use E r  
V
1 V
and E  
to find the components of the electric field, and compare
r
r 
with the results of (a).
y
y
C(r,θ)
q(0,a)
A
A
0
B
Figure 1.
r
θ
x
x
0
B
-q(0,-a)
Figure 2.