課程名稱︰普通物理學甲下
課程性質︰系定必修
課程教師︰梁啟德
開課學院：
開課系所︰材料系
考試日期（年月日）︰2008年4月14日
考試時限（分鐘）：110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 prove the following statement. If an excess charge is placed on an
isolated conductor, that amount of charge will entirely to the surface of
the conductor. None of the excess charge will be found within the body of
the conductor. (10%)
2.An electric dipole in a uniform electric field is displaced slightly from
its equilibrium position, as shown in Figure 1, where θ is small. The
separation of the charges is 2a, and the moment of inertia of the dipole is
I. Assuming the dipole is released from this position, show that its angular
orientation exhibits simple harmonic motion with a frequency (10%)
1 2qaE
f = --(----)^1/2
2π I
---------------------------------->
(+)
----------------------/----------->
/θ
--------------------/------------->
/
------------------/--------------->
(-)
---------------------------------->
Figure 1
3. Please calculate the electric field E(z) (10%) and the electric potential
V(z) (10%) at points at the points at the center axis of a plastic disk of
radius R that has a uniform charge density of one surface. Here z
corresponds to the distance between any point at the center axis of the
disk and the center of the disk. The surface charge density of the disk is
given by σ (in units of C/m^2).
4.In the circuit of Fig. 2, the switch S has been open for a long time. It is
then suddenly closed. Determine the RC time constant (a) before the switch
is closed and (10%) (b) after the switch is closed. (10%) (c) Let the switch
be closed at t = 0. Determine the current in the switch as a function of
time. (10%)
50.0 kΩ
------------/\/\/\/----------------------
| | |
| / |
| / S |
--- 10.0 V | --- 10.0 μF
- | ---
| | |
| | |
--------------------------/\/\/\/--------
100 kΩ
Figure 2
5.A certain X-ray tube operates a current of 7.0 mA and a potential
difference of 80 kV. What is its power in Watt? (10%)
6.You are given a number of 10Ω resistors, each capable of dissipating only
1.0 W without being destroyed. What is the minimum number of such resistors
that you need to combine in series or in parallel to make a 10Ω resistance
that is capable of dissipating at least 5.0 W? (10%)
7.A parellel-plate capacitor whose capacitance C is 13.5 pF (1 pF = 1 x 10^-12
Farad) is charged to a potential difference V = 12.5 V between its plates.
The charging battery is now disconnected and a porcelain slab (dielectric
constant κ=6.50) is slipped between the plates. What is the electric
potential energy of the device, after the slab is introduced (10%)? ε_0 =
8.85 x 10^-12 C^2/N‧m^2
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