推 harveyhs :畫圖辛苦了XD系學會需要您的考卷～ 07/02 02:15
課程名稱︰普通物理學甲下
課程性質︰物理系必修
課程教師︰張寶棣
開課學院：理學院
開課系所︰物理學系
考試日期（年月日）︰2012/05/15
考試時限（分鐘）：200 min
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. Please answer the following questions.
a. Describe the Gauss' Law. If our space is four dimentional, what will
you expect the r dependence of the Coulomb's law? (5 %)
b. What is the origin of electric resistance in material? Please give an
argument to exlain why capacitance depends on the geometry of the
capacitor. (5 %)
c. Why was the Maxwell displacement current introduced? Suppose that the
space between a capacitor is filled with a dielectric, what is the
change of the Maxwell displacement current inside the capacitor? (5 %)
2. The charge density in a region of space of spherically symmetric is given by
ρ(r) = C e^(-r/a) when r < R and ρ= 0 when r > R. Find the electric field
as a function of x. (10 %)
3. Three concentric conducting spherical shells have radii a, b, and c such
that a < b < c. Initially the inner shell is uncharged, the middle shell has
a positive charge Q, and the outer shell has a negative -Q.
(a) Find the electric potential of the three shells.
(b) If the inner and outer shells are now connected by a wire that is
insulated as it passes through the middle shell, what is the electric
potential of each of the three shells, and what is the final charge on
each shell? (15 %)
4. A parallel plate capacitor of area A and separetion d is charged to a
potential difference V and is then removed from the charging source. A
dielectric slab of constant κ= 2, thickness d, and area 1/2 A is inserted
as shown in Fig. 1. Let σ_1 be the free charge density at the conductor -
dielectric surface and σ_2 be the free charge density at the condutor-air
surface.
(a) Why must the electric field have the same value inside the dielectric as
in the free space between the plates?
(b) Please find relation beween σ_1 and σ_2.
(c) Find the new capacitance and new potential difference. (15 %)
---------------------
/ /
-----------------------
| |
| κ | -----------
| | /
----------------------
Fig. 1
5. A digital voltmetre of internal resistance r is used to measure the voltage
across a capacitor in an RC circuit after the switch in Fig. 2 is closed.
Because the metre has finite resistance, part if the current supplied by the
battery passes through the metre.
(a) Apply Kirchhoff's rules to this circuit, and use the fact that
i_C = dq / dt to show that this leads to a differential equation
dq q r
R_eq ---- + - = ----- ε,
dt c r+R
where R_eq = rR/(r+R).
(b) Solve the differential equation using the method described in the class
to obtain q and V_C as a function of t. (10 %)
Voltmetre
----V----
| |
| |
------R-------------C-------
| |
| |
| ╱ |
---- -------------│｜-------
S ε
Fig. 2
6. A Hall-Effect probe operates with a 120-mA current. Whem the probe is
placed in an uniform magnetic field of magnitude 0.080 T, it produces a Hall
voltage of 0.700 μV.
(a) When it is measuring an unknown magnetic field, the Hall voltage is
0.330 μV. What is the magnitude of the unknown field?
(b) The thickness of the probe in the direction of B is 2.00 mm. Find the
density of charge carriers, each of which has charge of magnitude e.
(10 %)
7. The rectangular frame in Fig. 3 is free to rotate about the axis A-A on the
horizontal shaft. The frame is 10 cm long and 6 cm wide and the rods that
make up the frame have a mass per unit length of 20 g/cm. An uniform
magnetic field B = 0.2 T is directed as shown. A current may be sent around
the frame by means of the wires attached at the top.
(a) If no current passes through the frame, what is the period of this
physical pendulum for small oscillation?
(b) If a current of 8.0 A passes through the frame in the direction
indicated by the arrow, what is then the period of this physical
pendulum?
(c) Suppose the direction of the current is opposite to that shown. The
frame is displaced from the vertical by some angle θ. What must be the
magnitude of the current so that this frame will be in equilibrium?
(15 %)
|← wire → |
| |
＼＼ |
＼＼ ↙ ↙ |
↙ / ＼＼ |
6 / ↙＼＼ ↙ ↙|
/ ＼＼ |
cm / ↙ ＼＼↙ |
/ ↙ ＼＼ | Fig. 3
↗ / ↙ ＼＼|
/ ↙ ＼＼
╲ ↙ ↙ / ＼＼
↙ ╲ / ＼＼
╲ ↙ ↙ / A
↙ ╲ ↙ / B↙
↙ ╲ /
↙ ↙ ╲ ↙ /
↙ ╲ /
8. A long cylindrical conductor of radius a has two cylindrical cavities of
diametre a through its entire length, as shown in Fig. 4. A current I is
directed out of the paper and is uniform through a cross section of the
conductor. Find the magnitude and direction of the magnetic field in terms
of μ_0, I, r, and a at (a) point P_1 and (b) point P_2. (10 %)
--------------P_1
↑
|
r ↑
| a
↓ ↓
-------------x-------------P_2
↑ |
a |
↓ |
|←----r----→|
Fig. 4
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.4.202