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課程名稱︰普通物理甲下
課程性質︰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）︰2010/04/30
考試時限（分鐘）：180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.Using the energy band diagram to describe the difference among conductor,
semiconductor, and insulator. (8%)
2. Describe the working principle of scan tunneling microscope. (10%)
3. State briefly the phenomenon of Hall effect and its application. (8%)
4. Explain the mechanism of the low-temperature superconductivity. (8%)
5. Describe the operating principle of time- of-flight mass spectroscopy. (8%)
6. From the "molecular point of view", why the electric field in a capacitor
should decrease when a dielectric is inserted? (8%)
7. In Fig. 1, a conductor carries 6.0 A along the closed path abedefgha running
along 8 of the 12 edges of a cube of edge length 10 cm. (a) Taking the path
to be a combination of three square current loops (befgb, abgha, and cdefc),
find the net magnetic moment of the path in unit-vector notation. (b) What is
the magnitude of the net magnetic field at the xyz coordinates of (0,5.0 m,
0)? (4%, 4%)
8. In Fig. 2, a rectangular loop carrying current lies in the plane of a
uniform magnetic field of magnitude 0.040 T. The loop consists of a single
turn of flexible conducting wire that is wrapped around a flexible mount such
that the dimensions of the rectangle can be changed. (The total length of the
wire is not changed.) As edge length x is varied from approximately zero to
its maximum value of approximately 4.0 cm, the magnitude τ of the torque on
the loop changes. The maximum value of τ is 4.80 x 10^-8 N . m. What is the
current in the loop? (8%)
┌────────┐
│ │
│ │
│ │
└────────┘
├─── x ───┤
Fig. 2
9. The circuit of Fig. 3 shows a capacitor, two ideal batteries, two
resistors, and a switch S. Initially S has been open for a long time. If it
is then closed for a long time, what is the charge on the capacitor? Assume C
= 10μF ε_1= 1.0 V, ε_2= 3.0 V, R_1 = 0.20 Ω ,and R_2 = 0.40 Ω. (8%)
switch
┌─*／*─────┬────────┐
- │ ε_1 │ ε_2 │-
┴ ↓ │ ↓ ┴
+ ￣￣ ─┴─ ￣￣+
│ ─┬─ C │
＜ │ ＜
R _1 ＞ │ ＞ R_2
＜ │ ＜
＞ │ ＞
│ │ │
└────────┴────────┘
Fig. 3
10. Figure 4 shows wire section 1 of diameter D_1 = 4.00R and wire section 2
of diameter D_2 = 2.00R, connected by a tapered section. The wire is copper.
and carries a current. Assume that the current is uniformly distributed
across any cross-sectional area through the wire's width. The electric
potential change V along the length L = 2.00 m shown in section 2 is 10.0μV.
The number of charge carriers per unit volume is 8.49×l0^28 m^-3. What is
the drift speed of the conduction electrons in section 1? (8%)
──╥──╮╞══L══╡
║ ╰────╥─
D_1 D_2
║ ╭────╨─
──╨──╯
(1) (2)
Fig.4
11. In Fig. 5, a nonconducting spherical shell of inner radius a = 2.00 cm
and outer radius b = 2.40 cm has (within its thickness) a positive volume
charge density ρ= A/r, here A is a constant and r is the distance from the
center of the shell. In addition, a small ball of charge q = 45.0 fC is
klocated at that center. What value should A have if the electric field in
the shell (a<=r<= b) is to be uniform? (8%)
12. Fig. 6 shows an electric quadrupole. It consists of two dipoles with
dipole moments that are equal in magnitude but opposite in direction. Show
that the value of E on the axis of the quadrupole for a point P a distance z
from its center (assume z>>d) is given by E = 3Q/(4π．ε_0． z^4) in which
Q (=2qd^2) is known as the quadrupole moment of the charge distribution. (10%)
├──────z───────┤
├─ d─┼─ d─┤ │
●-----○○-----●───────── ⊙
+q -q-q +q p
Fig.6
圖在課本都有(v. 8)
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