課程名稱︰普通物理學甲下
課程性質︰必修
課程教師︰陸駿逸
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰2008/04/17
考試時限（分鐘）：110 + 30(額外) 分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
．Use enough words (in Chinese or English) to explain your reasoning and
thought (GREADS VERY MUCH DEPENDS ON THIS)
．Read the questions carefully. Answer accurately the questions asked.
1. (20 pts) Write down the definition of the following terms:
(a) Electric field
(b) Electric flux
(c) Gauss' law
(d) Dielectric constant
(e) Capacitance
2. (10 pts) Sketch the electric field lines of the given charge systems.
(a) (b)
．-2q
．+2q ．-q ．+3q (此三電荷形成一正三角形)
．-q
3. (10 pts) Use the Gauss' law to calculate the capacitance of a cylindrical
capacitor, which is formed by two coaxial cylinders of length L, radii a
and b.
4. (15 pts) In 1819, Pierre Louis Dulong and Alexis Therese Petit proposed
that, regardless of the nature of the crystal, the specific heat capacity
(measured in joule per kelvin per kilogram) is equal to 3R/M, where R is
the gas constant (measured in joule per kelvin per mole) and M is the molar
mass (measured in kilogram per mole). Assume that every atoms in the
crystal can vibrate within the spring potential U(x,y,z) = (k/2)(x^2+y^2+
z^2). Use the Boltzmann's fctor to show that the Dulong-Petit law should
work.
∞ ∞ √π
(Hint: ∫e^(-x^2)dx = √π, ∫x^2 e^(-x^2)dx = ----- )
-∞ -∞ 2
5. (10 pts) Dulong-petit law does not work well at the low temperature.
Briefly explain the reason of its failure.
6. (20 pts) Suppose that the C2H2 molecule has posiive charge q = 0.5x10^-19C
on the hydrogen atoms, and -q on the carbon atoms. The H-C distance is 1.1
埃 and C-C distance is 1.2埃. Consider a sodium ion on the axis of the C2H2
molecule with the distance z from the conter of mass of C2H2. Show the the
electrostatic potential energy between C2H2 and Na+ is of the approximate
from U(z)= C0 / z^3. Calculate the constant C0. (ε0 = 8.9x10^-12 F/m)
7. (20 pts) Water molecule has the permanent dipole 6 x 10^-30 Cm. Suppose
that the molecules can only be parallel or anti-parallel with the applied
electric field. Use the Boltamann's factor to estimate the (static)
dielectric constant of the water at the room temperature where kB*T =
4 x 10^-21 J. (ε0 = 8.9 x 10^-12 F/m. Also you know that the density of
the water is roughly 1g/mL.)
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