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6月16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 write down Maxwell's equations.[Hint: There are four of them in
total.](20%)
2.A capacitor in an LC oscillator has a maximum potential difference of 17 V
and a maximum energy of 160 μJ. When the capacitor has a potential
difference of 5 V and an energy of 10 μJ, what are (a) the emf across the
inductor (10%) and (b) the energy stored in the magnetic field (10%)?[Hint:
Conservation of energy]
3.Please describe two experiments which demonstrate the particle-like nature
of light.(實驗證明光的粒子性質)?(10%)
4.Hall effect two-dimensions(二維系統之霍爾效應). Please prove that in a two-
dimensional (2D) electron system, the Hall resistance (霍爾電阻) is given by
R_H=V_H/I=B/(ne), where V_H is the Hall potential difference, I is the
current, B is the applied magnetic field perpendicular to the 2D electron
system, n is the carrier concentration (in m^-2) and e is the electron
charg, respectively.(10%) (In 2D, the current density is given by J=I/w
where w is the width of the 2D system. Ohm's law is given by E=ρ_H/J where
ρ_H=R_H is the Hall resistivity in 2D.)
5.A catfish is 2.00 m below the surface of a smooth lake. What is the diameter
of the circle on the surface through which the fish can see the world outside
the water (10%)? [Hint: the index of refraction of water is 4/3]
6.In Fig. 1, a broad beam of light of wavelength 630 nm is incident at 90
degree on a thin wedge-shaped film with index of refraction 1.50. An observer
intercepting the light transmitted by the film sees 10 bright and 9 dark
fringes along the length on the film. By how much does the film thickness
change over this length ?(10%)
incident light
↓ ↓ ↓
▁▂▃▄▅▆▇█
████████
████████
↓ ↓ ↓
Figure 1
7.Light of wavelength 440 nm passes through a double slit, yielding a
diffraction pattern whose graph of intensity versus angular position is shown
in Fig.2. Calculate (a) the slit width (5%) and (b) the slit separation.(5%)
Figure 2 (The first dark fringe for sigle-slit is at 5 degree, and there are
4 bright fringes for double-slit in the central bright fringe for sigle-slit.
Where the 5th bright fringe for double-slit is also at 5degree.Only the right
side of the graph is shown.)
8.The root mean square (rms) value of the electric field in a certain light
wave is 0.200 V/m. What is the amplitude of the associated magnetic field?
(10%)
The permittivity constant ε_0=8.85x10^-12 C/Nm^2, the permeability constant
μ_0=4πx10^-7 Tm/A
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