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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