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4月14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 prove the following statement. If an excess charge is placed on an isolated conductor, that amount of charge will entirely to the surface of the conductor. None of the excess charge will be found within the body of the conductor. (10%) 2.An electric dipole in a uniform electric field is displaced slightly from its equilibrium position, as shown in Figure 1, where θ is small. The separation of the charges is 2a, and the moment of inertia of the dipole is I. Assuming the dipole is released from this position, show that its angular orientation exhibits simple harmonic motion with a frequency (10%) 1 2qaE f = --(----)^1/2 2π I ----------------------------------> (+) ----------------------/-----------> /θ --------------------/-------------> / ------------------/---------------> (-) ----------------------------------> Figure 1 3. Please calculate the electric field E(z) (10%) and the electric potential V(z) (10%) at points at the points at the center axis of a plastic disk of radius R that has a uniform charge density of one surface. Here z corresponds to the distance between any point at the center axis of the disk and the center of the disk. The surface charge density of the disk is given by σ (in units of C/m^2). 4.In the circuit of Fig. 2, the switch S has been open for a long time. It is then suddenly closed. Determine the RC time constant (a) before the switch is closed and (10%) (b) after the switch is closed. (10%) (c) Let the switch be closed at t = 0. Determine the current in the switch as a function of time. (10%) 50.0 kΩ ------------/\/\/\/---------------------- | | | | / | | / S | --- 10.0 V | --- 10.0 μF - | --- | | | | | | --------------------------/\/\/\/-------- 100 kΩ Figure 2 5.A certain X-ray tube operates a current of 7.0 mA and a potential difference of 80 kV. What is its power in Watt? (10%) 6.You are given a number of 10Ω resistors, each capable of dissipating only 1.0 W without being destroyed. What is the minimum number of such resistors that you need to combine in series or in parallel to make a 10Ω resistance that is capable of dissipating at least 5.0 W? (10%) 7.A parellel-plate capacitor whose capacitance C is 13.5 pF (1 pF = 1 x 10^-12 Farad) is charged to a potential difference V = 12.5 V between its plates. The charging battery is now disconnected and a porcelain slab (dielectric constant κ=6.50) is slipped between the plates. What is the electric potential energy of the device, after the slab is introduced (10%)? ε_0 = 8.85 x 10^-12 C^2/N‧m^2 --

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