課程名稱︰普通物理學甲下 課程性質︰機械系必修 課程教師︰李慶德 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰2012/4/27 考試時限（分鐘）：180 是否需發放獎勵金： 是 試題 : 1. Useful Info and Formulas → → ．Gauss' law: ∫E．dA = q/ε0, where q is the net charge enclosed in the Gaussian surface. -12 2 2 ．Permittivity constant: ε0 = 8.85 × 10 C / N．m ．Electric field and electric potential: b → ∂V Vb - Va = －∫ E．ds, Es = －—. a ∂s -19 ．Elementary or fundamental charge: e = 1.602 × 10 C. → → ．Current density and drift velocity: J = neVd, where the product ne is carrier charge density. l ．Resistance and resistivity: R = ρ- for a wire of length l and cross section A. → m ．Resistivity and current density: E = ρJ , where ρ = ── with τ and 2 e nτ m respectively being the mean free time and the mass of the electron. ．Electric energy stored in a capacitor: 1 2 q U = - CV = ─ 2 2C 2. Do any 5 of the problems given below! 1. Two charges q and -q are located at (0,0,d/2) and (0,0,-d/2) on the z-axis, respectively. (a) Find the electric field for points on the z-axis. (b) Find the electric field for points on the y-axis. (c) For points on the z- and y- axes far away from the electric dipole, check if your result for (a) and (b) are consistent with the general formula → 1 ^ → ^ → 3 E = ─── {3(r．p)r - p}/r , 4πε0 → → where p = qdk is the electric dipole moment and r >> d. 2. A hollow spherical conductor has an inner of 10cm and an outer radius of 20cm. The electric field at point P just outside the outer surface of this hollow spherical conductor has magnitude 450 N/C and is directed outward. When an unknown charge Q is introduced into the center of the sphere, the electric field at P is still directed outward but is now 180 N/C. (a) What is the net charge enclosed by the outer surface before Q was introduced? (b) What is the charge Q? (c) After Q is introduced, what are the charges on the inner and outer surfaces of the conductor? 3. A plastic plate of radius a has a uniform charge density σ on one surface. (a) Find the electric potential V(z) at any point on the central axis of the disk, which is taken as the z-axis. (b) From the result of (a), evaluate the electric field for points on the central axis of the charged disk. (c) What does the electric field become for points on the central axis with z >> a and z << a? 4. A wire 8.00 m long and 6.00 mm in diameter has a resistance of 30.00 mΩ. A potential difference of 24.0 V is applied between the ends. (a) What is the current in the wire? (b) What is the magnitude of the current density? (c) Calculate the resistivity of the wire material. 5. A 150 kΩ resistor and a capacitor are connected in series, and a 12.0 V potential difference is suddenly applied across them. The potential difference across the capacitor rises to 5.00 V in 1.3 μs. (a) Calculate the time constant of the curcuit. (b) Find the capacitance of the capacitor. 6. In the circuit shown in Fig. 1, ε = 1.2 kV, C = 6.5μF, R1 = R2 = R3 = 0.73 MΩ. With the capacitor C completely uncharged, switch S is suddenly closed (at t = 0). (a) What are the currents in resistors R1, R2, and R3 at t = 0? (b) What are the currents in resistors R1, R2, and R3 at t = ∞ (that is, after many time constants)? (c) What is the potential difference across resistor R3 at t = 0 and t = ∞? ／ ┌﹋﹌— S ┬───┐ │ R1 │ R3 ︴ │ │ ︴ ▂ ︴ ┴ -- R2 ︴ C ┬ │ │ │ └─────┴───┘ Figure 1: A circuit of one capacitor and three resistors --

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