課程名稱︰普通物理學甲下 課程性質︰系必修 課程教師︰李慶德 開課學院：工學院 開課系所︰機械系 考試日期（年月日）︰2011/4/22 考試時限（分鐘）：150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. Useful Info and Formulas → → ． Guass' law ∮E ˙dA = q/ε0, where q is the net charge enclosed in the Gaussian surface. ． Permittivity constant:ε0 = 8.85 ×10^-12 C^2/N×m^2 ． Electric field and eletric potential: b → → Vb-Va=-∫ E ˙ds , Es= - dV/ds a ．Elementary of fundamental charge: e=1.602 ×10^-19 C. → → ．Current density and drift velocity: J = nevd , where the product ne is carrier charge density. ．Resistance and resistivity: R=ρ×(L/A) for a wire of length L and cross section A. → → ．Resistivity and current density: E =ρJ ,where ρ= m/(e^2nτ) with τ and m respectively being the mean free time and the mass of the electron. ．Electric energy stored in a capacitor: U = (1/2)CV^2 = q^2/(2C) 2. Do any 5 of the exam problems given below! 1. A solid sphere of radius a = 2.00cm is concentric with a spherical cunducting shell of inner radius b = 4.00cm and outer radius c = 5.00cm. The sphere has a net uniform charge q1 = +2.00pC; the shell has a net charge q2 = -4.00pC. (a) Find the magnitudes of the electric field at radial distances r = 1.00cm, r = 3.00cm, and r = 6.00cm. (b) What are the net charges on the inner and outer surfaces of the shell? 2. Fig. 1 shows a nonconducting disk of radius a withe a net charge q uniformly distributed on its upper surface. → (a) Find the electric field E at a distance y from the center along the central axis. (b) Use the result you obtain for (a) to show that the electric field strength due to an infinite of charge with unifrom surface charge density σ is given by E=σ/2ε0 3. Two charges q and -q are located in the x-y plane at (0,a) and (0,-a) on the y-axis, respectively. (a) Find the electric potential V(x,y) at the point (x,y). (b) Use V(x,y) obtained for (a) to find the electric field along the x-axis. 4. An isolated conducting sphere whose radius R is 6.25cm has a charge q = 1.20nC. (a) Show that an isolated sphere has capacitance given by C = 4πε0R. (b) Evaluate the potential energy stored in the electric field of this charged conductor. (c) What is the energy density at the surface of sphere? 5. Fig. 2 shows capacitor 1(C1=8.00μF), capacitor 2(C2=6.00μF), and capacitor 3(C3=8.00μF) connected to a 12.0V battery. (a) When switch S is closed so as to connect uncharged capacitor 4 (C4=6.00μF), find the amount of charge passing through point P and the amount of charge showing up on capacitor 4. (b) Explain the discrepancy in the two results (i.e., amounts of charge) you have obtianed for (a). 6. A wire 2.00m long and 3.00mm in diameter has a resistance of 30.0mΩ. A potential difference of 23.0V 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. Figure 2: Capacitors connected to a batter P　　　　　　　　　S ┌─˙─┤ ├──┬─˙／˙─┐ │　　　　C1 │ │ ┴ C2 ┴ ┴ C4 V – ┬ ┬ │ │ │ └───┤ ├──┴─────┘ C3 --

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