課程名稱︰普通物理學甲下 課程性質︰大一必修 課程教師︰李慶德 開課學院：電資學院 開課系所︰電機工程學系 考試日期（年月日）︰2015/4/30 考試時限（分鐘）：110 分鐘 試題 : =============================================================================== General Physics A - Midterm Exam April 30, 2015 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 x 10 C / N m ◎ Electric field and electric potential: b → \partial V Vb - Va = -∫ E．ds, Es = - ────── ( partial derivative ). a \partial s -19 ◎ Elementary or fundamental charge: e = 1.602 x 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 A 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: 2 1 2 q U = ─ CV = ── 2 2C I. Multiple-choice problems: (each problem accounts for 5 points) 1. Two identical conducting spheres A and B carry equal charge. They are seperated by a distance much larger than their diameters. A third identical conducting sphere C is uncharged. Sphere C is first touched to A, then to B, and finally removed. As a result, the electrostatic force between A and B, which was originally F, becomes: (a) F/2 (b) F/4 (c) 3F/8 (d) F/16 (e) 0 2. The dipole moment of a dipole in a 300 N/C electric field is initially perpendicular to the field, but it rotates so it is in the same direction as the field. If the moment has a magnitude of 2 x 10^(-9) C．m the work done by the field is: (a) -12 x 10^(-7) J (b) -6 x 10^(-7) J (c) 0 (d) 6 x 10^(-7) J (e) -12 x 10^(-7) J 3. A particle with charge 5.0 μC is placed at the corner of a cube. The total electric flux in N m^2 /C through all sides of the cube is: (a) 0 (b) 7.1 x 10^4 (c) 9.4 x 10^4 (d) 1.4 x 10^5 (e) 5.6 x 10^5 4. Positive charge Q is distributed uniformly throughout an insulating sphere of radius R, centered at the origin. A particle with a positive charge Q is placed at x = 2R on the x axis. The magnitude of the electric field at x = R/2 on the x axis is: (a) Q / 18πε0 R^2 (b) 17Q / 18πε0 R^2 (c) Q / 72πε0 R^2 (d) 17Q / 72πε0 R^2 (e) none of the above 5. If the electric field is in the positive x direction and has a magnitude given by E = Cx^2, where C is a constant, then the electric potential V is given by: (a) 2Cx (b) -2Cx (c) Cx^3/3 (d) -Cx^3/3 (e) -3Cx^3 6. A parallel-plate capacitor has a plate area of 0.2 m^2 and a plate seperation of 0.1 mm. If the charge on each plate has a magnitude of 4 x 10^-6 C, the potential difference across the plates is approximately: (a) 0 (b) 4 x 10^(-2) V (c) 1 x 10^2 V (d) 2 x 10^2 V (e) 4 x 10^8 V 7. Copper contains 8.5 x 10^28 free electrons/m^3. A copper wire of cross- sectional area 7.4 x 10^(-7) m^2 carries a current of 1A. The electron drift speed is approximately: (a) 3 x 10^8 m/s (b) 10^3 m/s (c) 1 m/s (d) 10^(-4) m/s (e) 10^(-7) m/s 8. A 20 μF capacitor is charged to 200 V. Its stored energy is: (a) 4000 J (b) 4 J (c) 0.4 J (d) 2000 J (e) 0.1 J 9. It is better to send 10,000 kW of electric power long distances at 10,000V rather than at 220V because: (a) there is less heating in the transmission wires (b) the resistance of the wires is less at high voltages (c) more current is transmitted at high voltages (d) the insulation is more effective at high voltages (e) the iR drop along the wires is greater at high voltage 10. Two wires made of the same material have the same length but different diameters. They are connected in series to a battery. The quantity that is the same for the wires is: (a) the end-to-end potential difference (b) the current (c) the current density (d) the electric field (e) the electron drift velocity II. Calculation problems: ( accounts for 50 points in total ) 11.[10%] A hollow spherical conductor has an inner radius of 10 cm and an outer radius of 20 cm. 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 center of the sphere, the electric field at P is still directed outward but is now 180 N/C. (a) What was the net charge enclosed by the outer surface before Q was introduced? (b) What is charge Q? (c) After Q is introduced, what are the charges on the inner and outer surfaces of the conductor? 12.[15%] An electric dipole consisting of a positive charge +q located at (0,0,a) and a negative charge of the same magnitude, i.e. -q, located at (0,0,-a), where a > 0. (a) Find the electric potentials produced by this electric dipole on the x-axis and the y-axis. (b) Find the electric field produced by this electric dipole on the x-axis and the y-axis. (c) What are the electric fields on the x-axis and the y-axis when |x| >> a? 13.[10%] A copper wire of cross-sectional area 2.40 x 10^(-6) m^2 and length 4.00 m has a current of 2.00 A uniformly distributed across that area. The resistivity of copper is ρ = 1.69 x 10^(-8) Ω．m. (a) What is the magnitude of the electric field along the wire? (b) How much electrical energy is transferred to thermal energy in 30 minutes? 14.[15%] In the circuit shown in Fig.1, ξ = 1.2 kV, C = 5.0 μF, R1 = R2 = R3 = 0.20 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 are the potential differences across resistor R3 at t = 0 and t = ∞? (d) What are the stored energies in the capacitor at t = 0 and t = ∞? Figure 1: A circuit of one capacitor and three resistors Link: http://imgur.com/86DBEim ================================== 試題完 =================================== --

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