課程名稱︰普通物理學甲下 課程性質︰必修 課程教師︰楊忠喜 開課學院： 開課系所︰生機系 考試日期（年月日）︰2012/5 考試時限（分鐘）：120 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 應該是從課本習題影印來，所以題號、圖號不規則或缺失請見諒，課本都找得到吧 21. Figure 32- shows a rod of length l caused to move at constant velocity v along horizontal conducting rails. In this case the magnetic field in which the rod moves is not uniform but is provided by a current i in a long parallel wire. Assume that v = 2.0m/sec, a = 10 mm, l = 10 cm, and i = 200 A. (a) Caculate the emf induced in the rod. (b) What is the current in the conducting loop? Assume that the resistance of the rod is 0.40Ω and that the resistance of the rails is negligible. (c) At what rate is thermal energy being generated in the rod by an external agent to maintain its motion? (e) At what rate does this external agent do work on the rod? Compare this answer to (c). 51. An electric field exists in the cylindrical region shown and is parallel to the cylinder axis. The magnitude of the field might vary with time according to any of the four graphs shown. Rank the four variations according to the magnitudes of the magnetic field induced at the edge of the region, least to greatest. A. 2, 4, 3, 1 B. 3 and 4 tie, then 1, 2 C. 4, 3, 2, 1 D. 4, 3, 1, 2 E. 2, 1, 3, 4 66. Consider the four Maxwell equations: 1. ∫E‧dA = q/ε 2. ∫B‧dA = 0 3. ∫E‧ds = -dΦB/dt 4. ∫B‧ds = μ0i + μ0ε0dΦE/dt Which of these must be modified if magnetic poles are discovered? A. Only 1 B. Only 2 C. Only 2 and 3 D. Only 3 and 4 E. Only 2, 3, and 4 68. The diagrams show three circuits with identical batteries, identical inductors, and identical resistors. Rank them according to the current through the battery just after the switch is closed, from least to greatest. 45. A uniform magnetic field B fills a cylindrical volume of radius R. A metal rod of length L is placed as shown in Fig.. If B is changing at the rate dB/dt, show that the emf that is produced by the changing magnetic field and that acts between the ends of the rod is given by dB L ＿＿＿＿＿＿＿ ε = ── ─ ∕ dt 2 V R^2 - (L/2)^2 (13) A parallel-plate capacitor has square plates 1.0 m on a side as shown in Fig.. A current of 4.0 A charges the capacitor, producing a uniform electric field E between the plates, with E perpendicular to the plates. (a) What is the displacement current id through the region between the plates? (b) What is dE/dt in this region? (c) What is the displacement current through the square dashed path between the plates? (d) What is ∫B‧ds around this square dashed path? (7) When f = ＿＿＿＿＿Hz, Pavg 為maximum? Z = ? Pavg = ? (27) Consider the mechanical system consisting of two springs and a block, as shown. Which one of the five electrical circuits (A, B, C, D, E) is the analog of the mechanical system? Why? 15. A coil C of N turns is placed around a long solenoid S of radius R and n turns per unit length, as in Fig.. Find the coefficient of mutual inductance for the coil-solenoid combination is given by. M = ? (20) Figure shows a rectangular loop of wire immersed in a nonuniform and varying magnetic field B that is perpendicular to and directed into the page. The field's magnitude is given by B = 4t^2 - x^2 , with B in teslas, t in seconds, and x in meters. The loop has width W = 3.0 m and height H = 2.0 m. What are the magnitude and direcion of induced emf ε around the loop at t = 0.2 sec. --

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