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253-hwk-31b - v parallel to a long straight wire carrying a...

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HPHY 253 Homework 31b Electromagnetic Induction: Motional Emf Dr. A. E. Bak Name 1. Serway & Jewett Problem 31 : 20 . An automobile has a vertical radio antenna that is 1 : 20 m long. The automobile travels at 65 : 0 km=h on a horizontal road where Earth°s magnetic ±eld is 50 : 0 °T directed toward the north and downward at an angle of 65 : 0 ° below the horizontal. (a) Specify the direction the automobile should move so as to generate the maximum motional emf in the antenna, with the antenna°s top positive relative to its bottom. (b) Calculate the magnitide of this induced emf. 2. Serway & Jewett Problem 31 : 56 . A conducting rod of length moves with velocity v in a direction perpendicular to a long, straight wire carrying a steady current I . The axis of the rod is maintained parallel to the wire as shown in Figure P 31 : 56 . Show that jEj = ° 0 I‘v 2 ±r is the magnitude of the emf induced in the rod. In this case, note that the emf decreases with increasing r as you might expect. 3. Serway & Jewett Problem 31 : 61 . A conducting rod of length moves with velocity
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Unformatted text preview: v parallel to a long, straight wire carrying a steady current I as shown in Figure P 31 : 61 . The axis of the rod is maintained perpendicular to the wire with the near end at a distance r away as shown in Figure P 31 : 61 . Show that jEj = & Iv 2 ± ln & 1 + ‘ r ± is the magnitude of the emf induced in the rod. 4. Serway & Jewett Problem 31 : 66 . A thin 30 :-cm wire is held parallel to and 80 : cm above an in²nitely long, thin, straight wire carrying 200 A and resting on the horizontal ³oor. See Figure P 31 : 66 . The short wire is released from rest at time t = 0 and subsequently free falls, remaining parallel to the current-carrying wire as it descends. (a) Derive an equation for the emf induced in the short wire. Express your result as a function of the fall time t . (b) What is the minimum value of the induced emf? (c) What is the maximum value? (d) What is the induced emf : 300 s after release? 1...
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