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Problem Set 10 Due: 11/19/09, Thursday Chapter 30: Induction & Inductance Exercises & Problems: 1, 17, 19, 35, 55, 63, 80, 95 Chapter 30 Even Answers 120, 0.600 mH Question A A car stops for a red light at an intersection. As it comes to a halt, it moves over a coil embedded in the surface of the road. As a result, the light soon changes from red to green. Explain how the coil is able to signal the light to change. Question B A farmer claimed that the high-voltage transmission lines running parallel to his fence induced dangerously large voltages on the fence. Is this with the realm of possibility? Explain. (The lines carry alternating current that changes direction 120 times each second.) Question C Some modern stove burners are based on induction. That is, an ac current passes around a coil that is the “burner,” a burner that never gets hot. Explain why it will heat a metal pan but not a glass container. Question D A region where no magnetic field is desired is surrounded by a sheet of low-resistivity metal. (a) Will this sheet shield the interior from a rapidly changing magnetic field outside? Explain. (b) Will it act as a shield to a static magnetic field? (c) What if the sheet is superconducting (resistivity = 0)? ******EXAM 2 Alert****** November 19, Thursday Problem 30.1 In Fig. 30-37, the magnetic flux through the loop increases accord ing to the relation B = 6.0t2 + 7.0t, where B is in milliwebers and t is in seconds. (a) What is the magnitude of the emf induced in the loop when t = 2.0 s? (b) Is the direction of the current through R to the right or left? Problem 30.17 An electric generator contains a coil of 100 turns of wire, each forming a rectangular loop 50.0 cm by 30.0 cm. The coil is placed entirely in a uniform magnetic field with magnitude B = 3.50 T and with B initially perpendicular to the coil's plane. What is the maximum value of the emf produced when the coil is spun at 1000 rev/min about an axis perpendicular to B? Problem 30.19 One hundred turns of (insulated) copper wire are wrapped around a wooden cylindrical core of cross-sectional area 1.20 103 m2. The two ends of the wire are connected to a resistor. The total resistance in the circuit is 13.0 Ω. If an externally applied uniform longitudinal magnetic field in the core changes from 1.60 T in one direction to 1.60 T in the opposite direction, how much charge flows through a point in the circuit during the change? Problem 30.35 Figure 30-59 shows a rod of length L = 10.0 cm that is forced to move at constant speed v = 5.00 m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance 0.400 Ω; the rest of the loop has negligible resistance. A current i = 100 A through the long straight wire at distance a = 10.0 mm from the loop sets up a (nonuniform) magnetic field through the loop. Find the (a) emf and (b) current induced in the loop. (c) At what rate is thermal energy generated in the rod? (d) What is the magnitude of the force that must be applied to the rod to make it move at constant speed? (e) At what rate does this force do work on the rod? Problem 30.55 A solenoid having an inductance of 6.30 μH is connected in series with a 1.20 kΩ resistor. (a) If a 14.0 V battery is connected across the pair, how long will it take for the current through the resistor to reach 80.0% of its final value? (b) What is the current through the resistor at time t = 1.0L? SSM Problem 30.63 A coil is connected in series with a 10.0 kΩ resistor. An ideal 50.0 V battery is applied across the two devices, and the current reaches a value of 2.00 mA after 5.00 ms. (a) Find the inductance of the coil. (b) How much energy is stored in the coil at this same moment? SSM Problem 30.80 The inductance of a closely wound coil is such that an emf of 3.00 mV is induced when the current changes at the rate of 5.00 A/s. A steady current of 8.00 A produces a magnetic flux of 40.0 μWb through each turn. (a) Calculate the inductance of the coil. (b) How many turns does the coil have? Problem 30.95 In the circuit of Fig. 30-80, R1 = 20 k, R2 = 20 , L = 50 mH, and the ideal battery has = 40 V. Switch S has been open for a long time when it is closed at time t = 0. Just after the switch is closed, what are (a) the current ibat through the battery and (b) the rate dibat/dt? At t = 3.0 s, what are (c) ibat and (d) dibat/dt? A long time later, what are (e) ibat and (f) dibat/dt? SSM