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Unit 13 Solutions_Page_06

# Unit 13 Solutions_Page_06 - (C 2010 McGraW—Hill:1 Find...

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Unformatted text preview: (C) 2010 McGraW—Hill (:1) Find the induced emf in one of the windings. 8 L AI _ #UN2a(%)2 AI 1 d2 AI —=——— ———=——,uﬂim N N Ar EN A: 4 A: _ 1 —7 —1 2 2 _ —5 ——Z(47r><10 H/m)¢r(160 cm )(10 cm/m)(0.0075 In) (—35.0 A/s)— 3.1><10 V (b) Find the induced emfin the entire solenoid. g: N{%) ng£§j (160 cm‘1)(2.8 chC3-1><10'5 V) :- Chapter 20 CQ [12], 13, [14], [20] 12. 13. 14. 20. (a) The mutual inductance of two identical circular coils of wire separated by a fixed distance is maximized when the coils are aligned parallel to each other. (b) Their mutual inductance is minimized when the coils are perpendicular to each other. (a) A transformer only works for alternating currents because its operation is based upon the principle of magnetic induction. A current can only be induced by a changing magnetic ﬂux which requires a changing primary current—impossible to achieve with a direct current. (b) The back emfin the primary coil limits the size ofthe cunent. For dc emf, no back ernfeXists, and thus, the current is much too large (limited only by the small resistance of the coils). Machines that read information encoded on the magnetic strip of a credit card operate via the principle of magnetic induction. The machine interprets digital bits from changing currents produced as the magnetic ﬂux varies from one part of the strip to another. If the card is moved too slowly, the magnetic flux does not change quickly enough to produce a large enough emf. The farmer could place wire loops around the edge of his ﬁeld near the high voltage wires. The alternating current would produce a changing magnetic flux through the wire loops, and therefore, produce a current in the farmer’s loops. If the farmer were then to connect these loops to a circuit, they would act as a source of emf—all of this without any physical connection to the actual power lines. Problem 20.85 85. Strategy According to Faraday’s law, the magnitude of the induced emf around a loop is equal to the rate of change of the magnetic flux through the loop. According to Lenz’s law, the direction of an induced current in a loop always opposes the change in magnetic flux that induces the current. Solution As the bar magnet travels from 1 to 2, B is increasing and to the left at the coil. As viewed from the left, a CW cunent is induced in the coil that generates a magnetic field to the right to oppose the increasing magnetic field due to the bar magnet Thus, the current is negative and increasing in magnitude. As the bar magnet travels from 2 to 3, B is decreasing and to the left at the coil. The induced current flows CCW to oppose the decreasing 776 ...
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