SM_chapter31

# SM_chapter31 - 31 Faradays Law CHAPTER OUTLINE 31.1 31.2...

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31 Faraday’s Law CHAPTER OUTLINE 31.1 Faraday’s Law of Induction 31.2 Motional emf 31.3 Lenz’s Law 31.4 Induced emf and Electric Fields 31.5 Generators and Motors 31.6 Eddy Currents ANSWERS TO QUESTIONS Q31.1 Magnetic ﬂ ux measures the “ﬂ ow” of the magnetic F eld through a given area of a loop—even though the F eld does not actually ﬂ ow. By changing the size of the loop, or the orientation of the loop and the F eld, one can change the magnetic ﬂ ux through the loop, but the magnetic F eld will not change. *Q31.2 The emf is given by the negative of the time derivative of the magnetic ﬂ ux. We pick out the steepest downward slope at instant ± as marking the moment of largest emf. Next comes A. At B and at D the graph line is horizon- tal so the emf is zero. At E the ﬂ ux graph slopes gently upward so the emf is slightly negative. At C the emf has its greatest negative value. The answer is then ± > A > B = D = 0 > E > C. *Q31.3 (i) c (ii) b. The magnetic ﬂ ux is Φ B BA = cos θ . Therefore the ﬂ ux is a maximum when r B is perpendicular to the loop of wire and zero when there is no component of magnetic F eld perpendicular to the loop. The ﬂ ux is zero when the loop is turned so that the F eld lies in the plane of its area. *Q31.4 (i) Answer (c). The magnetic ﬂ ux through the coil is constant in time, so the induced emf is zero. (ii) Answer (a). Positive test charges in the leading and trailing sides of the square experience a r r r Fv B ( ) q force that is in direction (to the right) × (perpendicularly into the plane away from you) = toward the top of the square. The charges migrate upward to give positive charge to the top of the square until there is a downward electric F eld large enough to prevent more charge separation. Q31.5 By the magnetic force law r r r B ( ) q : the positive charges in the moving bar will feel a magnetic force in direction (right) × (perpendicularly out of the page) = downward toward the bottom end of the bar. These charges will move downward and therefore clockwise in the circuit. If the bar is moving to the left, the positive charge in the bar will ﬂ ow upward and therefore coun- terclockwise in the circuit. *Q31.6 (i) No. A magnetic force acts within the front and back edges of the coil, but produces no current and has no inﬂ uence on the forward motion of the coil. (ii) Yes. An induced current exists in the bar, which we can attribute either to an induced emf in the loop or to magnetic force on free charges in the bar. Then a backward magnetic force acts on the current and an external force must counterbalance it to maintain steady motion. (iii) No. A magnetic force acts within the bar, but produces no current and has no inﬂ uence on the forward motion of the bar. 201

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202 Chapter 31 Q31.7 As water falls, it gains speed and kinetic energy. It then pushes against turbine blades, transfer- ring its energy to the rotor coils of a large AC generator. The rotor of the generator turns within a strong magnetic F eld. Because the rotor is spinning, the magnetic ﬂ ux through its turns changes in time as Φ B BA t = cos .
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## This note was uploaded on 01/19/2012 for the course PHY 232 taught by Professor Williams,frank during the Spring '11 term at Ohio State.

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SM_chapter31 - 31 Faradays Law CHAPTER OUTLINE 31.1 31.2...

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