SM_PDF_chapter23

# SM_PDF_chapter23 - Faraday's Law and Inductance CHAPTER...

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635 Faraday’s Law and Inductance CHAPTER OUTLINE 23.1 Faraday’s Law of Induction 23.2 Motional emf 23.3 Lenz’s Law 23.4 Induced emfs and Electric Fields 23.5 Self-Inductance 23.6 RL Circuits 23.7 Energy Stored in a Magnetic Field 23.8 Context Connection The Repulsive Model for Magnetic Levitation ANSWERS TO QUESTIONS Q23.1 The magnetic flux is Φ B BA = cos θ . Therefore the flux is maximum when r B is perpendicular to the loop of wire and zero when there is no component of magnetic field perpendicular to the loop. The flux is zero when the loop is turned so that the field lies in the plane of its area. Q23.2 (a) The south pole of the magnet produces an upward magnetic field that increases as the magnet approaches. The loop opposes change by making its own downward magnetic field; it carries current clockwise, which goes to the left through the resistor. (b) The north pole of the magnet produces an upward magnetic field. The loop sees decreasing upward flux as the magnet falls away, and tries to make an upward magnetic field of its own by carrying current counterclockwise, to the right in the resistor. Q23.3 The force on positive charges in the bar is r r r Fv B q ej . If the bar is moving to the left, positive charge will move downward and accumulate at the bottom end of the bar, so that an electric field will be established upward. Q23.4 No. The magnetic force acts within the bar, but has no influence on the forward motion of the bar. Q23.5 By the magnetic force law r r r B q : the positive charges in the moving bar will flow downward and therefore clockwise in the circuit. If the bar is moving to the left, the positive charge in the bar will flow upward and therefore counterclockwise in the circuit. Q23.6 We ignore mechanical friction between the bar and the rails. Moving the conducting bar through the magnetic field will force charges to move around the circuit to constitute clockwise current. The downward current in the bar feels a magnetic force to the left. Then a counterbalancing applied force to the right is required to maintain the motion. Q23.7 As water falls, it gains speed and kinetic energy. It then pushes against turbine blades, transferring its energy to the rotor coils of a large AC generator. The rotor of the generator turns within a strong magnetic field. Because the rotor is spinning, the magnetic flux through its turns changes in time as Φ B BA t = cos ω . Generated in the rotor is an induced emf of ε = Nd dt B Φ . This induced emf is the voltage driving the current in our electric power lines.

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636 Faraday’s Law and Inductance Q23.8 Yes. The induced eddy currents on the surface of the aluminum will slow the descent of the aluminum. It may fall very slowly. Q23.9 The increasing counterclockwise current in the solenoid coil produces an upward magnetic field that increases rapidly. The increasing upward flux of this field through the ring induces an emf to produce clockwise current in the ring. The magnetic field of the solenoid has a radially outward component at each point on the ring. This field
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## This note was uploaded on 10/18/2008 for the course PHYS 3Q2341234 taught by Professor Dafsf during the Spring '08 term at UCLA.

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SM_PDF_chapter23 - Faraday's Law and Inductance CHAPTER...

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