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Chapter 31

Chapter 31 - 31 Faraday's Law CHAPTER OUTLINE 31.1 31.2...

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31 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 31.7 Maxwell’s Equations Faraday’s Law ANSWERS TO QUESTIONS Q31.1 Magnetic flux measures the “flow” of the magnetic field through a given area of a loop—even though the field does not actually flow. By changing the size of the loop, or the orientation of the loop and the field, one can change the magnetic flux through the loop, but the magnetic field will not change. Q31.2 The magnetic flux is Φ B BA = cos θ . Therefore the flux is maximum when 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. Q31.3 The force on positive charges in the bar is F v B = × q a f . 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. Q31.4 No. The magnetic force acts within the bar, but has no influence on the forward motion of the bar. Q31.5 By the magnetic force law F v B = × q a f : 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. Q31.6 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. Q31.7 A current could be set up in the bracelet by moving the bracelet through the magnetic field, or if the field rapidly changed. Q31.8 Moving a magnet inside the hole of the doughnut-shaped toroid will not change the magnetic flux through any turn of wire in the toroid, and thus not induce any current. 213

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214 Faraday’s Law Q31.9 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. Q31.10 Yes. Eddy currents will be induced around the circumference of the copper tube so as to fight the changing magnetic flux by the falling magnet. If a bar magnet is dropped with its north pole downwards, a ring of counterclockwise current will surround its approaching bottom end and a ring of clockwise current will surround the receding south pole at its top end. The magnetic fields created
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