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Summary

13.1 Faraday’s Law

  • The magnetic flux through an enclosed area is defined as the amount of field lines cutting through a surface area A defined by the unit area vector.
  • The units for magnetic flux are webers, where 1Wb=1T·m2.
  • The induced emf in a closed loop due to a change in magnetic flux through the loop is known as Faraday’s law. If there is no change in magnetic flux, no induced emf is created.

13.2 Lenz's Law

  • We can use Lenz’s law to determine the directions of induced magnetic fields, currents, and emfs.
  • The direction of an induced emf always opposes the change in magnetic flux that causes the emf, a result known as Lenz’s law.

13.3 Motional Emf

  • The relationship between an induced emf ε in a wire moving at a constant speed v through a magnetic field B is given by ε=Blv.
  • An induced emf from Faraday’s law is created from a motional emf that opposes the change in flux.

13.4 Induced Electric Fields

  • A changing magnetic flux induces an electric field.
  • Both the changing magnetic flux and the induced electric field are related to the induced emf from Faraday’s law.

13.5 Eddy Currents

  • Current loops induced in moving conductors are called eddy currents. They can create significant drag, called magnetic damping.
  • Manipulation of eddy currents has resulted in applications such as metal detectors, braking in trains or roller coasters, and induction cooktops.

13.6 Electric Generators and Back Emf

  • An electric generator rotates a coil in a magnetic field, inducing an emf given as a function of time by ε=NBAωsin(ωt) where A is the area of an N-turn coil rotated at a constant angular velocity ω in a uniform magnetic field B→.
  • The peak emf of a generator is ε0=NBAω.
  • Any rotating coil produces an induced emf. In motors, this is called back emf because it opposes the emf input to the motor.

13.7 Applications of Electromagnetic Induction

  • Hard drives utilize magnetic induction to read/write information.
  • Other applications of magnetic induction can be found in graphics tablets, electric and hybrid vehicles, and in transcranial magnetic stimulation.
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