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Physics LibreTexts

9.S: Electromagnetic Induction (Summary)

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Key Terms

back emf emf generated by a running motor, because it consists of a coil turning in a magnetic field; it opposes the voltage powering the motor
eddy current current loop in a conductor caused by motional emf
electric generator device for converting mechanical work into electric energy; it induces an emf by rotating a coil in a magnetic field
Faraday’s law induced emf is created in a closed loop due to a change in magnetic flux through the loop
induced electric field created based on the changing magnetic flux with time
induced emf short-lived voltage generated by a conductor or coil moving in a magnetic field
Lenz’s law direction of an induced emf opposes the change in magnetic flux that produced it; this is the negative sign in Faraday’s law
magnetic damping drag produced by eddy currents
magnetic flux measurement of the amount of magnetic field lines through a given area
motionally induced emf voltage produced by the movement of a conducting wire in a magnetic field
peak emf maximum emf produced by a generator

Key Equations

Magnetic flux Φm=SBˆndA
Faraday’s law ε=NdΦmdt
Motionally induced emf ε=Blv
Motional emf around a circuit ε=Edl=dΦmdt
Emf produced by an electric generator ε=NBAωsin(ωt)

Summary

13.2 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=1Tm2.
  • 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.

13.3 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.

13.4 Motional Emf

  • The relationship between an induced emf εε 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.

13.5 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.

13.6 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.

13.7 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.

13.8 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.


This page titled 9.S: Electromagnetic Induction (Summary) is shared under a CC BY license and was authored, remixed, and/or curated by OpenStax.

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