Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo


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·m2.1Wb=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 εε in a wire moving at a constant speed v through a magnetic field B is given by ε=Blv.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)ε=NBAωsin(ωt) where A is the area of an N-turn coil rotated at a constant angular velocity ωω in a uniform magnetic field B.B.
  • The peak emf of a generator is ε0=NBAωε0=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.
Order a print copy

As an Amazon Associate we earn from qualifying purchases.


This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at
Citation information

© Jan 19, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.