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6: Electromagnetic Induction

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    In our development thus far, we have found the electric and magnetic fields to be uncoupled. A net charge generates an electric field while a current is the source of a magnetic field. In 1831 Michael Faraday experimentally discovered that a time varying magnetic flux through a conducting loop also generated a voltage and thus an electric field, proving that electric and magnetic fields are coupled.

    • 6.1: Faraday's Law of Induction
      Faraday's original experiments consisted of a conducting loop through which he could impose a dc current via a switch. Another short circuited loop with no source attached was nearby, as shown in Figure 6-1.
    • 6.2: Faraday's Law for Moving Media
      Various alloys of iron having very high values of relative permeability are typically used in relays and machines to constrain the magnetic flux to mostly lie within the permeable material.
    • 6.3: Energy Stored in the Magnetic Field
      If a point charge q travels with a velocity v through a region with electric field E and magnetic field B, it experiences the combined Coulomb-Lorentz force
    • 6.4: The Energy Method for Forces
      If the current distribution is known, the magnetic field can be directly found from the Biot-Savart or Ampere's laws. However, when the magnetic field varies with time, the generated electric field within an Ohmic conductor induces further currents that also contribute to the magnetic field.
    • 6.5: Energy Stored in The Magnetic Field
      The differential amount of work necessary to overcome the electric and magnetic forces on a charge q moving an incremental distance ds at velocity v is
    • 6.6: The Energy Method for Forces
      In Section 6-5-1 we calculated the energy stored in a current-carrying loop by two methods. First we calculated the electric energy input to a loop with no mechanical work done.
    • 6.7: Problems

    Thumbnail: Animation showing operation of a brushed DC electric motor. (CC BY-SA 3.0; Abnormaal via Wikipedia)​​​​​​

    This page titled 6: Electromagnetic Induction is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Markus Zahn (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.