13.9: Electromagnetic Induction (Summary)

University Physics II: Thermodynamics, Electricity, & Magnetism · LibreTexts

0%

Contents

    Text

    Size
    100%
    Theme
    Typeface
    Line length
    Spacing

    From LibreTexts, under CC BY 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    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 \(\displaystyle Φ_m=∫_S\vec{B}⋅\hat{n}dA\)
    Faraday’s law \(\displaystyle ε=−N\frac{dΦ_m}{dt}\)
    Motionally induced emf \(\displaystyle ε=Blv\)
    Motional emf around a circuit \(\displaystyle ε=∮\vec{E}⋅d\vec{l}=−\frac{dΦ_m}{dt}\)
    Emf produced by an electric generator \(\displaystyle ε=NBAωsin(ωt)\)

    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 \(\displaystyle 1Wb=1T⋅m^2\).
    • 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 \(\displaystyle ε=Blv\).
    • 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 \(\displaystyle ε=NBAωsin(ωt)\) where A is the area of an N-turn coil rotated at a constant angular velocity \(\displaystyle ω\) in a uniform magnetic field \(\displaystyle \vec{B}\).
    • The peak emf of a generator is \(\displaystyle ε_0=NBAω\).
    • 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 13.9: Electromagnetic Induction (Summary) was last modified on Mon, 03 Mar 2025 00:52:24 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.