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	\(\displaystyle Φ_m=∫_S\vec{B}⋅\hat{n}dA\)
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.

Contributors and Attributions

Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).