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# 13.S: Electromagnetic Induction (Summary)

## 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

• 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.

#### 13.2 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 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.

#### 13.4 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 $$\displaystyle ε=NBAωsin(ωt)$$ 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.

#### 13.7 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.

## Contributors

Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).