University Physics Volume 2

# Summary

### 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 $1Wb=1T·m2.1Wb=1T·m2.$
• 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.

### 13.2Lenz'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.

### 13.3Motional 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.

### 13.4Induced 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.

### 13.5Eddy 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.

### 13.6Electric 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.

### 13.7Applications 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.