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.