# Physics equations/Faraday law/Faraday law example

## Spinning coil in a magnetic field^{[1]}

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Faraday's law of induction|Faraday's law of electromagnetic induction states that the induced electromotive force is the negative time rate of change of magnetic flux through a conducting loop.

where
is the electromotive force (emf) in volts and
Φ_{B} is the magnetic flux in Weber (Wb)|webers. For a loop of constant area, A, spinning at an angular velocity of in a uniform magnetic field, B, the magnetic flux is given by

where θ is the angle between the normal to the current loop and the magnetic field direction. Since the loop is spinning at a constant rate, ω, the angle is increasing linearly in time, θ=ωt, and the magnetic flux can be written as

Taking the negative derivative of the flux with respect to time yields the electromotive force.

Electromotive force in terms of derivative | |

Bring constants (A and B) outside of derivative | |

Apply chain rule and differentiate outside function (cosine) | |

Cancel out two negative signs | |

Evaluate remaining derivative | |

Simplify. |