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 ΦB 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.

References

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