Physics equations/Faraday law/Faraday law example

Spinning coil in a magnetic field
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.

$$ \mathcal{E} = -{{d\Phi_B} \over dt},$$

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

$$ \Phi_B = B\cdot A \cdot \cos(\theta),$$

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 $$ \Phi_B = B\cdot A \cdot \cos(\omega t).$$

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