Faraday's first law: whenever the magnetic flux linked with a circuit changes, an EMF is induced. Faraday's second law: the magnitude of the induced EMF equals the rate of change of flux linkage: $\varepsilon = -N\frac{d\Phi_B}{dt}$. The flux $\Phi_B = \vec{B} \cdot \vec{A} = BA\cos\theta$ can change due to: (1) change in $B$ (varying field), (2) change in $A$ (moving boundaries), (3) change in $\theta$ (rotating coil), or (4) any combination. The negative sign reflects Lenz's law. If the circuit is closed with resistance $R$: $I = \varepsilon/R = -\frac{N}{R}\frac{d\Phi}{dt}$.