Faraday's Law and Lenz's Law

$e = -N\frac{d\Phi}{dt}$

The minus sign is Lenz's law: the induced current creates a field that opposes the change that caused it.

A conductor of length $l$ moving at velocity $v$ through field $B$ (motional EMF): $e = Blv$.

Faraday's law explains generators, transformers, induction motors, inductive charging, eddy currents and induction cooktops.