Magnetic field. Ampere's Law. Biot-Savart Law. Faraday's Law. Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil. No matter how the change is produced, the voltage will be generated. The change could be produced by changing the magnetic field strength, moving a magnet toward or away from the coil, moving the coil into or out of the magnetic field, rotating the coil relative to the magnet, etc. Faraday's law is a fundamental relationship which comes from Maxwell's equations.
It serves as a succinct summary of the ways a voltage (or emf) may be generated by a changing magnetic environment.
Magnetic forces. The magnetic field B is defined from the Lorentz Force Law, and specifically from the magnetic force on a moving charge: The implications of this expression include: 1.