A hand$-$held induction flashlightLinks to an external site. is constructed such that there is a set of coils attached to the handle, and a loose magnet within the handle.$$ When you shake the flashlight, the relative motion between the coils and the magnet induces an emf that can be used to recharge a battery.

In the reference frame of the coils $($where the coils are not moving$),$ which aspect of Faraday's Law is responsible for the induced emf?