The motor effect states that:
When a charge carrying conductor is in a magnetic field it will experience a force.
Faradays Law states that:
When there a change in flux an EMF is induced (Note that Lenz's law is an extension of Faradays law).
So to answer your question:
An example of a induction motor is a wound up AC motor or the commonly talked about one is the 3 phase induction motor. The principle it operates under is pretty much you have a mechanical lever that lets you wind up the axel of the motor. When the axel is released it begins to rotate within a set of magnets. This rotation causes the wire (current carrying conductor) to experience a force because it is in the magnetic field. In terms of Faradays, since the axle is spinning in a magnetic field this causes a change in flux and therefore induces an EMF.
Hope that helped!
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