Can a Moving Magnetic Field Induce Eddy Currents in a Conductor?

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A moving magnetic field can indeed induce eddy currents in a conductor, as demonstrated by the example of a magnet moving in and out of a solenoid, which generates a current. The principle of electromagnetic induction states that a changing magnetic field creates an electromotive force (emf) in a conductor, necessitating relative motion between the magnetic field and the conductor. In induction motors, the moving stator field induces emf in the rotor bars, illustrating this concept in practical applications. Therefore, the presence of eddy currents in a conductor is linked to the dynamics of the magnetic field's movement. Understanding these interactions is crucial for applications in electromagnetism and electrical engineering.
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Can a moving magnetic field create eddy currents in a conductor ?
Moving a magnet in and out of a solenoid makes a current flow in the solenoid. I know that a changing magnetic field induces emf in a conductor but what about a moving magnetic field ? Are eddy currents present in the solenoid (above) ?
 
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There has to be a relative motion between the field and the conductor for induction of emf. In induction motors, the stator field is moving, which induces emf in the rotor bars.
 
Thread 'Motional EMF in Faraday disc, co-rotating magnet axial mean flux'

Thread 'Motional EMF in Faraday disc, co-rotating magnet axial mean flux'

So here is the motional EMF formula. Now I understand the standard Faraday paradox that an axis symmetric field source (like a speaker motor ring magnet) has a magnetic field that is frame invariant under rotation around axis of symmetry. The field is static whether you rotate the magnet or not. So far so good. What puzzles me is this , there is a term average magnetic flux or "azimuthal mean" , this term describes the average magnetic field through the area swept by the rotating Faraday...
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