Electromagnetic induction
Mutually inductance between two magnetically coupled coils depends on

The number of their turns
Cross-sectional area of their common core
Permeability of the core
All of the listed here

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Electromagnetic induction
A laminated iron core has reduced eddy-current losses because

The magnetic flux is concentrated in the air gap of the core
The laminations are insulated from each other
The laminations are stacked vertically
More wire can be used with less D.C. resistance in coil

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