induction: When magnetic field changes, no matter what's the reason of the change, a simultaneous electric field exists. Induction happens in magnetic field, it's one of the basic relations between magnetic and electric field.
Some common reasons for a change in a magnetic field:
- someone moves a magnet or a wire or coil which has current
- the observer of a magnetic field moves, he sees an electric field
- current in a wire or coil changes
As you know, metallic coils are often used to create the changing magnetic field, but the induction happens in the field, it's as well outside the coil. As said, no coil is needed to make induction to happen, a changing magnetic field is enough.
If a wire is in electric field, a voltage is generated between the ends of the wire. Electric field created by induction is circularly around the lines of the magnetic field. That's why a coil is useful to collect substantial voltage. The thickness of the wire isn't essential, the voltage depends on the strength of the generated electric field and how long wire there's placed along the electric field. In transformers the voltage is proportional to the number of turns in a winding.
It's useful to make tight windings to get intensive magnetic fields and catch effectively power from the electric field caused by induction. Transformer and electric machine engineering is very much an art of these. As well one wants to keep the winding resistance low to keep losses low and have low cost materials which are easy to work with. Minimizing total costs guides us to have windings made of copper instead of gold, silver or aluminium which also have low resistance when compared to iron.