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[Tellos Athenaios]

On the top of my head: the first coil emanates an electromagnetic field, wich creates electric currents in the second coil. Having coils of different sizes causes the voltage to differ; i.e. a transformer.

No, [ideal] transformers work without electric current passing through the air, and crucially only work properly on an AC circuit because they rely on induction as a result of change in magnetic field. (Namely: alternating direction of magnetic field, the differences in field strength is what determines the difference in output potential and current [ignore the effects of resistance in the coil system] and the field strength is determined by more than just size).