Final answer:
A steady-state current in the primary coil would not induce current in the secondary coil, regardless of the number of wire turns, according to Faraday's law of induction. However, an alternating current would indeed induce an alternating voltage and current in the secondary coil, proportional to the turns of wire.
Step-by-step explanation:
If Faraday had wound enough turns of wire on the secondary coil of his iron ring transformer, and a steady-state current was flowing in the primary coil, he would not have observed an induced current in the secondary coil. This is grounded in Faraday's law of electromagnetic induction, which states an induced emf and hence current is produced by a change in magnetic flux. In the case of a steady-state or constant current in the primary coil, the magnetic flux through the secondary coil would be constant, thus not inducing a current.
However, if an alternating current (AC) was used, a time-varying magnetic flux would be sent through the secondary coil. This would indeed induce an AC voltage and current in the secondary coil, as is the principle of operation for a transformer. The amount of induced voltage is proportional to the number of turns in the secondary coil. An increase in the number of turns would result in a higher induced voltage under an alternating current.
Therefore, the key factor for inducing current in the secondary coil is the presence of a time-varying magnetic field, not merely the presence of a large number of turns in the wire coil.