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Imagine a transformer. The primary has an integer number of turns. Now imagine the secondary has less than 1 turn, i.e., just a piece of wire passing through, forming essentially half a turn.

I know voltage is induced in this piece of wire. It doesn't form a closed loop, but faraday's law relates the induced electric field around a CLOSED loop to the time varying magnetic flux passing through the loop.

Can I assume that the wire itself forms PART of a closed loop and hence an electric field is indiced across the two ends?