Final answer:
The correct statement is that the wire is not moving relative to the magnet. This conclusion is based on the principle of electromagnetic induction, with no induced electric current signifying no change in magnetic flux and therefore no relative motion. (Option A)
Step-by-step explanation:
If there is no electric current in a coil of wire with a permanent magnet at its center, it must be true that the wire is not moving relative to the magnet. According to electromagnetic principles, emf (electromotive force) is induced in a coil when there is relative motion between the magnet and the coil.
This concept is encapsulated by Faraday's law of electromagnetic induction, which tells us that a current is induced in a loop when the magnetic flux through the loop changes. Therefore, if there is no induced current, the magnetic flux is not changing, indicating that there is no relative motion between the coil and the magnet.