Referring to bellow, what is the direction of the current induced in the coil if the current in the wire is constant?

None.

Explanation:

If the current in the wire is constant, this means that the magnetic field due to it, it's constant too.Therefore, assuming thet the coil remains fixed in space, the magnetic flux across the coil remains constant also.So, ss an induced current in the coil only happens if there is a change in the magnetic flux through the coil, we can conclude that no current is induced in it.

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