The permanent bar magnet is moved to the left, toward a loop of wire (as shown). The north pole of the magnet is closer to the loop, as shown. What direction will the (induced) magnetic field be in the center of the loop of wire?

The direction of the induced magnetic field will be the same as the direction of the external magnetic field.
As per Felhming's right-hand rule: The direction of the magnetic field is perpendicular to the wire and is in the direction of the fingers of your right hand.
The direction of induced current in the coil is clockwise. Since the magnet is being moved away, the magnetic flux linked with the coil must be decreasing. Hence the induced magnetic field must be in the same direction as the external magnetic field.
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