Motion can only produce a current in the wire if the wire is moved up or down in the field cutting through the lines of the magnetic field.
Side-to-side or end-to-end motion produces no current.
1. A current is produced when either the wire or magnet move (the wire must cut the magnetic field lines).
2. The faster the relative movement of the magnet or the wire the bigger the current.
3. Changing the direction of the movement changes the direction of the current
4. The stronger the magnet, the bigger the current.
5. The more coils of wire, the bigger the current.
Lenz's law: The induced current is always trying to prevent the change.
NB – strictly speaking in all these experiments it is a voltage that is generated and this then gives a current in the meter if the circuit is complete.