Causing an electrical current in a solenoid
Not only can you pass a wire between a north and south pole of a magnet and induce an electrical current in a wire, you can also move the end of a magnet in a solenoid and create an electrical current.
The electrical current that will be produced will be such that it will create a magnet that opposes the movement (Lenz's law).
So a magnet whose north pole travels towards a solenoid will produce a north pole.
Like two opposing north poles in a magnet the two north poles repel and will try to prevent the movement.
As the north pole of the magnet is then pulled away from the solenoid again the electrical current that will be produced will create a magnet that opposes this opposite movement. The solenoid will produce a south pole.
Like a north and south pole of a magnet trying to attract each other.