$(a)$ What happens if a bar magnet is cut into two pieces: $(i)$ transverse to its length,$(ii)$ along its length?
$(b)$ $A$ magnetised needle in a uniform magnetic field experiences a torque but no net force. An iron nail near a bar magnet,however,experiences a force of attraction in addition to a torque. Why?
$(c)$ Must every magnetic configuration have a north pole and a south pole? What about the field due to a toroid?
$(d)$ Two identical-looking iron bars $A$ and $B$ are given,one of which is definitely known to be magnetised. (We do not know which one.) How would one ascertain whether or not both are magnetised? If only one is magnetised,how does one ascertain which one? [Use nothing else but the bars $A$ and $B$.]

(N/A) In either case,one gets two magnets,each with a north and south pole.
$(b)$ No net force acts if the magnetic field is uniform. The iron nail experiences a non-uniform magnetic field due to the bar magnet. There is an induced magnetic moment in the nail; therefore,it experiences both a force and a torque. The net force is attractive because the induced pole in the nail closer to the magnet's pole is of opposite polarity.
$(c)$ Not necessarily. This is true only if the source of the field has a net non-zero magnetic moment. This is not the case for a toroid or for a straight infinite conductor.
$(d)$ Try to bring different ends of the bars closer. $A$ repulsive force in some orientation establishes that both are magnetised. If it is always attractive,then one of them is not magnetised. In a bar magnet,the intensity of the magnetic field is strongest at the two ends (poles) and weakest at the central region. To determine which one is the magnet,pick up one bar (say,$A$) and bring one of its ends near the ends of the other bar $(B)$,and then near the middle of $B$. If you notice that in the middle of $B$,$A$ experiences no force,then $B$ is the magnet. If you do not notice any change in the force from the end to the middle of $B$,then $A$ is the magnet.