(a) What happens if a bar magnet is cut into two pieces (i) transverse to its length (ii) along its length?
(b) What happens if an iron bar magnet is melted? Does it retain its magnetism?
(c) A magnetized needle in a uniform magnetic field experiences a torque but no net force. However, an iron nail near a bar magnet experiences a force of attraction in addition to a torque, explain.
(d) Must every magnetic field configuration have a north pole and a south pole? What about the field due to a toroid?
(e) Can you think of magnetic field configuration with three poles?
(f) Two identical looking iron bars A and B are given, one of which is definitely known to be magnetized. How would one ascertain whether or not both are magnetized? If only one is magnetized how does one ascertain which one? Use nothing else but the bars A and B.

Explanation

(a) In both the cases, we get two magnets each having north and south poles.
When we cut transverse to the length, pole strength of each new magnet is same as that of original magnet but magnetic moment is halved because length is halved.
When we cut along the length, pole strength of each new magnet is half the pole strength of original magnet , magnetic moment is also halved, as length remains the same.
(b) On melting, iron bar magnet loses its magnetism to some extent. This is because its temperature exceeds Curie temperature `(~~750^@C)` for iron.
(c) When a magnetised needle is put in a uniform magnetic field, forces on north and south poles of the needle are equal and unlike. Therefore, net force is zero. But these forces form a torque which aligns the magnetic needle in the direction of the field.
An iron nail is unmagnetised. It experiences force of attraction, gets magnetised, then experiences a torque and gets aligned along the field.
(d) No, it is not necessary that every magnetic field configuration must have a north pole and a south pole. The poles exis only when the source has some net magnetic moment. For example, in case of a toroid and infinite straight conductor carrying current, there are no poles, as net magnetic moment in both the cases is zero.
(e) Magnetic poles always exist in pairs. However, one can imagine magnetic field configuration with three poles-when north poles of two magnets are glued together or south poles of two magnets are glued together to provide a three pole fied configuration.
(f) Place bar B horizontally on a table. Take bar A. Touch any one end of A at the middle of B. If A experiences no force then B is magnetised and A is unmagnetised.
However, if A experiences the same force at the middle of B as at the ends of B, then A is magnetised and B is not magnetised.