(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.]
In both cases—(i) transverse to length and (ii) along the length—cutting a bar magnet results in two magnets, each with a north and south pole. Magnetic poles cannot be isolated; we cannot have isolated north or south poles. Each piece becomes a complete magnet with somewhat weaker properties.
In a uniform magnetic field, a magnetised needle experiences no net force but does experience a torque (τ = m × B). However, an iron nail near a bar magnet experiences a non-uniform field. This induces a magnetic moment in the nail, causing both force and torque. The net force is attractive because the induced south pole in the nail is closer to the north pole of the magnet than the induced north pole.
Not necessarily. Every magnetic configuration must have a north and south pole only if the source has a net non-zero magnetic moment. A toroid does not have a net non-zero magnetic moment, so it does not have distinct north and south poles. Similarly, a straight infinite conductor does not have isolated poles.
To check if both are magnetised: Bring different ends of the bars closer. A repulsive force in any situation confirms both are magnetised. If only attractive forces are observed, only one is magnetised.
To identify which one: Pick up one bar (say A) and lower one of its ends first on one end of B, then on the middle of B. If A experiences no force at the middle of B, then B is magnetised (since field is weakest at the center). If there's no change from end to middle of B, then A is magnetised.
Explanation
This question tests understanding of magnetic poles, torque vs force in magnetic fields, and practical identification of magnets. The textbook explicitly states that magnetic poles cannot be isolated—cutting a magnet produces two complete magnets. For torque vs force, the key distinction is uniform vs non-uniform fields. A toroid is a special case where net magnetic moment is zero, hence no distinct poles. The identification method relies on the fact that magnetic field is strongest at poles and weakest at the center of a bar magnet.