Question

When a bar magnet is cut parallel to the magnetic axis its pole strength and magnetic moment decreases.
(A) True
(B) False

Answer 1

Hint : The magnetic axis of a magnet is along the line passing through the magnet joining the south pole and the north pole. The magnetic moment and pole strength is directly related to the cross sectional area of the magnet.

Formula used: In this solution we will be using the following formula;
$\Rightarrow m = IA$ where $m$ is the magnetic dipole moment, $I$ is the current in the loop, and $A$ is the area covered by the loop.

Complete step by step answer
In general, for a bar magnet, the magnetism is caused by the net orientation of the atoms of the material, and their magnetic field is caused by the orbiting electrons around the nucleus. Hence, for a particular material, when there are more atoms of the material having the same orientation, there is a stronger magnetic field in the atom. If some of the atoms are removed, the magnetic field, hence, the strength decreases.
The magnetic axis of a magnet is defined to be the straight line joining the two poles of the magnet within the magnet. Hence, if a magnet is cut along its magnetic axis, the cross section area of the magnet decreases leaving us with two magnets of equal magnetism whose sum will be equal to the original.
However, since for one of the magnets, the number of atoms has been decreased, then the magnetic field, thus, the pole strength of the magnet decreases. Magnetic moment is also proportional to magnetic field, hence, they both decrease. Thus the statement is true.
The correct option is A.

Note
Alternatively, in many cases the magnetic moment is taken mathematically to be the magnetic dipole moment. For a loop of current, the magnetic dipole moment can be given as
$m = IA$ where $I$ is the current in the loop, and $A$ is the area covered by the loop.
Usually a bar magnet’s magnetism can be considered to be generated by a loop of current. Hence, if we cut the bar magnet in two along the magnetic axis, we would be dividing the area, hence the magnetic moment decreases.