(a) What happens if a bar magnet is cut into two pieces: (i) transverse to its length, (ii) along its length ?

Explanation

(a) Consider a bar magnet with pole strength `q_m` and magnetic length `2 overset(to) (l)` as shown below.

Magnetic dipole moment of magnetic dipole (or bar magnet) is defined as follows:
`{:("Magnetic"),("dipole moment"):}=({:("Magnitude of"),("pole strength"):})({:("Magnetic"),(" length"):})`
`therefore m= (q_m) (2l)`
Considering directions, `overset(to) (m) = q_m (2 overset(to) (l) )`
Above direction is from south pole to north pole.
Here, straight line passing through magnetic poles of a bar magnet is called its magnetic axis and perpendicular bisector of this axis is called its magnetic equator.
(i) When a bar magnet is cut into two equal pieces, transverse to its length (means it is cut through its equator), we get two identical half sized bar magnets.
Here, pole strength remains constant but magnetic dipole moment becomes half (because magnetic length becomes half) See the figure given below.

(Note : Above figures are drawn in two dimension for the sake of simplicity and ease. Actually, bar magnets are three dimensional objects)
(ii) When a bar magnet is cut along its axis, we get two identical half sized bar magnets. Here, magnetic length remains constant but magnetic dipole moment becomes half (because pole strength becomes half) See the figure given below.

`m= (q_m) (2l)`
`m. = ((q_m)/( 2) ) (2l)`
`= (q_m) (l)`
`therefore m. = (m)/(2)`