Let the magnetic moment of a bar magnet be `vec(p_(m))` whose mangetic length is d = 2l and pole strenght is `q_(m)`. Compute the magnetic moment of the bar magnet when it is cut into two pieces.
(a) along its length (b) perpendicular to its length

Explanation

A bar magnet cut into two pieces along its length :

When the bar is cut along the axis into two pieces. New magnetic pole strength is `q_(m)^(.) = (q_(m))/(2)` but magnetic length does not change . So. The magnetic moment is `p_(m)^(.) = q_(m)^(.)` 2l
`p_(m)^(.) = (q_(m))/(2) 2l = (1)/(2) (q_(m) 2l) = (1)/(2) p_(m)`
In vector notation. `vec(P.)m = (1)/(2) vec(P)`m
(b) a bar magnet cut into two pieces perpendicular to the `a xx` is :
When the bar magnet is cut perpendicular to the axis into two pieces, magnetic pole strength will not change but magnetic length will be halved. So the magnetic moment is
`p._(m) = q_(m) xx (1)/(2) (2l) = (1)/(2) (q_(m) . 2l) = (1)/(2) p_(m)`
`vec(p._(m)) = (1)/(2) vec(P_(m))`