Bar mangnet bent into a semicircle

 

Let

L-  be the length of the bar magnet which now is bent into a semi circle.

m- pole strength

M- original magnetic moment
M' - the new magnetic moment

r - radius of the semicircle that has been made.

M = m x L

The distance between the poles now becomes 2r from L(earlier) .
Also L= r (beacuse the length is now the circumference of the semi circle)
That gives r = L/

Hence, M' = m x 2 r = mx 2 (L / ) = (2/) M