Question

A wire of magnetic dipole moment M and L is bent into shape of semicircle of radius r. What will be its new dipole moment

Answer 1

$\bold{\text{new dipole moment}= \frac{2ML}{\pi}}$

see attachment, 
length L ,long wire is bent in the shape of semicircle of radius r .
then, length of wire = circumference of semicircle 
L = πr => r = L/2π 

now, magnetic dipole = magnetic dipole moment × minimum separation between two dipoles 

here ( in pic ) it is clear that , minimum separation between dipoles is 2r = 2L/π 

hence, magnetic dipole = M × 2L/π = 2ML/π

Answer 2

Let us consider a wire of length L  and radius r.

It is bent in a semiircular shape.

HenceLength of wire=circumference of semicircle

L=πr
r=L/π
Formula to be used Dipole moment=magnetic moment x minimum separation between two dipoles

Minimum seperation is 2r=2[L/π] [ since shape is semicircle]

Magnetic dipole=Mx 2L/π=2ML/π