Question

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

Answer 1

$ans : \frac{2M}{\pi}$


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 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 = 2M/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] [ sine shape is semicircle]

Magnetic dipole=Mx 2L/π=2ML/π