Question

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

Answer 1

A wire has length L and 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

minimum separation between dipoles is 2r = 2L/π

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