A magnetised wire of moment M is bent into an arc of a circle subtending an angle of 60^(@) at the centre. The new magnetic moment is

Options

A. `(2M//pi)`
B. `(M//pi)`
C. `(3 sqrt3M//pi)`
D. `(3M//pi)`

Answer

D

Explanation

`"sin" (theta)/(2)= (x)/(r)`
`rArr x= r "sin" (theta)/(2)`

New magnetic moment `M.= m(2x)= m 2 r "sin" (theta)/(2)`
`= m (2l)/(theta)."sin"(theta)/(2)= (2ml "sin"(theta)/(2))/(theta)= (2M sin ((pi)/(6)))/((pi)/(3))= (3M)/(pi)`