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. `(3sqrt(3)M//pi)`
D. `(3M//pi)`

Answer

D

Explanation

From figure
`sin' (theta)/2=x/r`
`implies x=r(sin)(theta)/2`
Hence, new magnetic moment
`M^(')=m(2x)=m.2r sin' (theta)/2`
`=m.(2l)/theta"sin"(theta)/2=(2ml sin'theta//2)/theta`
`(2M "sin" (pi//6))/(pi//3)=(3M)/pi`