A bar magnet of moment M is cut into two identical pieces the length.One piece is bent in the form of a semi circle.The two pieces are arranged as shown.The resulting moment is

Options

A. `M((1)/(2)+pi)`
B. `(M)/((2+pi))`
C. `M((pi+2)/(2pi))`
D. `M(2pi/(pi+2))`

Answer

C

Explanation

Magnetic moment of semicircle
`M'_(1)=(2M_(1))/(pi)=(2)/(pi)xx(M)/(2)=(M)/(pi)`
Magnetic moment of bar magnet
`M'_(2)=M_(2)=(M)/(2)`
Thus,the resultant magnetic moment`M'_(1)+M'_(2)`
`(M)/(pi)+(M)/(2)=M((1)/(pi)+(1)/(2))=M((2+pi)/(2pi))`