A thin circular wire carrying a current I has a magnetic moment M. The shape of the wire is changed to a square and it carries the same current. It will have a magnetic moment

Options

A. M
B. `(4)/(pi^(2))""M`
C. `(4)/(pi)""M`
D. `(pi)/(4) "" M`

Answer

D

Explanation

`M_("square") = IA = I ((L)/(4))^(2) = (iL^2)/(16)`
`M_("circle") = I pi r^(2) = I pi ((L)/(2pi))^(2) = (iL^2)/(4pi)`
`M_("square") = (pi)/(4) M_("circle") ` or `(pi)/(4) M`