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 = I . pi a^(2)`
`2 pia = 4d rArr d = pia//2`

`M' = Id^(2)`
`(M')/(M) = (d^(2))/(pi a^(2)) = (pi a//2)^(2)/(pi a^(2)) = (pi)/(4)`
`M' = (pi)/(4)M`