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

Initially for circular coil `L=2pir` and `M=ixxpir^(2)`
Finally for square coil `M'=ixx((L)/(4))^(2)=(iL^(2))/(16)`

Solving equations (`i`) and (`ii`) `M'=(piM)/(4)`