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^2M`
C. `4/piM`
D. `pi/4M`

Answer

D

Explanation

Initially for circular coil `L = 2 pi r and M = ixxpir^2`
`=ixxpi(L/(2pi))^2=(iL^2)/(4pi)`
Finally for square coil side `a = L/4` and
`M.=ixx(L/4)^2=(iL^2)/16" ".....(ii)`

Solving equation (i) and (ii) `M. = (piM)/4`