Two wires of same length are shaped into a square and a circle. If they carry same current, ratio of the magnetic moment is

Options

A. `2:pi`
B. `pi:2`
C. `4:pi`
D. `pi:4`

Answer

D

Explanation

When length l is in the form of a square, then length of each side is `l//4`.
Area of square, `A=l//4xxl//4=l^2//16`
`:.` Magnetic moment `M=IA=Ixxl^2//16` …(i)
When length l is in the form of a circle of radius r, then `l=2pir`
or `r=l//(2pi)`
Area of square, `A^'=pir^2=pil^2(2pi)^2=l^2//4pi`
Magnetic moment `M^'=IA^'=Il^2//4pi`
`:. M/M^'=(Il^2//16)/(Il^2//4pi)=pi/4=pi:4`