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. `pi : 4`
D. `4 : pi`

Answer

C

Explanation

Suppose length of each wire is `l`.
`A_("square") = ((l)/(4))^(2) = (l^(2))/(16)`
`A_("circle") = pi r^(2) = pi((l)/(2pi))^(2)`
`= (l^(2))/(4pi)`

Magnetic moment
`M iA`
`implies (M_("square"))/(M_("circle")) = (A_("square"))/(A_("circle")) = (l^(2)//16)/(l^(2)//4pi) = (pi)/(4)`