A circular loop and a square loop are formed from the same wire and the same current is passed through them . Find the ratio of their dipole moments.

Options

A. `4pi`
B. `(4)/(pi)`
C. `(2)/(pi)`
D. `2pi`

Answer

B

Explanation

Suppose the length of wire is l .
When , wire formed in circular loop then radius of loop ,
`r = (l)/(2pi) " " [because l = 2pi r]`
Magnet dipole , `M_(1) = iA`
`= ipi r^(2) = ipi xx ((l)/(2pi))^(2)`
= `ixx (l^(2))/(4pi)`
When wire formed in square loop then the side of loop ,
a = `(l)/(4)`
Magnet loop , `M_(2) = IA`
`=i xx a^(2)`
`= i xx (l^(2))/(16)`
`therefore " " (M_(1))/(M_(2)) = (4)/(pi)`