Two wires of the same length are shaped into a square of side 'a' and a circle with radius 'r'. If they carry same current, the ratio of their magnetic moment is

Options

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

Answer

C

Explanation

Magnetic moment, m=IA
For square : 4=aL
`a=(L)/(4)`
`A=a^(2)=(L^(2))/(16)`
`m_("square")=(L^(2)I)/(16)`
For circle `2piR=L`
`rArr r=(L)/(2pi)`
`:. a=pir^(2)`
`=(piL^(2))/(4pi^(2))=(L^(2))/(4pi)`
`m_("circle")=(L^(2)I)/(4pi)`
`(m_("square"))/(m_("circle"))=(L^(2)I)/(16)xx(4pi)/(L^(2)I)`
`=(pi)/(4)=pi:4`