A straight wire carrying current I is made into a circular loop. If M is the magnetic moment associated with the loop, then the length of the wire is

Options

A. `sqrt((4piM)/(I))`
B. `sqrt((2piM)/(I))`
C. `sqrt((piM)/(I))`
D. `sqrt((piM)/(2I))`

Answer

A

Explanation

Magnetic moment `M=IA`
According to question,
`2piR=L`
`piR=(L)/(2)`
`M=(I)/(pi)pi^(2)R`
`=I((L)/(2))^(2)`
`M=(I)/(pi)((L)/(2))^(2)`
`M=(I)/(pi)(L^(2))/(4)`
Length of the wire, `L=sqrt((4Mpi)/(I))`