A current I flows in a conducting wire of lenth L. If we bent it in a circular form, then calculate its magnetic dipole moment.

Options

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

Answer

D

Explanation

Magnetic moment of a circular coil `=IA`
When the conductor of length L is bent in the form of a circular loop,
`L=2pi r" ":. r=L/(2pi)`
and Area of the circular loop `=pir^(2)=(pi L^(2))/(4pi^(2))=L^(2)/(4pi)`
`:. M=IA =(L^(2)I)/(4pi)`