Two identical pieces of metal wires are used to make a circular loop and a square loop same current is passed through both the loops what is the ratio of magneitc dipole moment associated with the circular loop that of the square loop ?

Options

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

Answer

B

Explanation

The magnetic dipole moment of a coil =IA Let L be the length of the wire .Then for the circular coil `L=2pi r`
for the square loop the length of each side =`(L)/(4)` and the area `(A_(2))=Lxxb=(L)/(4)xx(L)/(4)=(L^(2))/(16)`
`therefore (M_(1))/(M_(2))=(IA_(1))/(IA_(2))=(piL^(2))/(4pi^(2))xx(16)/(L^(2))=(4)/(pi)`