A circular coil of N turns and radius R carries a current I. It is unwound and rewound to make another coil of radius `R//2.` Current I remaining the same. Calculate the ratio of the magnetic moments of the new coil and the original coil.

Explanation

M=NIA
Original circular coil. Magnetic Moment = NIA
Length of wire remains same thus,
`N(2piR)=N_(1)(2pi((R)/(2)))`
`"Now, "N_(1)=2N`
`m_(1)=NIA_(1),m_(1)=NI(pir_(1)^(2))=NIpiR^(2)`
`m_(2)=N_(1)IA_(2)=2NI(pir_(2)^(2))=2NI(pi((R)/(2))^(2))=(1)/(2)NIpiR^(2)`
`(m_(2))/(m_(1))=((1)/(2))/(1)=(1)/(2).`