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A circular coil of N turns and radius R ...

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.

Text Solution

Verified by Experts

We have :
`N_(1).2piR = N_(2).2pi(R//2)`
`therefore N_(2) = 2N_(1)`
Magnetic moment of a coil, M = NAI
For the coil of radius .R.
`M_(1) = N_(1)IA_(1) = N_(1)IpiR^(2)`
For the coil of radius R/2
`M_(2) = N_(2)IA_(2) = 2N_(1)IpiR^(2)//4 = N_(1)I.piR^(2)//2`
`rArr M_(2) : M_(1) = 1:2`
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