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A coil of N turns and radius R carries a...

A 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 remaining the same. Calculate the ratio of magnetic moments of the new coil and the original coil.

Text Solution

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If L is length of the wire, then
`L=Nxx2piR=N^'xx2piR//2 :. N^'=2N`
Original magnetic moment, `M=NIA=NI(piR^2)`
New magnetic moment,
`M^'=N^'IA^'=(2N)I(piR^2)/(4)`
`=1/2NIpiR^2:. M^'/M=1/2=1:2`
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