A circular coil of N turns and diameter D carries current I. It is unwound and rewound to make another coil of diameter 2D, current I remaining the same. The ratio of magnetic moments of the original coil to the new coil is

Step-by-step solution

The length of the wire remains constant when unwound and rewound. L = N D = N' (2D) N' = N 2 The magnetic moment of a circular coil is given by M = NIA . For the original coil: M₁ = NI ( D^2 4 ) For the new coil: M₂ = N' I ( (2D)^2 4 ) = ( N 2 ) I ( D^2) = 2 NI ( D^2 4 ) Taking the ratio of the magnetic moments: M₁ M₂ = 1 2 Answer: 1:2