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 new coil to the original coil is

Step-by-step solution

Length of the wire remains constant. L = N d = N' (2d) N' = N 2 Magnetic moment of the original coil is M₁ = N I A₁ = N I ( d^2 4 ) Magnetic moment of the new coil is M₂ = N' I A₂ = ( N 2 ) I ( (2d)^2 4 ) = N 2 I ( d^2) Ratio of magnetic moments is M₂ M₁ = N 2 I d^2 N I d^2 4 = 1/2 1/4 = 2 The ratio is 2:1 . Answer: 2:1