A long straight wire is first bent into a single circular loop and carries a steady current, producing a magnetic field B at its centre. The same wire is then unwound and rewound into a circular coil of 3 turns. If the same current is passed through the coil, the new magnetic field at its centre will be:

Step-by-step solution

Let the length of the wire be L . When bent into a single loop of radius R , the length is L = 2 R . The magnetic field at the centre is: B = ₀ I 2R When rewound into a coil of n = 3 turns of radius r , the total length remains the same: L = n 2 r 2 R = 3 2 r r = R 3 The new magnetic field B' at the centre of the 3 -turn coil is: B' = ₀ n I 2r Substituting n = 3 and r = R 3 : B' = ₀ (3) I 2 ( R 3 ) B' = 9 ( ₀ I 2R ) B' = 9B In general, when a wire is rewound from 1 turn to n turns, the new magnetic field becomes n^