The electric current in a circular coil of 2 turns produces a magnetic induction B 1 at its centre. The coil is unwound and is rewound into a circular coil of 5 turns and the same current produces a magnetic induction B 2 at its centre. The ratio of B 2 B 1 is:

Step-by-step solution

Magnetic field on the centre of a circular current coil is given by B = N μ 0 i 2 R , here, N is number of turns, i is current and R is radius of loop. Now, for, N = 2 , magnetic field, B 1 = N 1 μ 0 i 2 R 1 For N 2 = 5 Radius of coil = R 2 = N 1 × R 1   N 2 Magnetic field, B 2 = N 2 μ 0 i 2 R 2 Thus, the ratio is B 2   B 1 = N 2   N 1 R 1 R 2 = N 2   N 1 × N 2   N 1 B 2   B 1 = 25 4