The radius of the current carrying circular coil is doubled keeping the current passing through it the same. Then the ratio of the magnetic field produced at the centre of the coil before the doubling of the radius to the magnetic field after doubling of the radius.

Step-by-step solution

The magnetic field B at the centre of a circular coil of radius R carrying current I is given by the formula B = ₀ I 2R . Let the initial radius be R₁ = R and the initial magnetic field be B₁ = ₀ I 2R . After doubling the radius, the new radius is R₂ = 2R . The current I remains the same. The new magnetic field is B₂ = ₀ I 2R₂ = ₀ I 2(2R) = ₀ I 4R . The ratio of the magnetic field before doubling to the magnetic field after doubling is B₁ B₂ = ₀ I 2R ₀ I 4R = 4R 2R = 2 1 . Therefore, the ratio is 2 : 1 . Answer: 2