A coil having 9 turns carrying current produces magnetic field B ₁ at the centre. Now that coil is rewounded into 3 turns carrying same current. Then magnetic field at the centre B₂ is

Step-by-step solution

The magnetic field at the center of a circular coil is given by B = ₀ N I 2R , where N is the number of turns, I is the current, and R is the radius. For the initial coil with 9 turns, B₁ = 9 ₀ I 2R₁ . Rewinding the same length of wire into 3 turns requires 9R₁ = 3R₂ , so R₂ = 3R₁ . The new magnetic field becomes B₂ = 3 ₀ I 2(3R₁) = ₀ I 2R₁ . Substituting B₁ = 9 ₀ I 2R₁ yields ₀ I 2R₁ = B₁ 9 , hence B₂ = B₁ 9 . The answer is A .