A long wire is bent into a circular coil of one turn and then into a circular coil of smaller radius having n turns. If the same current passes in both the cases, the ratio of magnetic fields produced at the centre for one turn to that of n turns is

Step-by-step solution

Magnetic field at the centre of coil is, B ₁= ₀ I 2 r ₁ Magnetic field of n turns coil at the centre: aligned & B ₂= ₀ nI 2 r ₂ B ₁ ~B ₂ & = ₀ I 2 r ₁ ₀ nI 2 r ₂ = r ₂ nr ₁ aligned But, radius: r₁= 1 2 and r₂= 1 2 n array ll & r ₂ r ₁ = 1 n & B ₁ ~B ₂ = 1 n ^2 array