Two toroids 1 and 2 have total number of turns 200 and 100 respectively, with average radii 40 cm and 20 cm respectively. If they carry the same current i, the ratio of the magnetic fields along the two loops is

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(1) 1:1. Given: toroid 1 has N₁=200 at r₁=0.40 m; toroid 2 has N₂=100 at r₂=0.20 m; the same current i in both. Idea: Ampere's law round the central circle of a toroid gives B(2π r)=μ₀Ni, so B=(μ₀Ni)/(2π r). The field therefore depends on the turns and the radius only through the ratio N/r. Toroid 1: (N₁)/(r₁)=(200)/(0.40)=500 per metre. Toroid 2: (N₂)/(r₂)=(100)/(0.20)=500 per metre. They are equal, so B₁:B₂=1:1. Halving both the turns and the radius leaves the field untouched.

Two toroids 1 and 2 have total number of turns 200 and 100 respectively, with average radii 40 cm and 20 cm respectively. If they carry the same current i, the ratio of the magnetic fields along the two loops is

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