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Two toroids 1 and 2 have total no. of turns 200 and 100 respectively with average radii 40 cm and 20 cm respectively. If they carry same current i, the ratio of the magnetic fields along the two loops is:
- 1 : 2
- 1 : 1
- 4 : 1
- 2 : 1
Correct answer: 2 : 1
Solution
The magnetic field inside a toroid is given by B = (μ₀ * N * I) / (2πr), where N is the number of turns, I is the current, and r is the average radius. For toroid 1, B₁ ∝ N₁/r₁ = 200/40, and for toroid 2, B₂ ∝ N₂/r₂ = 100/20. The ratio B₁:B₂ = (200/40):(100/20) = 2:1.
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