The magnetic field at the center of current carrying circular loop is B₁. The magnetic field at a distance of √3 times radius of the given circular loop from the center on its axis is B₂. The value of B₁ / B₂ will be

Solution

Physics sir · 3 steps

Divide the centre field by the axial field and only (1 + x²/R²)^(3/2) survives.

1. Two formulas. At the centre, B₁ = (μ₀ I)/2R. At a distance x on the axis, B₂ = (μ₀ I R²)/2(R² + x²)^(3/2).

   B₁/B₂ = (R² + x²)^(3/2)/R³ = (1 + x²/R²)^(3/2)

2. Put in numbers. With x = √3R, x² = 3R², so the bracket is 1 + 3 = 4. Then 4^(3/2) = (√4)³ = 2³ = 8.
3. So. B₁ : B₂ = 8 : 1, which is option (c).

The idea to keep. For any point on the axis of a loop, B_(centre)/Bₐₓᵢₛ = (1 + x²/R²)^(3/2). Find the bracket first, then take the square root and cube it.

Answer from the NTA final answer key. Solution by PrepWiser.