The ratio of magnetic field at the centre of a current-carrying coil of radius r to the magnetic field at a distance r from the centre of the coil on its axis is √x : 1. The value of x is ______.
Physics · Circular Motion
JEE Mains 8 April 2023 Shift 2 Evening Shift

Question

The ratio of magnetic field at the centre of a current-carrying coil of radius r to the magnetic field at a distance r from the centre of the coil on its axis is √x : 1. The value of x is ______.

G1 Physics · Accepted Answer

For a circular coil of radius r, field at the centre is B(0) = μ₀I/(2r) Field on the axis at distance x is B(x) = μ₀Ir² / [2(r² + x²)³ᐟ²] At x = r: B(r) = μ₀Ir² / [2(2r²)³ᐟ²] = μ₀I / [2×2³ᐟ² r] Therefore, B(0)/B(r) = 2³ᐟ² = √8 So if the ratio is written as √x : 1, √x = √8 and therefore x = 8. Final value: 8