The magnetic field at the centre of a circular current carrying conductor of radius r is B _ c . The magnetic field on its axis at a distance r from the centre is B _ a . The value of B _ c : B _ a will be

Step-by-step solution

Magnetic induction at the centre of the coil of radius is B _ c = ₀ nI 2 r Magnetic induction on the axial line of a circular coil at a distance from the centre is B_ a = ₀ n² I 2 (r²+x² )^ 3 / 2 Given x=r B_ a = ₀ n r² I 2 (2 r² )^ 3 / 2 From Eqs. (i) and (ii), we get B _ c B _ a = 2 2 1