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 field at the centre of circular carrying conductor, B_ c = ₀ I 2 r Magnetic on the axis at a distance x from the centre is given as B_ axis = ₀ I r² 2 (r²+x² )^ 3 / 2 Here, x=rB_ axis = ₀ I r² 2 (r²+r² )^ 3 / 2 = ₀ I r² 2 (2 r² )^ 3 / 2 = ₀ I r² 2 2 2 r³ B_ axis = ₀ I 4 2 r B_ axis =B_ a = ₀ I 4 2 r B_ c B_ a = ₀ I / 2 r ₀ I 4 2 r = 4 2 r 2 r =2 2 B_ c : B_ a =2 2 : 1