A circular loop of radius R is carrying current I. The ratio of magnetic field at the center of circular loop and at a distance R from the center of the loop on its axis is

Step-by-step solution

The magnetic field at the center of a circular loop of radius R carrying current I is given by: B_ center = ₀ I 2R The magnetic field on the axis of the circular loop at a distance x from the center is given by: B_ axis = ₀ I R^2 2(R^2 + x^2)^ 3/2 Substituting x = R , we get: B_ axis = ₀ I R^2 2(R^2 + R^2)^ 3/2 = ₀ I R^2 2(2R^2)^ 3/2 = ₀ I R^2 2(2 2 R^3) = ₀ I 4 2 R The ratio of the magnetic fields is: B_ center B_ axis = ₀ I 2R ₀ I 4 2 R = 4 2 2 = 2 2 = 8 The required ratio is 8 : 1 .