The fractional change in the magnetic field intensity at a distance r from centre on the axis of current carrying coil of radius a to the magnetic field intensity at the centre of the same coil is: (Take r < a )

Step-by-step solution

As we know, B axis = μ 0 iR 2 2 R 2 + x 2 3 / 2     where ,   R = a   B centre  = μ 0 i 2 a ∴ B axis  = μ 0 ia 2 2 a 2 + r 2 3 / 2 ∴ fractional change in magnetic field = μ 0 i 2 a - μ 0 i a 2 2 a 2 + r 2 3 / 2 μ 0 i 2 a = 1 - 1 1 + r 2 a 2 3 / 2 ≈ 1 − 1 − 3 2 r 2 a 2 = 3 2 r 2 a 2