The field normal to the plane of a wire of n turns and radius r which carries a current i is measured on the axis of the coil at a small distance h from the centre of the coil. This is smaller than the field at the centre by the fraction

The magnetic field on the axis of a current i carrying coil of turns n, radius r and at a distance i from the centre of the coilB=μ04π×2πir2r2+h23/2…………………(1)The field at the centre is given byBcentre =μ04π×2πir…………………….(2)                                    (∵ At centre h=0)BBcentre =r3r2+h23/2=r3r31+h2r23/2=11+32h2r2 or B1+32h2r2=Bcentre∴ Bcentre −B/B=32h2r2