The field due to a wire of n turns and radius r which carries a current J is measured on the axis of the coil at a small distance h from the center of the coil. This is smaller than the field at the center by the fraction:

The magnetic field on the axis of a coil carrying current d having n turns, radius r and at a distance h from the centre of the coil, is given byB=μ04π×2πNIr2r2+h23/2 The field at the centre is given by BC=μ04π×2πNIr ∴  BBC=r3r2+h23/2=r3r31+h2r23/2=1-32h2r2  We have to find: f=BC-BBC=1=BBC=32h2r2