The dipole moment of a coil of area ‘A’ and no. of turns N and carrying current (i) will be

We know magnetic field induction at a point ‘P’ at a distance r from the center of the circular coil is B=μ0nir22(r2+x2)32                If  r>>x B=μ0nir22(r)3×2π2π⇒B=2(μ0nir2)4πr3=μ  0 4π2niAr3-------------(1)We know magnetic field induction at a point ‘p’ on the axial line due to short bar magnet isB=μ  0 4π2Mr3--------------(2)Comparing  (1) & (2) we get  M=niA