On the axis of a circular current loop of radius R, at a distance x ≫ R, the magnetic field can be written in terms of the moment m as:

1. Axial field: $B = \dfrac{\mu_0 I R^2}{2(x^2+R^2)^{3/2}}$. 2. For $x \gg R$, drop $R^2$: $B \approx \dfrac{\mu_0 I R^2}{2x^3}$. 3. Using $m = I\pi R^2$, write $B = \dfrac{\mu_0 m}{2\pi x^3}$. 4. Rearranged: $B = \dfrac{\mu_0}{4\pi}\dfrac{2m}{x^3}$, the axial dipole form. _Source: syllabus Physics Ch 4 "Moving Charges and Magnetism", p.155_