1) What is the decay of the magnetic field of a magnetic dipole?
It can be modelled as a ciruclar current with infinitesimal small radius. The decay of a current carrying wire can be easily calculated with Amperes law to be $$\vec{H}_\varphi=\frac{I}{2\pi R}\vec{e}_\varphi$$ with the radius \$R\$ and the current \$I\$ (cylinder coordinates). For a magnetic dipole, the field distribution can be calculated via Biot-Savarts law, and in my calculations it results in a \$\propto\frac{1}{r^2}\$ decay of the field. Measurements show a decay of \$\propto\frac{1}{r^2}\$ and \$\propto\frac{1}{r^3}\$ further away from the source. I should also mention the theoretical formulas for a magnetic dipole $$\vec{H}(\vec{r})=m\frac{1}{4\pi\mu_0}\bigg\{\vec{e}_r2\bigg(\frac{jk}{r}+\frac{1}{r^2}\bigg)\frac{e^{.jkr}}{r}\cos\vartheta+\vec{e}_\vartheta\bigg(-k^2+\frac{jk}{r}+\frac{1}{r^2}\bigg)\frac{e^{-jkr}}{r}\sin\vartheta\bigg\}.$$ From this formula (spheric coordinates: \$r\$, \$\vartheta\$, \$\varphi\$ ), I conclude that there are three different regions such as farfield etc. However, I do not know the boundaries of the regions and neither how this formula can coexist with Biot-Savarts law which yields (in my calculations) only one region. So:
2) What are the boundaries for farfield, nearfield?
3) How can I merge the analytic results from Biot-Savart and the magnetic dipole Formula above?