# Why Earth is like a magnetic dipole?

Earth’s magnetic field is mostly caused by electric currents in the liquid outer core, which is composed of conductive, molten iron. Loops of currents in the constantly moving, liquid iron create magnetic fields.

However , we can say that the Earth's magnetic field obeys the magnetic dipole equation .

The dipole model of the Earth's magnetic field is a first order approximation of the rather complex true Earth's magnetic field. Due to effects of the interplanetary magnetic field, and the solar wind, the dipole model is particularly inaccurate at high L-shells (e.g., above L=3), but may be a good approximation for lower L-shells. For more precise work, or for any work at higher L-shells, a more accurate model that incorporates solar effects, such as the Tsyganenko magnetic field model, is recommended.

Why all this huge random liquid iron movements seem to generate a magnetic field similar with a magnetic dipole , for low L shells ( below L=3 )? Is just an empirical coincidence ?

The magnetic field $\vec B=\nabla \times \vec A$ of any localized current $\vec J(\vec r)$ distribution can be approximated by a multi-pole expansion of its vector potential $\vec A$. The lowest order term of this multi-pole expansion gives you a magnetic dipole field $$\vec A \approx \frac {\mu_0}{4\pi}\frac{\vec m \times \vec r}{|\vec r|^3}$$ where $$\vec m=\frac {1}{2} \int_V \vec r' \times \vec J(\vec r')d^3r'$$ is the magnetic dipole moment. Thus the first approximation of earth's magnetic field is a magnetic dipole field.
• This is only part of the answer. Being the lowest order term does not mean that the dipole moment is the largest. However, in the expansion of a magnetic field, the dipole term drops off as $1/r^3$, the quadrupole term as $1/r^4$ and so on. The surface of the Earth is at about twice the radius of the Earth's core, so compared to the dipole term, the quadrupole term is half as strong as it is at the surface of the core. See en.wikipedia.org/wiki/…. – A. Newell Mar 27 '18 at 5:09