Planet Atmospheres and Magnetic Fields

In our solar system, there are planets with very strong magnetic fields and planets with virtually no magnetic field, and the reason for this variability is a bit of a mystery. No one quite knows why this is so. However, one thing is known for sure, the magnetic fields are due to charge in motion. There must be an electric current somewhere for a magnetic field to be generated.

But where is this current to be found? Is it deep inside planets, or is it in the atmosphere?

For the internals of a planet, we can only speculate. However, the external features of planets are well known, so there we can do an objective analysis to see what we can find.

And indeed, there seem to be some external features that correlate quite well with the strength of magnetic fields of planets. All planets with a magnetic field have an atmosphere and they rotate on their axis at least as fast as Earth. They are also at least as large in diameter as Earth.

Characteristics of planets with virtually no magnetic field:

Mercury is small, rotates slowly, has very little atmosphere.
Venus is about as big as Earth, rotates extremely slowly, has a thick atmosphere.
Mars is small, rotates like Earth, has very little atmosphere.

On the other hand we have the gas giants, all big with thick atmospheres:

Jupiter is biggest, rotates in 10 hours has a magnetic field 19519 times stronger than Earth.
Saturn is second biggest,  rotates in 11 hours has a magnetic field 578 times stronger than Earth.
Uranus is third biggest, rotates in 17 hours has a magnetic field 48 times stronger than Earth.
Neptune is the smallest, rotates in 16 hours has a magnetic field 27 times stronger than Earth.

Note that the magnetic field is exponentially related to size and rotation speed. Jupiter has a magnetic field 40 times stronger than Saturn. Saturn has a magnetic field 10 times stronger then Uranus, and Uranus has a magnetic field 2 times stronger than Neptune.

The correlation is definitely there.

Hubble Captures Vivid Auroras in Jupiter's Atmosphere

By NASA, ESA, and J. Nichols (University of Leicester) - http://hubblesite.org/newscenter/archive/releases/2016/24, Public Domain, Link