This picture is from a model of how the earth's magnetic field is generated.
Click on image for full size
Glaztmeir and Roberts of LANL
The Generation of Neptune's Magnetosphere
Magnetospheres are generated with 1.) magnetic materials and 2.) with motions within the magnetic material. As long as a planet has these two ingredients scientists believe that it can generate a magnetic field.
The Earth-like planets generate magnetospheres within the iron cores at their centers. However, Neptune has almost no iron core.
The magnetic material of Neptune is found within its icy shell. Motions within that shell produce the magnetic field.
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