Interesting question. We know the earth acts as a magnet, and the standard idea is that this is because there is a kind of dynamo at the earth's core, due to rotating conductors.
You can compare the earth's field lines to the chart of the field lines of a solenoid and they are basically identical:
Now, with a solenoid, just the current moving through the coils creates that kind of magnetic field on its own. The earth, however, is rotating. If you have a rotating conductor exposed to an external magnetic field, then that field would induce a current in the conductor, and if the conductor were arranged correctly, the current passing through it could form its own magnetic field just like a solenoid. So it's possible that the whole magnetic field of the earth is a consequence of the sun's magnetosphere combined with the composition and motion of the earth.
Exactly. I was thinking more like a transformer (or maybe a an induction motor, motor meaning a moving charged mass, the earth’s core) that is driven by a source, the Sun’s charged particles flowing within it and the charged particles moving through space away from the Sun thus creating a magnetic fields that in turn causes the earth core to “move” or diminishes or adds to the Earths magnetic field.
And depending upon the magnetic force lines of the earth and the Sun and their respective strengths the two mag fields would complement (attract) or cancel (repel each other).
Also, what affect might the magnetic field have on the molecules in the earth’s atmosphere that have a slight charge.