No doubt. Fluid dynamics. But it follows Faraday’s Laws. Moving charges create a mag field and a changing field causes charge flow. What about all of the beta particles flying off the Sun? - re moving charges. That should be added to the Suns mag field. Those particles hit the Earths atmosphere.
yes they do!
More then just Beta particles off the sun, thermonuclear processes so energetic heavy particles!
The atmosphere shields but not completely, the earth’s magnetic field re-directs charged particles (beta, proton, etc.), of course how much defection depends on their energy. Also there earth’s field is not static but dynamic, strengthens and weakness even goes to zero & flips polarity. (There is evidence that is now happening!) Also the field is not simple, earth’s field is not like a simple bar magnet there are other components project another field in a different direction much weaker but there.
As you said fluid dynamics governs the core, but not a true fluid has plastic qualities, also has internal currents, dynamics magnetic field therefore its electromagnetic fluid dynamics or MHD - magnetohydrodynamics. All very very non-linear mathematics very hard to understand it well.