It's the math that generates quantitative predictions that allow theories to be tested against measurements of how nature actually behaves. Without that, you don't have a theory of physics, you're just waving your hands around. On your favoured electric sun model for instance, unless that model can produce quantitative statements about things like the average kinetic energy of the electrons in the current, the current density, the size of the current, the power delivered to the sun by that current, and the size of the magnetic field such a current would induce, which can all be tested against measurements, you don't have a theory. You have an untested hypothesis. It's easy to test that one with known data and a few reasonable assumptions. There's an upper limit on the average kinetic energy of the electrons in the current, for instance, or we'd see a flood of x-rays from the sun as they strike the matter in the sun, there's a lower limit on the power in the current, it must at least equal the sun's power output, and there's an upper limit on the size of the induced magnetic field, it must be smaller than the earth's field at our distance from it or compasses wouldn't work.
I'll give you a hint: it's easiest to work backwards from the magnetic field strength. The magnetic induction B a distance R from a line of current of J amperes is B = uJ/2pπR, where u is the permeability constant. Usually the symbol is the lower case Greek letter mu with a small subscript of 0, but I can't show that with the character set available to me here. B cannot be more than about half a gauss, that's how big the earth's field is, u and R you can look up, π I presume you know, and figure out what the maximum current J can be in amperes. Then you can figure out how many watts a current that size can generate subject to certain reasonable assumptions about the density of electrons in the current and their average velocity, knowing that the wattage of the sun is about 4x10^26. You'll find that no possible combination of current density and electron velocity can match the sun's observed power output and at the same time induce a magnetic field that would not overpower compasses on the earth.
Elementary physics busts the electric sun model Beave. There's no way around it. It's wrong. Quite apart from the fact that neutrinos are observed flowing away from the sun, and only nuclear processes produce neutrinos...
