If I may run a bit further with that thought, assuming that all stars are powered the same way:
1) Does the consistent stellar mass/luminosity relationship mean that the galactic currents have consistent strength throughout the galaxy, rather than being weaker as one gets farther from the center of the galaxy?
There is a "peer-reviewed paper" published by a journal under the IEEE's auspices which sets out to show that the H-R (or colour-magnitude) diagram is a consequence of the currents which power each star.
For example, the spectral class (or colour) - which is usually plotted on the x-axis - is proportional to the current density (amps per square metre) at the surface of the star (photosphere).
If you should get your hands on a copy of that "paper", you are in for some surprises.
2) Why does the mass/luminosity relationship work so well for binary stars? Wouldn't they be sharing their portion of the galactic current?
AFAIK, no EU/ES proponent has ever answered that question!
As you can imagine, it's not for want of being asked it ...
3) What powers extragalactic stars?
Easy question; each galaxy has its own set of giant Birkeland currents, and there are also lots of these (even bigger ones) connecting galaxies.
You see, plasma laws scale ...
4) Most stars, including the sun, are in elliptical orbits about the center of the galaxy. Shouldn't the sun have a tail like a huge comet? (in the interest of completeness, I can't rule out the possibility that we're at one of the apses).
There are several different answers to this; some EU/ES proponents say that it does indeed have one; others point to some recent astronomical observations showing that at least one star does have what they call a tail.
5) Do these galactic currents light up any nebulae?
Sure they do!
You'll get, when you ask this question, dozens of links to images in various press releases, together with statements to the effect of "Look! See there! That's a Birkeland current!!"
And why are they so sure what they see is such a thing? Because of its shape! You know, all
cats are black Birkeland currents are filamentary,
this animal is black this thing is filamentary,
therefore this animal is a cat therefore this thing is a Birkeland current.
It should be noted that, again AFAIK, no EU/ES proponent has ever provided any numbers to go with any of this - such as how many amps a particular current is carrying, or what current density corresponds to what spectral class - nor what powers the currents, nor where the circuits close.
It should also be noted that PC proponents - the ones who are not also EU/ES proponents - generally try to avoid being associated with EU/ES proponents.