Kudos on digging up Faraday's Law from the graveyard of my mind. I probably havent heard that term in ten years.
But everything you've said is right.
And I suspect that if you did the calculations (and you seem more capable than me of doing so) that the Earth's own magnetic field would yield a greater "per unit cost" of electric force within a few thousand kilometers of Earth's surface rather than the solar energy captured by the 8 million km radius ring suggested by Gundam.
For the record I'm not from NASA either. But I do have a Masters degree in Computer Science and a load of various practical science electives under my belt (multiple courses in physics, chemistry, and astronomy) so I'm something of an egghead.