Science Nerds: Could Jupiter's Magnetic Field be harvested for energy?

[vulcanlogician]

Could Jupiter's Magnetic Field (in theory) be harvested for energy?

Context: I'm doing some science fiction world building where the Jovians (who live on the moons of Jupiter) have built megastructures where they harness the energy from Jupiter's magnetic field. But I'd like to know how plausible this is. I'm trying to keep things well-grounded in science... no FTL travel, maybe no nuclear fusion, just stuff we know will work today. Huge planet-spanning structures ARE on the table however.

It's a pet project I've been tinkering with for years. A space opera that occurs in our own solar system involving several alien races: Mercurials, Venetians, Humans, Martians, Jovians, Kypers, and Oorts (who are all humans evolved, hundreds of thousands of years into the future).

Anyway, I know there are science geeks here who could give me a good analysis of the problem. The reason I care is that I want the solar system to have gone through several  cataclysms (maybe due to enormous solar flares that impacted the advancement of the inner planet civilizations negatively). But -for plot reasons- I need the Jovians to be largely unaffected by the solar flare activity. I'm thinking that Jupiter's magnetosphere might protect them. Is that plausible? I guess that's another thing I'm wondering about.

Anything is possible in fiction. Bible, Koran, Torah, Talmud, Vedas. 

I think it is hard in si-fi to not have some sort of innaccuracies. I know Neil Degrasse Tyson has picked on a few movies. 

Movies, TV shows, books,  of any genre greately rely on suspension of disbelief. 

I think it is more about your story telling skills than accuracy. Stephen King didn't make his career by accuracy. I've never seen an old car go on a killing spree.

It's very true that I could write a compelling story set in a universe with impossible science. But I'm trying to make this work Hard science fiction. I'm working within that structure. Think about when you are writing a poem. Let's say you want to write a sonnet or use iambic pentameter. While these structures limit you in certain ways, they also give you a structure to work with. And that (counterintuitively) gives you creative avenues that "anything goes" does not.

I WILL and I MUST break with hard science-- or at least bruise it a bit-- to create my "Star Trek, but in our own solar system" world that I want to make. But I'm trying to do that as little as possible. That structure is helping me develop what the Martians, Jovians, and Mercurials ultimately are.

The themes of the story involve climate change, a critique of capitalism/colonialism, the absurdity of religion, and the importance of unity among different peoples. The story has a sad ending. The inhabitants of the solar system realize that they are soon to be consumed by Von Neumann probes... probes that were created by Centurions (human ancestors that traveled to a nearby star to create AI that they could worship).

Turns out the probes have lain waste to multiple civilizations across the galaxy and there is no way to stop them. And, worst of all, they are returning to our solar system to dismantle every planet in it.

THAT'S the story. But as far as worldbuilding, I want it to be as consistent as possible with known physics and biology. ("Hard science fiction.") That's the structure I've decided on, just like, at the outset of composing a poem, you may choose iambic pentameter. I mean, sure, you could write in free verse... but not this time...