Did you get caught up with the release of the new Star Wars toys and merchandise this past week?
It turns out that one of the toys, the BB-8, is quite astonishing. Rhett Allain has an interesting article on how this toy works.
The last part on inductive charging shouldn't be a puzzle anymore, should it? I've had a tea kettle for at least 6 years that used inductive heating. So inductive charging shouldn't be unusual anymore, I would think.
Still, like he said, this might be a toy that could be a very good physics class demo.