Air transformers, like you’re talking about here, are bloody hopeless. You know how you can charge up an iPhone wirelessly? (Well, you can if you’ve got a Qi (pronounced for some reason as chee) charger and not one of those PMA ones).
It’s a gimmick. They’re slow and inefficient and you’d be better off by far sticking a cabled charger into the wall and then into your phone.
The thing is that you have one coil chopping an applied voltage to cause a rise and fall in the primary coil. A coil’s an inductor, and what an inductor does is to store charge in a magnetic field. If you give it DC, it just grows the magnetic field as big as it can and then acts like a wire. If you give it a changing current, though, the magnetic field will rise and fall.
Here’s the clever bit. If you put another coil where the magnetic field can affect it, you get a current induced in that coil from the rise and fall. That’s what charges your battery. Really slowly.
How near does your iPhone need to be to the first coil? Bang on top of it. If you move it a couple of inches off, it’ll stop charging.
This is really, really inefficient. Go and suggest it to that Thunderbird kid and tell her how much more power we’d need to generate to make this work. It’ll be really funny to see her face.