It is not practicable to transfer significant power across a 50cm air gap.
The nearest to this would be anti-theft tags. Read here: http://www.explainthatstuff.com/rfid.html
Agreed. There are examples of using a field to temporarily power a low-power transmitter. Chips that runners wear during a race sometimes use this principle, but the amount of power is tiny - just enough to chirp the transmitter.