Yes, you can transmit power wirelessly, but at the cost of either interference, short distance, or giant antennas and low efficiency. (In any case, 60 Hz is not such a good idea: without some fancy engineering tricks, a 60Hz antenna would involve a wire that was some significant fraction of 3100 miles long.)A crystal radio reciever is an early type of radio that is powered entriely by the radio station. It consists of just earphones, an antenna, a tuner, and a diode.Transmitting power across less than an inch is quite practical. I suspect that in the next few years, Apple designers will come up with a model of iPod that charges and transmits signals wirelessly, so they will no longer have to destroy the perfect smoothness of the case with a power/data jack.An MIT demonstration some years back showed transmission across a room. It used a 10MHz radio signal to transmit 60 watts of power (with 45% efficiency) between a pair of antenna coils that were separated by 7 feet. It was hardly iPod-ready, though. The coils were each two feet across.
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Actually, the antenna would be 1553.03 miles long; not very practical. Better off using a cord.
. Possible, but not very practical. You will better off using a much higher frequency but it's still not going to be very efficient and range is severely limited (inverse square).