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Various methods of wireless power transmission have been known for decades. Radio, after all, is nothing more than wirelessly transmitted power: sound is converted to a varying electrical current in the transmitter, which generates electromagnetic waves that set up a matching varying electrical current in the receiver, which amplifies it and uses it to drive a speaker, recreating the original sound.
But radio radiates in all directions, meaning very little power is actually transmitted to any one receiver, and most of it is altogether wasted.
WiTricity doesn't use electromagnetic radiation at all: instead, it's based on magnetism and the physics of coupled resonant objects.
Two objects resonating at the same frequency exchange energy extremely efficiently.
The MIT design consists of two copper coils. One, attached to the power source, is the sending unit. Rather than send out electromagnetic waves, it fills the space around it with a magnetic field oscillating at a particular frequency. The second copper coil is designed to resonate with that oscillating magnetic field. A copper coil within an oscillating magnetic field generates a current, enough, in MIT's case, to power a light bulb.
Power transformers make use of something similar, called magnetic induction, to transmit power between coils over short distances. But those coils aren't designed to resonate with each other. Resonant coupling makes the transfer of energy almost a million times more efficient.
Since the magnetic field doesn't radiate, most of the power that isn't picked up by the receiving unit is bound to the originating coil, rather than being lost into the environment.
The only question I would have for them is, are there any long-term health risks of living with this system in your home?