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I was reading about WiTricity (http://en.wikipedia.org/wiki/WiTricity) a technology developed by MIT to wirelessly transmit electricity through resonance, and I have this question:

Given the phenomenon of resonant inductive coupling which wikipedia defines as:

the near field wireless transmission of electrical energy between two coils that are tuned to resonate at the same frequency. http://en.wikipedia.org/wiki/Resonant_inductive_coupling

And the Schumann resonances of the earth ( ~7.83Hz, see wikipedia), would it be theoretically possible to create a coil that resonates at the same frequency or one of it's harmonics (7.83, 14.3, 20.8, 27.3 and 33.8 Hz) to generate electricity?

I have a feeling that these wavelengths may be too big to capture via resonance (they are as large as the circumference of the earth if I understand it correctly), so alternatively would it be possible to create a coil that resonates with one of the EM waves that the sun sends our way?

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In principle of course you try something like that. But there are three issues that will kill you:

  1. $Q$. Every resonance has a quality factor which represents how quickly the energy in the mode drains away by assorted dissipative processes. I don't know what it is for the Schumann resonances, but I'll give you long odds that it is not good: much of the energy you put into the field will just dribble away into space.
  2. Power density. Whatever energy you pump into these modes will spread out over the whole cavity, and you'll only be able to draw as much as there is in the region covered by your antenna, which will be effective nothing even with gigawatts driven into the resonance. Not only couldn't you power a iPhone, you couldn't power the little shoplifting-prevention tag that retailers put onto bits of mobile merchandise.
  3. Antenna dimensions. The naive way to design an antennas to use at frequency $f$ requires conductors of length on order of $c f$. Bit of a problem for frequencies of a few or few tens of Hertz.
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excellent answer, thanks. But why do you mention antennas? The way I understood it is that simply by having a coil that resonates at the same frequency as the EM wave is enough to transmit the energy.... did I not understand this correctly? –  Andy Jan 30 '13 at 9:48
    
That coil is an antenna. Any widget that picks up the signal is an antenna, and you need some widget to get at the energy. –  dmckee Jan 30 '13 at 14:39
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