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Could one use wireless recharging technology (see http://home.howstuffworks.com/question292.htm) to power a light-emitting diode (which does not have a filament that gets hot (see http://oaicorp.com/digital-led-faq.aspx)) to display this week's parsha in shul on Shabbos? This is a theoretical question.

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wireless charging stations now exist for all sorts of technologies. Can you phrase your question using an example that isn't itself muktzah? Or find a way to suggest that moving the toothbrush at all isn't muktzah? –  avi Sep 10 '11 at 21:35
    
@avi Point taken. What would you say to this reformulation, "Could one use the wireless recharging technology (see home.howstuffworks.com/question292.htm) to power a light-emitting diode (which does not have a filament that gets hot (see oaicorp.com/digital-led-faq.aspx ) on Shabbos? This is a theoretical question." –  Avrohom Yitzchok Sep 11 '11 at 8:43
    
Yes that sounds more plausible. Maybe even throw in a use for the diode, such as displaying this weeks parsha in shul? :) –  avi Sep 11 '11 at 8:55
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Assuming the words on the sign are a sort of stencil, and this only gives it back lighting...

According to the poskim who say that all eletricty usage is an issur of Binyan, it seems that this would not be allowed.

However, according the poskim, (such as Rav Aurbach) who see 'the normal usage' as not falling under the category of binyan (such as a door or a window in a house) it seems like there would not be any real issur with the charging itself.

The charging is really no different than static eletricity which appears to be allowed. Shemiras Shabbos Kehilchaso 15:72. "Clothes made of synthetic materials may be worn, even though they give off sparks when being put on or taken off".(Vol.1, Chapter 15, No.72)

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It was the issue of binyan that I wanted to explore. Where there is a switch, I understood (rightly?) that the circuit is completed (built) by throwing the switch. Here there is no switch. The fluctuating magnetic field on one side generates current in the other side. –  Avrohom Yitzchok Sep 11 '11 at 10:47
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The concept of a switch physically completing a circuit has not been valid for many years now. switches often only change the state of a transistor and do not connect wires that were previously unconnected. Here the same is happening. the 'circuit' is being completed. By pure proximity. –  avi Sep 11 '11 at 10:53
    
Thank you @avi. –  Avrohom Yitzchok Sep 11 '11 at 11:08
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