So out of curiosity I took apart an ignition assembly from an old E90 and you can see the coil windings under the cover. You can see the little tiny coil within the key will line up inside of the bigger winding within the ignition housing when inserted.
I'm not sure using a toothbrush charger would be the best thing....with that sort of setup you'd get a very weak coupling with the winding in the key and also you'd probably be heating up all the other pieces of metal within the key as well like the battery and ICs.
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