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> I've always wondered if you could harvest that same radio energy to power other things without batteries

That's how passive RFID tags work. The tag has a tiny little computer, and you hold it near a thing that emits an electric field that energizes it.

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I think the poster wants this to work without the “you hold it near a thing” part.

But it still works almost the same way. You hold it near a thing to get energy is mostly required because it works with very little power, let's say some milliwatts. Whereas old AM stations where sending in the range of megawatts.

That broadcast power is required to provide range. Radio waves obey the inverse-square law: for every doubling of the distance from source you get four times less power. This is also why wireless power transmission at a distance isn't really viable.

RFID can absolutely work at long range. Most applications don't by design because they don't want the data on the chip stolen. But there are applications that can read RFID from tens or hundreds of meters away.

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