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The downside is induced electric current in everything conductive within the transmission area.
oh
thats bad
Yeah, kind of a hazard, especially in a time when a lot of structures like bridges were made of iron.
Also you have the inverse square law issue - the energy imparted by the induction field drops off exponentially with distance, so the farther away you want to transmit power the higher the output transmission has to be, and it starts to get really impractical because the field strength varies significantly with distance from the transmitter. A device at the edge of the induction field will recieve a much lower amount of energy than a device in the middle. Assuming that you want to be able to run something useful (say, a refrigerator) at the edge of the field, well now you have to do something to shield similar devices that are closer to the transmission point or they'll melt - maybe you ground them so they can dump excess energy, but now you're wired again anyway, so what was the point of wireless power?
Wouldn't it be similar to radio waves where we can bounce them off the atmosphere and drastically increase their range?
Ah, no. Electromagnetic induction and electromagnetic radiation are related but different - induction doesn't produce radiation (radio) waves that would travel longer distances.
It is possible to power a device with radio waves - the most basic crystal radio just drives a speaker using the acquired radio signal. In 1945 the USSR "gifted" a concealed listening device (The Thing) to the US ambassador which worked this way - it was only "on" when an external radio was transmitting the correct frequency, making it very hard to detect. RFID tags also work the same - they don't require batteries because the chip is activated when the tag's antenna gets hit by the radio from the scanner.
This is only practical for very low-power devices, because transmitting high-power radio waves is dangerous.
It would likely be sufficient for things like smart wearables, though. Maybe even smart watches
Maybe, but then you run into difficulty with antenna size. An RFID chip uses a tiny antenna but it's only expected to work within a range of about 1cm. To make the listening device I linked above work with a radio source in another room required an antenna 23cm long.
I doubt you could ever transmit enough power to drive a display this way, at least not safely because the output from the transmitter would have to be orders of magnitude higher, and the circuitry on the receiving end would have to be bulkier as a consequence or risk overheating.
You mean the field drops off by the inverse square. Exponential drop off would be much faster.
Just make everything you don't want electricity in out of rubber.