He pereslushal (see above). The battery is not needed.
You are a person who is familiar with the science. So you've most likely understand
In this case it is a passive device and reflects the radiation of the emitter, right? Therefore you should consider the distance from the transducer to the pendant, because it is more in the hundreds of thousands of times than the distance from the pendant to the operator.
And as you rightly said, the radiation power is inversely proportional to the square of the distance. But this distance... Well, even in the framework of Moscow - tens of kilometers, but the device bought and probably out of town residents?
Then to the pendant at a distance of one kilometer - radiation power reaches a million times less than is emitted by the antenna. While the pendant is at a distance of 10 km - power will fall by a hundred million. Hence the conclusion actually follows:
1. No matter at what distance pendant of the operator. Step to the left - change the distance to the emitter, which has a larger effect
2. Power down pendant is not just small, it's tiny. About the same pickup, and even more give you hundreds of sources: radio stations, TV, just current in the socket
3. Due to the quadratic reduction of power with distance - pendants needs to work differently for each operator. Who is closer to the station, and the king. It would seem so, if not p. 2