The radio transmitter is the external power. The crystal set is a way to grab a tiny amount of the electrical power being paid for by whatever entity is running the transmitter. You can play around with the inverse square law and figure out how little power the set is grabbing, but it's working on the basis of what it does grab.
[1] https://en.wikipedia.org/wiki/The_Thing_(listening_device)
There was a small booklet with circuits and connection lists, like 1-12-14 meaning that you where supposed to put wires between those connections.
Absolutely no explenation about how the circuits worked.
https://en.wikipedia.org/wiki/Ferrite_bead
So, in theory, a crystal set should still be a good way to pick up conservative talk radio and sports talk and you kinda get the idea it wouldn't be a popular project for kids these days given the current media landscape.