A short wire (1 m) and a long wire (tens of meters or even 100m) in the AM broadcast band actually have about the same induced voltage for any given field intensity.*
The problem is a short wire has a much higher impedance -- hundreds or thousands of ohms of capacitive reactance.
If the receiver has a high input impedance, such as a source follower, the short wire will delivery plenty of signal at the source follower output. If the receiver has a low input impedance, such as 50 ohms, then the short wire won't put much voltage into the receiver input, but the longer wire will.
*think about the typical automobile AM radio receiver. The antenna is a vertical whip 1 or 2 meters in length and yet the AM radio works well. This is because the automobile receiver is designed with a high input impedance, quite often a source follower.