Obviously the answer will pop out of Faraday's Law, but to apply that we need to know:
- the area of the loops,
- the size of the (wave) magnetic field and
- the rate of change of the magnetic field.
The amplitude of the wave's magnetic field component is a little more tricky. There are some signals, like those from transmitters, which are pretty much stable in amplitude. But the majority of the noise in the Very Low Frequency (VLF) band comes from the impulsive bursts of radiation generated by lightning, known as sferics. These can also vary in amplitude depending on the intensity of the lightning and the distance from the antenna. Reference to R. K. Said, “Accurate and Efficient Long-Range Lightning Geo-Location Using a VLF Radio Atmospheric Waveform Bank,” PhD Thesis, Stanford University, 2009 gives an amplitude of around 500 pT for a sferic at night.
Finally the rate of change is related to the frequency of the wave and we can just assume that this is around 5 kHz.
So, putting that all together gives
V ~ ω A B = 2 * π * 5 kHz x 58 m2 x 500 pT ≈ 1 mV.
Which seems pretty small and is why you need a rather good preamplifier.