I received an interesting question in connection with building
the proton magnetometer.
What is an optimal size for the water bottle?
I could speak only of the bottle size which I used.
(abt 6 X 10 cm. diam x height)
At first blush, it seems that the precession signal would increase with
diameter cubed, while the wire used in winding the coil would grow only
with the diameter squared - a clear advantage for larger bottles.
But I recall that field inhomogeneities readily quench the signal and I
imagine that a larger bottle would capture more field nonuniformity.
Because the same coil is also used for polarizing the water,
it seems that a given battery power would provide a polarizing
field inversely proportional to diameter squared.
It seems to me however, that if there is sufficient field to
rotate the nuclear axis of susceptible atoms, then further increases would
not be productive.