  We report the discovery of a new magnetic DA white dwarf (WD), WD0011-721,
which is located within the very important 20pc volume-limited sample of the
closest WDs to the Sun. This star has a mean field modulus <|B|> of 343 kG, and
from the polarisation signal we deduce a line-of-sight field component of 75
kG. The magnetic field is sufficiently weak to have escaped detection in
classification spectra. We then present a preliminary exploration of the data
concerning the frequency of such fields among WDs with hydrogen-rich
atmospheres (DA stars). We find that 20 +- 5% of the DA WDs in this volume have
magnetic fields, mostly weaker than 1 MG. Unlike the slow field decay found
among the magnetic Bp stars of the upper main sequence, the WDs in this sample
show no evidence of magnetic field or flux changes over several Gyr.
