We report the discovery of a new magnetic DA white dwarf ( WD ) , WD 0011 -721 , which is located within the very important 20 pc volume-limited sample of the closest WDs to the Sun .
This star has a mean field modulus \langle|B| \rangle 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 \pm 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 .