We have detected longitudinal magnetic fields between 2 and 4 kG in three ( WD 0446 - 790 , WD 1105 - 048 , WD 2359 - 434 ) out of a sample of 12 normal DA white dwarfs by using optical spectropolarimetry done with the VLT Antu 8 m telescope equipped with FORS1 . With the exception of 40 Eri B ( 4 kG ) these are the first positive detections of magnetic fields in white dwarfs below 30 kG . Although suspected , it was not clear whether a significant fraction of white dwarfs contain magnetic fields at this level . These fields may be explained as fossil relics from magnetic fields in the main-sequence progenitors considerably enhanced by magnetic flux conservation during the shrinkage of the core . A detection rate of 25 % ( 3/12 ) may indicate now for the first time that a substantial fraction of white dwarfs have a weak magnetic field . This result , if confirmed by future observations , would form a cornerstone for our understanding on the evolution of stellar magnetic fields .