  The surface magnetic field strength of white dwarfs is observed to vary from
very little to around 10^9 G. Here we examine the proposal that the strongest
fields are generated by dynamo action during the common envelope phase of
strongly interacting stars that leads to binary systems containing at least one
white dwarf. The resulting magnetic field depends strongly on the electrical
conductivity of the white dwarf, the lifetime of the convective envelope and
the variability of the magnetic dynamo. We assess the various energy sources
available and estimate necessary lifetimes of the common envelope. In the case
of a dynamo that leads a randomly oriented magnetic field we find that the
induced field is confined to a thin boundary layer at the surface of the white
dwarf. This then decays away rapidly upon dispersal of the common envelope. The
residual field is typically less than 10^-8 times the strength of the external
field. Only in the case where there is some preferential direction to the
dynamo-generated field can an induced field, that avoids rapid decay, be
produced. We show that a surface field of magnitude a few per cent of the
external field may be produced after a few Myr. In this case the residual field
strength is roughly proportional to the lifetime of the dynamo activity.
