  Observational estimates of the lifetimes and inferred accretion rates from
debris discs around polluted white dwarfs are often inconsistent with the
predictions of models of shielded Poynting-Robertson drag on the dust particles
in the discs. Moreover, many cool polluted white dwarfs do not show any
observational evidence of accompanying discs. This may be explained, in part,
if the debris discs had shorter lifetimes and higher accretion rates than
predicted by Poynting-Robertson drag alone. We consider the role of a magnetic
field on tidally disrupted diamagnetic debris and its subsequent effect on the
formation, evolution, and accretion rate of a debris disc. We estimate that
magnetic field strengths greater than $\sim$10kG may decrease the time needed
for circularisation and the disc lifetimes by several orders of magnitude and
increase the associated accretion rates by a similar factor, relative to
Poynting-Robertson drag. We suggest some polluted white dwarfs may host
magnetic fields below the typical detectable limit and that these fields may
account for a proportion of polluted white dwarfs with missing debris discs. We
also suggest that diamagnetic drag may account for the higher accretion rate
estimates among polluted white dwarfs that cannot be predicted solely by
Poynting-Robertson drag and find a dependence on magnetic field strength,
orbital pericentre distance, and particle size on predicated disc lifetimes and
accretion rates.
