  We find two new classes of exact solutions to the Einstein-Maxwell system of
equations. The matter content satisfies a linear equation of state consistent
with quark matter; a particular form of one of the gravitational potentials is
specified to generate solutions. The exact solutions can be written in terms of
elementary functions, and these can be related to quark matter in the presence
of an electromagnetic field. The first class of solutions generalises the Mak
and Harko model. The second class of solutions does not admit any singularities
in the matter and gravitational potentials at the centre.
