  We analyze different stages of magnetized quark star evolution incorporating
baryon number conservation and using an anisotropic energy momentum tensor. The
first stages of the evolution are simulated through the inclusion of trapped
neutrinos and fixed entropy per particle, while in the last stage the star is
taken to be deleptonized and cold. We find that, although strong magnetic
fields modify quark star masses, the evolution of isolated stars needs to be
constrained by fixed baryon number, which necessarily lowers the possible star
masses. Moreover, magnetic field effects, measured by the difference between
the parallel and perpendicular pressures, are more pronounced in the beginning
of the star evolution, when there is a larger number of charged leptons and up
quarks. We also show that having a spatially varying magnetic field allows for
larger magnetic fields to be supported.
