  We study the dynamical generation of masses for fundamental fermions in
quenched quantum electrodynamics in the presence of weak magnetic fields using
Schwinger-Dyson equations. Contrary to the case where the magnetic field is
strong, in the weak field limit the coupling should exceed certain critical
value in order for the generation of masses to take place, just as in the case
where no magnetic field is present. The weak field limit is defined as eB <<
m(0)^2, where m(0) is the value of the dynamically generated mass in the
absence of the field. We carry out a numerical analysis to study the magnetic
field dependence of the mass function above critical coupling and show that in
this regime the dynamically generated mass and the chiral condensate for the
lowest Landau level increase proportionally to (eB)^2.
