  The renormalized fermionic determinant of QED in 3 + 1 dimensions,
$\mbox{det}_{{ren}}$, in a static, unidirectional, inhomogeneous magnetic field
with finite flux can be calculated from the massive Euclidean Schwinger model's
determinant, $\mbox{det}_{{Sch}}$, in the same field by integrating
$\mbox{det}_{{Sch}}$, over the fermion's mass. Since $\mbox{det}_{{ren}}$ for
general fields is central to QED, it is desirable to have nonperturbative
information on this determinant, even for the restricted magnetic fields
considered here. To this end we continue our study of the physically relevant
determinant $\mbox{det}_{{Sch}}$. It is shown that the contribution of the
massless Schwinger model to $\mbox{det}_{{Sch}}$ is cancelled by a contribution
from the massive sector of QED in 1 + 1 dimensions and that zero modes are
suppressed in $\mbox{det}_{{Sch}}$. We then calculate $\mbox{det}_{{Sch}}$
analytically in the presence of a finite flux, cylindrical magnetic field. Its
behaviour for large flux and small fermion mass suggests that the zero-energy
bound states of the two-dimensional Pauli Hamiltonian are the controlling
factor in the growth of $\ln \mbox{det}_{{Sch}}$. Evidence is presented that
$\mbox{det}_{{Sch}}$ does not converge to the determinant of the massless
Schwinger model in the small mass limit for finite, nonzero flux magnetic
fields.
