We simulate Lattice QED in a constant and homogeneous external
magnetic field using the Rational Hybrid Monte-Carlo (RHMC) algorithm
developed for Lattice QCD. Our current simulations are directed towards
observing chiral symmetry breaking in the limit of zero electron bare mass
as predicted by approximate (Schwinger-Dyson) methods. Our earlier simulations
were performed on a $36^4$ lattice at the fine structure constant
$\alpha=1/137$, close to its physical value, with `safe' electron masses
$m=0.1$ and $m=0.2$. At this $\alpha$, the dynamical electron mass produced
by the external magnetic field, which is an order parameter for this chiral
symmetry breaking, is predicted to be far too small to be measurable. Hence we
are now simulating at the larger $\alpha=1/5$, where the predicted dynamical
electron mass at strong external magnetic fields accessable on the lattice is
large enough to be measurable. However this requires electron masses down to
$m=0.001$. Such a small $m$ requires lattices larger than $36^4$, but at
magnetic fields large enough to produce measurable dynamical electron masses,
$36$ is an adequate spatial extent for the lattice in the plane orthogonal to
the magnetic field because the electrons preferentially occupy the lowest
Landau level. We are therefore performing finite size analyses using
$36^2 \times N_\parallel^2$ lattices with $N_\parallel \geq 36$. We measure
the chiral condensate $\langle\bar{\psi}\psi\rangle$ as our order parameter for
chiral symmetry breaking, since it should remain finite as $m \rightarrow 0$
if chiral symmetry is broken by the magnetic field, but vanish otherwise. Our
preliminary results strongly suggest that chiral symmetry {\it is} broken
by the external magnetic field. In all our simulations, as well as measuring
other observables during these simulations, we are storing configurations at
regular intervals for further analysis. One such measurement planned for these
stored configurations is the determination of the effects that an external
magnetic field has on the coulomb field of a charged particle placed in this
magnetic field.