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.