  We consider Callan, Giddings, Harvey and Strominger's (CGHS) two dimensional
dilatonic gravity with electromagnetic interactions. This model can be also
solved classically. Among the solutions describing static black holes, there
exist extremal solutions which have zero temperatures. In the extremal
solutions, the space-time metric is not singular. We also obtain the solutions
describing charged matter (chiral fermions) collapsing into black holes.
Through the collapsing, not only future horizon but past horizon is also
shifted. The quantum corrections including chiral anomaly are also discussed.
In a way similar to CGHS model, the curvature singularity also appeared, except
extremal case, when the matter collapsing. The screening effects due to the
chiral anomaly have a tendency to cloak the singularity
