  We construct, by numerical means, static solutions of the spherically
symmetric Einstein-Vlasov-Maxwell system and investigate various features of
the solutions. This extends a previous investigation \cite{AR1} of the
chargeless case. We study the possible shapes of the energy density profile as
a function of the area radius when the electric charge of an individual
particle is varied as a parameter. We find profiles which are multi-peaked,
where the peaks are separated either by vacuum or a thin atmosphere, and we
find that for a sufficiently large charge parameter there are no physically
meaningful solutions. Furthermore, we investigate if the inequality
\sqrt{M}\leq \frac{\sqrt{R}}{3}+\sqrt{\frac{R}{9}+\frac{Q^2}{3R}}, derived in
\cite{An2}, is sharp within the class of solutions to the
Einstein-Vlasov-Maxwell system. Here M is the ADM mass, Q the charge, and R the
area radius of the boundary of the static object. We find two classes of
solutions with this property, while there is only one in the chargeless case.
In particular we find numerical evidence for the existence of arbitrarily thin
shell solutions to the Einstein-Vlasov-Maxwell system. Finally, we consider one
parameter families of steady states, and we find spirals in the mass-radius
diagram for all examples of the microscopic equation of state which we
consider.
