  In this manuscript, we undertake an examination of a classical plasma
deployed on two finite co-planar surfaces: a circular region $\Omega_{in}$ into
an annular region $\Omega_{out}$ with a gap in between. It is studied both from
the point of view of statistical mechanics and the electrostatics of continua
media. We employ a dual perspective: the first one is by using Molecular
Dynamics (MD) simulations to find the system's positional correlation functions
and velocity distributions. That by modeling the system as a classical
two-dimensional Coulomb plasma of point-like charged particles $q_1$ and $q_2$
on the layers $\Omega_{in}$ and $\Omega_{out}$ respectively with no background
density. The second one corresponds to a finite surface electrode composed of
planar metallic layers displayed on the regions $\Omega_{in}$, $\Omega_{out}$
at constant voltages $V_{in}$, $V_{out}$ considering axial symmetry. The
surface charge density is calculated by the Method of Moments (MoM) under the
electrostatic approximation. Point-like and differential charges elements
interact via a $1/r$ - electric potential in both cases. The thermodynamic
averages of the number density, and electric potential due to the plasma depend
on the coupling and the charge ratio $\xi=q_1/q_2$ once the geometry of the
layers is fixed. On the other hand, the fields due to the SE depend on the
layer's geometry and their voltage. In the document, is defined a protocol to
properly compare the systems. We show that there are values of the coupling
parameter, where the thermodynamic averages computed via MD agree with the
results of MoM for attractive $\xi=-1$ and repulsive layers $\xi=1$.
  Keywords: molecular dynamics, method of moments, Coulomb systems, long-range
interaction.
