  Macroscopic Wigner islands present an interesting complementary approach to
explore the properties of two-dimensional confined particles systems. In this
work, we characterize theoretically and experimentally the interaction between
their basic components, viz., conducting spheres lying on the bottom electrode
of a plane condenser. We show that the interaction energy can be approximately
described by a decaying exponential as well as by a modified Bessel function of
the second kind. In particular, this implies that the interactions in this
system, whose characteristics are easily controllable, are the same as those
between vortices in type-II superconductors.
