  This paper is the second in a series of studies working towards constructing
a realistic, evolving, non-potential coronal model for the solar magnetic
carpet. In the present study, the interaction of two magnetic elements is
considered. Our objectives are to study magnetic energy build up, storage and
dissipation as a result of emergence, cancellation, and flyby of these magnetic
elements. In the future these interactions will be the basic building blocks of
more complicated simulations involving hundreds of elements. Each interaction
is simulated in the presence of an overlying uniform magnetic field, which lies
at various orientations with respect to the evolving magnetic elements. For
these three small-scale interactions, the free energy stored in the field at
the end of the simulation ranges from $0.2-2.1\times 10^{26}$ ergs, while the
total energy dissipated ranges from $1.3-6.3\times 10^{26}$ ergs. For all
cases, a stronger overlying field results in higher energy storage and
dissipation. For the cancellation and emergence simulations, motion
perpendicular to the overlying field results in the highest values. For the
flyby simulations, motion parallel to the overlying field gives the highest
values. In all cases, the free energy built up is sufficient to explain
small-scale phenomena such as X-ray bright points or nanoflares. In addition,
if scaled for the correct number of magnetic elements for the volume
considered, the energy continually dissipated provides a significant fraction
of the quiet Sun coronal heating budget.
