  Laplace's equation appears frequently in physical applications involving
conservable quantities. Among these applications, miniaturized devices have
been of interest, in particular those using interdigitated arrays. Therefore,
we solved the two-dimensional Laplace's equation for a shallow or finite domain
consisting of interdigitated boundaries. We achieved this by using Jacobian
elliptic functions to conformally transform the interdigitated domain into a
parallel plates domain. The obtained expressions for potential distribution,
flux density and flux allow for arbitrary domain height, different band widths
and asymmetric potentials at the interdigitated array, besides considering
fringing effects at both ends of the array. All these expressions depend only
on relative dimensions, instead of absolute ones. With these results we showed
that the behavior in shallow or finite domains approaches that of a
semi-infinite domain, when its height is greater than the separation between
the centers of consecutive bands. We also found that, for any desired but fixed
flux, bands of equal width minimize the total surface of the interdigitated
array. Finally, we present approximate expressions for the flux, based on
elementary functions, which can be applied to ease the calculation of currents
(faradaic or non-faradaic), capacitances and resistances among other possible
applications.
