  We have calculated the spatial distribution of the electrostatic potential
created by an unbalanced charge $q$ in one of the conducting electrodes of a
long, uniform, linear array of small tunnel junctions. The distribution
describes, in particular, the shape of a topological single-electron soliton in
such an array. An analytical solution obtained for a circular cross section
model is compared with results of geometrical modeling of a more realistic
structure with square cross section. These solutions are very close to one
another, and can be reasonably approximated by a simple phenomenological
expression. In contrast to the previously accepted exponential approximation,
the new result describes the crossover between the linear change of the
potential near the center of the soliton to the unscreened Coulomb potential
far from the center, with an unexpected ``hump'' near the crossover point.
