  We consider a variational problem involving competition between surface
tension and charge repulsion. We show that, as opposed to the case of weak
(short-range) interactions where we proved ill-posedness of the problem in a
previous paper, when the repulsion is stronger the perimeter dominates the
capacitary term at small scales. In particular we prove existence of minimizers
for small charges as well as their regularity. Combining this with the
stability of the ball under small $C^{1,\gamma}$ perturbations, this ultimately
leads to the minimality of the ball for small charges. We cover in particular
the borderline case of the $1-$capacity where both terms in the energy are of
the same order.
