  We study a constrained minimum energy problem with an external field relative
to the Riesz kernel of an arbitrary order for a generalized condenser with
touching oppositely-charged plates. Conditions sufficient for the solvability
of the problem are obtained. Our arguments are mainly based on the definition
of an appropriate metric structure on a set of vector measures associated with
a generalized condenser and the establishment of a completeness theorem for the
corresponding metric space.
