  We study the vacuum (i.e., zero-temperature) Casimir energy for a system of
neutral conductors which are isolated, as opposed to grounded. The former is
meant to describe a situation where the total charge on each conductor, as well
as all of its fluctuations, vanishes, while the latter describes a situation
where the conductors are connected to a charge reservoir. We compute the
difference between the vacuum energies for a given system of conductors, but
subjected to the two different conditions stated above. The results can be
written in terms of a generalized, frequency-dependent capacitance matrix of
the system. Using a multipolar expansion, we show that the grounded Casimir
energy includes a monopole-monopole interaction term that is absent in the
isolated case in the large distance limit
