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