When a cluster or nanodroplet bears charge, its structure and thermodynamics are altered and, if the charge exceeds a certain limit, the system becomes unstable with respect to fragmentation. Some of the key results in this area were derived by Rayleigh in the nineteenth century using a continuum model of liquid droplets. Here we revisit the topic using a simple particle-based description, presenting a systematic case study of how charge affects the physical properties of a Lennard-Jones cluster composed of 309 particles. We find that the ability of the cluster to sustain charge depends on the number of particles over which the charge is distributed---a parameter not included in Rayleigh's analysis. Furthermore, the cluster may fragment before the charge is strong enough to drive all charged particles to the surface. The charged particles in stable clusters are therefore likely to reside in the cluster's interior even without considering solvation effects. ; Comment: 15 pages, 6 figures