  We study the (near or close to) ground state distribution of N softly
repelling particles trapped in the interior of a spherical box. The charges
mutually interact via an inverse power law potential of the form $1/r^\gamma$.
We study three regimes in which the charges form an single spherical shell at
the edge of the box ($\gamma=1$), a series of concentric shells of increasing
density ($\gamma=2$) and $\gamma=12$ for which the charges form shells with a
more uniform charge distribution. We conduct numerical simulations for clusters
containing up to 5000 charges and compare charge density across the system with
continuum limit results. The agreement between numerical (discrete) results and
the continuum limit is found to improve with increasing N.
