  We use a simple electrostatic treatment to model recent experiments on
quantum Hall systems, in which charging of localised states by addition of
integer or fractionally-charged quasiparticles is observed. Treating the
localised state as a compressible quantum dot or antidot embedded in an
incompressible background, we calculate the electrostatic potential in its
vicinity as a function of its charge, and the chemical potential values at
which its charge changes. The results offer a quantitative framework for
analysis of the observations.
