Binding of few-electron systems in two-dimensional potential cavities in the
presence of an external magnetic field is studied with the exact
diagonalization approach. We demonstrate that for shallow cavities the
few-electron system becomes bound only under the application of a strong
magnetic field. The critical value of the depth of the cavity allowing the
formation of a bound state decreases with magnetic field in a non-smooth
fashion, due to the increasing angular momentum of the first bound state. In
the high magnetic field limit the binding energies and the critical values for
the depth of the potential cavity allowing the formation of a bound system tend
to the classical values