Suppose that the radius of the metallic sphere is 1 cm and that the
excess charge is 1.6 nC (10^10 e). This means that a typical distance
between adjacent excess electrons is about 0.35 micrometers. The
corresponding electric potential energy, 0.004 eV, is six times less
than the average thermal energy at room temperature (0.025 eV).
The rms speed of electrons at room temperature is about 10^5 m/s.
And collisions between them (in a vacuum) are not very frequent.
The distance between "electrons in the vacuum" and the "layer
of exposed positive charges", which binds them, must be much
smaller that the mean distance between the adjacent electrons in
the outer layer. Otherwise the effect of electrostatic interaction
would be negligible at room temperatures. Working backward (and
demanding V=0.25 eV; factor of ten above thermal) one finds that
the distance between the outer layer of electrons and "the exposed
layer of induced positive charges" is about 0.005 microns or 50
Angstroms. From a distance of 10 A, which is reasonable (?), the
electrostatic interaction would be 50 times stronger than thermal.
What speculative suggestions can be made on the basis of these
trivial considerations?