This question was asked to me by a 'backyard scientist' and I'm having a frustrating difficulty answering it satisfactorily.
As an example of a charged object to focus attention on, I'll use this bench-top Van de Graaff generator (VDG):
The metal sphere is $0.25\:\mathrm{m}$ diameter, rated maximum voltage $375,000\:\mathrm{V}$ and maximum charge $5.2\:\mathrm{\mu C}$.
Based on this, I made a few 'back of an envelope' calculations and estimates for this VDG, at max. charge:
Number of electrons on the sphere $= \frac{5.2 \times 10^{-6}}{1.6\times 10^{-19}}=3.25\times 10^{13}$
Surface area of the sphere = $\pi D^2=\pi \times (0.25)^2=0.20\:\mathrm{m^2}$
Estimated distance between electrons (square packing) = $\sqrt\frac{0.2}{3.25\times 10^{13}}=7.8\times10^{-8}\:\mathrm{m}$
Repulsive force between two adjacent electrons (Coulomb's Law)$=9\times10^{9}\times\frac{(1.6\times 10^{-19})^2}{(7.8\times10^{-8})^2}=3.8\times10^{-14}\:\mathrm{N}$
Electron acceleration due to repulsive force: $F=ma$:
$a=\frac{3.8\times10^{-14}}{9.1\times10^{-31}}=4.2\times10^{16}\:\mathrm{ms^{-2}}$
That's quite a whopper! Hard to see how these electrons would not fly away from each other (and reduce their potential energy).
I found this P.S answer to a very similar question but don't find it very satisfying.
What am I missing?