Why doesn't electric charge immediately leak off charged objects? I will focus my question with a particular example: a metal sphere, surrounded by vacuum, is given a negative charge. I know that when this charge is great enough, electrons will be emitted from the sphere, but why is the threshold for this so high? As I understand it, the reason an electron stays on the negative sphere despite the electric repulsion is because of the metal's work function. But the work function of metals are typically ~4 eV. Wouldn't this suggest that -4 Volts would be the threshold for electron emission from the sphere in a vacuum? (Or a voltage even closer to zero, because of the thermal distribution of electron energies in the metal.) This seems way too small and I would think the threshold would concern a minimum field strength rather than minimum voltage.
 A: An electric field which would strip electrons from the metal would need to be strong enough to provide for a voltage difference of $4V$ over a distance related to the work function -- the distance between "electron is in the metal" and "electron is outside the metal".  One should expect this distance to be on the order of a few atomic layers, i.e., $\sim 10^{-10}\mathrm{m}$: Therefore, one would expect the electric field required to be on the order of $\mathrm{GV}/\mathrm{m}$.
On the other hand, $4\mathrm{eV}$ are a very high temperature, making electron loss due to thermal emission extremely unlikely. $0.025\mathrm{eV}$ are room temperature, and thus $4\mathrm{eV}$ are $160$ times room temperature -- at room temperature, the fraction of electrons with sufficiently high energy is thus around $e^{-160}$, an astronomically small number even compared to the number of electrons in a solid.
A: The threshold for electron emission from a metal is so high because at room temperature the work function of the metal of several 1eV (which acts as an emission barrier) is far above the thermal energy kT=0.026eV of the electrons in the metal. Therefore, at room temperature, only a minuscule fraction of electron can overcome this barrier according to the Fermi distribution. Significant emission can be achieved by heating of the metal which leads to thermionic emission over the barrier, which is used in thermionic cathodes of electron tubes. Another mechanism of electron emission from the metal is the field emission (Fowler-Nordheim emission) caused by high applied electric surface fields which reduce the surface barrier and enable quantum mechanical tunneling through the triangular potential barrier formed by the work function and the surface field, which becomes transparent to the (cold) electrons in the metal at high applied fields in the range of several MV/cm. Therefore it can be expected that with high enough negative charging of the metal sphere the surface electric field strength will reach a critical strength to cause significant field emission of the electrons. For the same applied electrical potential difference, this will occur for spheres with smaller radius. Field emission of electrons is used for field emission cathodes with sharp metal points, e.g., in electron microscopes.  
A: As an electron makes its way outside a metal surface, there is immediately
an image charge (positive virtual charge) on the other side of that surface
that attracts it back.   The 'work function' is the kinetic energy that the
free electron needs if it is to escape to a large distance, and has
to include both surface-binding-energy and the long-range attractive force
that a conductor exerts on a nearby charge.
The sphere, if it is very large, might have a local field completely dominated
by the (attractive) image charge, and not by the net (repulsive) charge on the sphere.  Net charge is one sphere radius away, and image charge is two
surface-to-electron steps away.
