From: info.ronse@skynet.be   
      
   Jos Bergervoet wrote:   
   > On 2/13/2018 5:36 PM, charly wrote:   
   >> Kerry Soileau wrote:   
   >>> If the negative charge on a sphere in a vacuum is increased   
   >>> sufficiently, do electrons begin to escape from the sphere into   
   >>> vacuum? If so, is the physics similar to that of the photoelectric   
   >>> effect work function concept?   
   >>>   
   >>> Thanks for any references/insight on this question.   
   >>>   
   >>> [[Mod. note -- I think the answers to your questions are "yes" and   
   >>> "yes".  More detailed discussions from the newsgroup would be welcome.   
   >>> -- jt]]   
   >>   
   >> Question : would this problem not be rather similar to a glass, filled   
   >> with water, inverted and under gravity? The water falls out, unless its   
   >> surface is stabilized by for example a sheet of paper.   
   >>   
   >> Quantum tunneling of electrons leeds to a formula (Fowler Nordheim). But   
   >> its results are reached only for sharp points. For flat surfaces there   
   >> is a disagreement with experiment : the field reached is lower by a   
   >> factor 10-20, even for well polished surfaces. Stability problem?   
   >   
   > Or maybe polished surfaces are not flat? Even if you have a   
   > perfectly stacked crystal, just one single atom adsorbed on   
   > its surface would create big field gradients and may already   
   > give you the order of magnitude difference you mention.   
   >   
      
   A single adsorbed atom would indeed create field gradients. But I   
   suppose that even on a perfectly stacked crystal, the field at the   
   surface is also not free from big gradients. An adsorbed atom would   
   probably just increase matters. As a model one could take the field   
   enhancement at the top of a semisphere on a flat plane : about a factor   
   3 (as I read in paper from the internet on vacuum breakdown some time   
   (years) ago). But of course, on top of this semisphere one could place   
   another semisphere an order of magnitude smaller, so that the top of the   
   larger one could be considered flat.: yet another factor 3  ... and so   
   on, every order of magnitude would result in a factor 3 increase in   
   field strength.   
      
   However increasing electrical potential eventually leads to a   
   flash-over, a catastrophic breakdown. That is why I was thinking of   
   stability questions as I mentionned at first. And most interesting is of   
   course : what is the max field that can practically be reached : 4e9 V/m   
   (~=Fowler Nordheim), or 1e9 V/m, 4e8 V/m , 2e8 V/m ???   
      
   A similar problem is the max field strength in a dielectricum, for   
   example with an error, a sphere inside where the dielectricum is missing   
   ... I read on wikipedia that the max field in diamond for example is 2e9   
   V/m. Or in a flash memory device 8e8 V/m is used to program the memory   
   ... So apparently the field in a dielectricum might be larger than at   
   the surface of a metal in a vacuum?   
      
   Charles   
      
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