This is an academic question among my coworkers. Some believe it is
infinite, however I believe at some voltage the electrons will jump the gap.
Any ideas?
A vacuum can support a huge electric field, infinite except for
obscure quantum effects at incredible field levels. But real
electrodes will have surface emission effects that will rip ions out
of the metals or whatever; once a few ions get loose and whack the
opposite electrode, all hell breaks loose. It takes something like
1e8v/m to rip ions out of metal, but you can get that sort of field at
the tip of a rough spikey bit using only kilovolts. Clean high-vacuum
systems can work in the tens of megavolts per meter range, as I
recall.
As in interesting aside, look up the Farnsworth Multipactor effect.
It's cause some serious grief in satellite RF systems.
John