Non-zero electric field inside a conductor, when applying an large external field I'm probably missing something, or does not understand conductors well enough. But I have a question related to the title of this message.
In many places you read that there can be no electric field inside a conductor. The arguments typically go something in line with, since there is an electric field, charges inside the conductor will rearrange themselves so cancel the field. Very simply stated.
That I don't understand, is that this seams to assume that there always is "enough" charge to redistribute. To clarify my confusion, let's say we have a conducting solid sphere with some charge. If we apply an "large" external static field to this sphere, charges inside it will tend to cancel it out. But, what if the total charge inside it is not enough? The total charge in the sphere can only generate a limited field, but the external one can be arbitrary large. What if the field outside is so large that the potential it generate, from one side of the sphere to the other, is larger than what the internal charge can generate?
As I said, I'm probably missing something essential, but can someone please point out the misstake in the above argument?
 A: In a static situation, there is no electric field inside a conductor.
If you have an energy source, and apply current to (for instance)
a conductive light bulb filament, Ohm's law gives a nonzero solution
for the electric field inside that filament.
So, 'no electric field' is correct for electrostatics,
and not for a variety of interesting technology where current
flows in conductors.   Still, there might be miles of wire
between me and the power plant, and there's little voltage drop
in a few millimeters of the transmission-line copper.   The field
really IS small, so it's a good approximation even for current-carrying conductors.

this seams to assume that there always is "enough" charge to redistribute. 

It took a LOT of work to produce field-effect transistors, that
actually DO have a practical limit to the amount of charge
that can redistribute, so that a channel could be depleted of
what would otherwise be free-charge.   So, yes, there are also
useful devices with depletion of a microinch or so of material
arranged by an external field.   It's not something you can do
with large samples, on a tabletop.   The semiconductor purity
requirements were somewhat challenging.
A: If the field gets stronger electrons near the surface of the conductor will feel a stronger residual field, until some fly off in a spark that will hit you voltage source and reduce the voltage it produces.
A: Let’s look at the numbers. 
Atoms are typically an angstrom ($10^{-10}$m) across.  A metal conductor will typically have one conduction electron per atom. 
A Coulomb is a big amount of charge: a macroscopic 1A current for a second. It’s also $6 \times 10^{18}$ electrons. 
Combining those, one Coulomb corresponds to the charge in just the first layer of atoms in a 60cm2 patch of conductor surface. The first nanometer is a factor 10 more; the first micron in ten-thousand time more. 
Unless you’re doing an experiment aimed at truly extreme conditions, you don’t run out of charges in metallic conductors. 
