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1) It is known that inside a metallic hollow sphere it will not experience outside electric field because of the charge separation of electrons and holes at the surface of sphere and creating an equal and opposite field. So it is better to stay inside the car during lightning.

Why stay in the car during thunderstorms?

But isn't there a maximum value of electric field the metallic surface can resist because at some point (higher value) of electric field the movement of electrons will get stopped because it can't generate more electron holes pairs and which will limit the further change in increment of electric field to zero. Since lighting produce such a high value of electric field is it safe to stay inside a car during lightning? assuming no heat generated during lightning

2) Similar case about charge inside a earthed metallic hollow sphere. If I keep some charge inside the metallic hollow sphere, outside field is zero and inside field is dependent upon the charge. If I increase the charge inside the metallic hollow sphere to such a level which is more than the total electron charge on the surface of sphere then the earthing has no effect because it has already neutralized the maximum amount of holes (+ve) by accepting the electrons from earth. So the field will escape outside.

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When lightning strikes a car, it is not simply charge separation that protects the occupants; the conductive skin provides a preferential path for a current. If the charge were to simply be deposited on the skin of the car, something exciting might happen, but in fact the charge is carried through the car to the ground. It is definitely possible to apply a large enough current that ordinary conduction no longer occurs, but this isn't because the metal skin runs out of electron/hole pairs -- it's because the skin heats up and vaporizes!

Your premise for part 2 isn't quite correct. If you stick an electron inside a neutral, conductive sphere, you can still see the charge outside the sphere. If the sphere is grounded, then you will not, but that's because you've essentially hidden the charge on the ground and given the sphere an opposing charge.

Conductive shells shield their contents from external fields, but they do not shield the external environment from the charges of their contents.

If you add charge, grounding will continue to cancel your fields. If you increase the charge rapidly, then you can gain a momentary field, but currents will eventually cancel the charge accumulation. (Essentially, you are charging a capacitor, which is leaky because of connection to the ground.)

To return to the question you posed in part 1; what happens if we apply a slowly increasing field to a hollow conductive sphere that is perfectly insulated from ground? At first, polarization will shield the interior of the sphere from the external electric field. The conduction electrons will flow to create a polarization across the sphere. Eventually, however, the material will breakdown.

Exactly how is a matter of conjecture, on my part. Because the sphere will polarize, with electrons accumulating on one side and bare ion lattice on the other, I hypothesize that the ends of the sphere will begin to smear out perpendicular to the electric field. The electric field balances the repulsion between like species along the electric field, but not across it. Therefore, the ends of the sphere will experience a shear that thins them and breaks them. These broken pieces, being charged, then fly along the electric field at colossal speeds, allowing electric field into the erstwhile interior, and badly damaging your lab.

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