What Factors Affect the Maximum Potential of a Van de Graaff Generator?

[Shreyas Shree]

What determines the maximum potential to which the dome of a Van de Graaff generator can be raised?
on one hand i have the equation V=1/4πε q/r then there V∝1/r
whereas on the other hand the natural tendency for positive charge is to move higher to lower potential. Thus, provided we are somehow able to introduce the small charged sphere into the larger one, we can in this way pile up larger and larger amount of charge on the latter. The potential of the outer sphere would also keep rising, at least until it reaches the breakdown field of air.

 

[stedwards]

That's right, the theoretical stress limit is classically infinite for vacuum. For air it is typically given as 30 KV/cm with the relative humidity left ambiguous, the last I looked.

Perhaps you could find practical values for air as a function of pressure and humidity on the internet. As the pressure increases the electric field stress limit also increases. Also, dry air supports greater electric field strength.