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Question
Is there any restriction on the upper limit of the high voltage set up in Van de Graff generator machine? Explain.
Solution
The main limiting factor on the value of high potential is the radii of sphere.
If the electric field just outside the sphere is sufficient for dielectric breakdown of air, no more charge can be transferred to it.
For a conducting sphere,
Electric field just outside sphere
`E = Q/(4pi in_0R^2)`
and electric potential
`V = Q/(4piin_0R)`
Thus, E = VR
Now, for E = 3 × 106 V/m (dielectric breakdown)
Radius of should be 1 m.
Thus, the maximum potential of a sphere of radius 1 m would be 3 × 106V.
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