In a Van de Graaff type generator, a spherical metal shell is to be a `15 xx 10^6V` electrode. The dielectric strength of the gas surrounding the electrode is `5 xx 10^7 Vm^(-1)`. What is the minimum radius of the spherical shell required? (You will learn from this exercise why one cannot build an electrostatic generator using a very small shell which requires a small charge to acquire a high potential.)

Explanation

`V=15 xx 10^(6)V, E=5 xx 10^(7) Vm^(-1) " "r=?, E=V/r`
`r=V/E=(15 xx 10^(6))/(5 xx 10^(7))=0.3m`