In a Van de Graff type generator a spherical metal shell is to be a `15xx10^6V ` electrode. The dielectric strength of the gas surrounding the electrode is `5xx10^7Vm^-1`. What is the minimum radius of the spherical shell required ? (You will learn from this excerise why one cannot build and electrostatic generator using a very small shell which requires a small charge to acquire a high potential. )

Explanation

Here `V=15xx10^6"volt"`
Dielectric strength `=5xx10^-7Vm^-1`
minimum rodius , `r=?`
`E=(10)/(100) xx5xx10^7=5xx10^6VM^-1`
As `E=(V)/(r)therefore r=(V)/(E)=(15xx10^6)/(5xx10^6)=3m`
obviously we cannot build an electrostatic generator , using a very small shell .