In a Van de graaf type generator a spherical metal shell is to be a `15xx10^(6)` volt electrode. The dielectric strength of the gas surrounding the electrode is `5xx10^(7) Vm^(-1). ` What is the minimum radius of the spherical shell required ?
[you will learn form 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

potential difference , `V=15xx10^(6) V`
Dielectric strength of the surrounding gas `=5xx10^(7) V//m`
Electric field intensity, E=dielectric strength =`5xx10^(7)V//m`
Minimum radius of the spherical shell require for the purpose is given by
`r=V/E`
`=(15xx10^(6))/(5xx10^(7))=0.3 m =30 cm `
Hence, the minimum radius of the spherical required is 30 cm .