Question

In a Van de graaf type genertor a sphrical metal shell is to be a `15xx10^(6)` volt electrode. The dielectric strength of the gas surrounding the elctrode 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.]

Answer 1

Here, `V = 15xx10^(6) vol t`, Dielectric strength `= 5xx10^(7) Vm^(-1)`, Minimum radius, `r = ?`
Max. electric field, `E = 10%` dielectric strength
`E = (10)/(100) xx5xx10^(7) = 5xx10^(6) Vm^(-1)`,
As `E = (V)/(r ) :. r = (V)/(E) = (15xx10^(6))/(5xx10^(6)) = 3m`
Obviously, we cannot build an electrostatic generator, using a very small sheet.