In a Van de Graaff type generator, a spherical metal shell is to be `15xx10^(6)V` electrode. The dielectric strength of the gas surrounding the electrode is `5xx10^(7)Vm^(-1).` The minimum radius of the spherical shell required is

Options

A. 0.1 m
B. 0.2 m
C. 0.5 m
D. 0.3 m

Answer

D

Explanation

Here, `V = 15 xx 10^(6) V`, dielectric strenght ` = 5 xx 10^(7) V m^(-1)`
Maximun electric field , E = 10% of dielectric strength
`therefore E = (10)/(100) xx 5xx 10^(7) = 5 xx 10^(6) V m^(-1)` As `E = (V)/(r)`
`therefore r = (V)/(E) = (15 xx 10^(6))/(5xx10^(6)) = 3m `