Question

In a van de Graaff generator, a spherical metal shell is to be a $15\times {10}^{6}V$ electrode . The dielectric strength of the gas surronding the electrode is $5\times {10}^{6}V/m$. What is the minimum radius of the spherical shell required?

Answer 1

Here $V=15\times {10}^{6}V$

Maximum electric field, $E=10$% of dielectric strength

$\therefore E=\frac{10}{100}\times 5\times {10}^6=5\times {10}^{5}V{m}^{-1}$

As we know,

$E=\frac{V}{r}$

$\therefore r=\frac{V}{E}=\frac{15\times {10}^6}{5\times {10}^5}$

$\Rightarrow r=30m$