Question

In a Van de Graaff type generator, a spherical metal shell is to be $15\times {10}^{6}V$ electrode. The dielectric strength of the gas surrounding the electrode is $5\times {10}^{7}V{m}^{-1}$. The minimum radius of the spherical shell required is :

• A. $1m$
• B. $2m$
• C. $1.5m$
• D. $3m$

Answer 1

Answer: (D)

$3m$

Here $V=15\times {10}^{6}V$
Maximum electric field, $E=10$% of dielectric strength
$\therefore E=\frac{10}{100}\times 5\times {10}^7=5\times {10}^{6}V{m}^{-1}$
As we know,
$E=\frac{V}{r}$
$\therefore r=\frac{V}{E}=\frac{15\times {10}^6}{5\times {10}^6}$
$\Rightarrow r=3m$
Hence the correct option is $\left(D\right)$