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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 $5 \times 10^{7} {Vm}^{- 1}$ . The minimum radius of the spherical shell required is:

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3 m

2 m

1.5 m

1 m

answer is D.

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Detailed Solution

Here, $V = 15 \times 10^{6} V, dielectric strength = 5 \times 10^{7} {Vm}^{- 1}$

Maximum electric field = 10% of dielectric strength

$∴ E = \frac{10}{100} \times 5 \times 10^{7} = 5 \times 10^{6} {Vm}^{- 1}$

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

$\Rightarrow r = \frac{V}{E} = \frac{15 \times 10^{6}}{5 \times 10^{6}} = 3 m$

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