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

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15 cm

30 cm

30 m

15 m

answer is B.

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Detailed Solution

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

Maximum electric field, E=10% of dielectric strength

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

As we know,

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

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