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

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150 cm

50 cm

30 cm

3 m

answer is C.

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Detailed Solution

$E_{\max} = k_{0} \frac{q}{R_{\min}^{2}}$ ; $V = k_{0} \frac{q}{R_{m}}$

$\frac{E_{\max}}{V} = \frac{1}{R_{\min}}$

$R_{\min} = \frac{V}{E_{\max}} = \frac{15 \times 10^{6}}{5 \times 10^{7}} = 0.3 m$

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