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NCERT Class XII Chapter
Electrostatic Potential and Capacitance
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Question : 35 of 37
Marks: +1, -0
In a Van-de-Graff type generator, a spherical metal shell is to be a 15 × 10610^6 V electrode. The dielectric strength of the gas surrounding the electrode is 5 × 107 V m−1m^{-1}. What is the minimum radius of the spherical shel l required?
Solution:  
V = 15 × 10610^6 V , E = 5 × 107Vm−110^7 \mathrm{V} \mathrm{m}^{-1}
As V = 14πϵ0qR\frac{1}{4\pi\epsilon_0} \frac{q}{R} and E = 14πϵ0qR2\frac{1}{4\pi\epsilon_0} \frac{q}{R^2}
R = VE\frac{V}{E} = 15×1065×107\frac{15 \times 10^6}{5 \times 10^7} = 3 × 10−110^{-1} m or R = 0.3 m = 30 cm
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