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In a Van de Graaff type generator a spherical metal shell is to be a $15 \times 10^{6} \vee$ electrode. The dielectric strength of the gas surrounding the electrode is $5 \times 10^{7} \mathrm{Vm}^{-1}$. What is the minimum radius of the spherical shell required? (You will learn from this exercise why one cannot build an electrostatic generator using a very small shell which requires a small charge to acquire a high potential.)
In a Van de Graaff type generator a spherical metal shell is to be a $15 \times 10^{6} \vee$ electrode. The dielectric strength of the gas surrounding the electrode is $5 \times 10^{7} \mathrm{Vm}^{-1}$. What is the minimum radius of the spherical shell required? (You will learn from this exercise why one cannot build an electrostatic generator using a very small shell which requires a small charge to acquire a high potential.)
Physics | Previous Year Question Papers
In a Van de Graaff type generator a spherical metal shell is to be a $15 \times 10^{6} \vee$ electrode. The dielectric strength of the gas surrounding the electrode is $5 \times 10^{7} \mathrm{Vm}^{-1}$. What is the minimum radius of the spherical shell required? (You will learn from this exercise why one cannot build an electrostatic generator using a very small shell which requires a small charge to acquire a high potential.)

Ans: Given that,
Potential difference is given as, $V=15 \times 10^{6} \mathrm{~V}$
Dielectric strength of the surrounding gas $=5 \times 10^{\top} \mathrm{Vm}^{-1}$
Electric field intensity is given as, $E=$ Dielectric strength $=5 \times 10^{7} \mathrm{~V} \mathrm{~m}^{-1}$
Minimum radius of the spherical shell required for the purpose is given by,
$$
\begin{array}{l}
r=\frac{V}{E} \\
\Rightarrow r=\frac{15 \times 10^{6}}{5 \times 10^{7}} \\
\Rightarrow r=0.3 \mathrm{~m}=30 \mathrm{~cm}
\end{array}
$$

i

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