Van de Graaff generator consists of a hollow metal sphere of diameter 2 m. If the potential on the surface of

Question 84 of 122

Q. Van de Graaff generator consists of a hollow metal sphere of diameter 2 m. If the potential on the surface of the sphere is 6 million volt, the charge accumulated over the surface of the sphere is :

(a) 0.66 milli coulomb

(b) 1 coulomb

(d) 0.33 micro coulomb

Puducherry TnboardTamil Nadu HSC (DGE) Board 2018MCQ· 1mImportance★★★★★

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The charge accumulated on the Van de Graaff sphere works out to about 0.66 millicoulomb.

A charged conducting sphere of radius $R$ carrying charge $Q$ has a surface potential $V = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{R} = \dfrac{kQ}{R}$ , where $k = 9\times10^9\ N\,m^2\,C^{-2}$ .

Given: diameter $=2\,m \Rightarrow R = 1\,m$ ; $V = 6\times10^6\,V$ .

$Q = \dfrac{VR}{k} = \dfrac{(6\times10^6)(1)}{9\times10^9} = 6.67\times10^{-4}\,C = 0.667\ \text{milli coulomb} \approx 0.66\ \text{milli coulomb}$

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Q.Van de Graaff generator consists of a hollow metal sphere of diameter 2 m. If the potential on the surface of the sphere is 6 million volt, the charge accumulated over the surface of the sphere is :

Concept understanding — Van de Graaff Generator

Q.Van de Graaff generator consists of a hollow metal sphere of diameter 2 m. If the potential on the surface of the sphere is 6 million volt, the charge accumulated over the surface of the sphere is :

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