Electrostatics

JEE Main level, single correct, medium

233 of 311

Question 233 of 311

A thin spherical conducting shell of radius R\mathrm{R} has a charge q\mathrm{q}. Another charge Q\mathrm{Q} is placed at the centre of the shell. The electrostatic potential at a point P\mathrm{P} a distance R2\frac{\mathrm{R}}{2} from the centre of the shell is

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Answer: (C) 2Q4πε0R+q4πε0R\frac{2 Q}{4 \pi \varepsilon_0 R}+\frac{q}{4 \pi \varepsilon_0 R}

Potential due to spherical shell, v1=q4πε0R\mathrm{v}_1=\frac{\mathrm{q}}{4 \pi \varepsilon_0 \mathrm{R}}. Potential difference due to charge at the centre
V2=2Q4πε0r;V=V1+V2=2Q4πε0R+q4πε0R\mathrm{V}_2=\frac{2 \mathrm{Q}}{4 \pi \varepsilon_0 r} ; \mathrm{V}=\mathrm{V}_1+\mathrm{V}_2=\frac{2 \mathrm{Q}}{4 \pi \varepsilon_0 \mathrm{R}}+\frac{\mathrm{q}}{4 \pi \varepsilon_0 \mathrm{R}}

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