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A metal sphere of radius $R$ carrying charge $q$ is surrounded by a thick concentric metal shell of inner and outer radii a and $\mathrm{b}$ respectively. The net charge on the shell is zero. The potential at the centre of the sphere, when the outer surface of the shell is grounded will be
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The correct answer is:
$\frac{\mathrm{q}}{4 \pi \epsilon_{0}}\left(\frac{1}{\mathrm{R}}-\frac{1}{\mathrm{a}}\right)$
\(V_{A}=V_{B}+V_{C}+V_{c}\)
\(V_{c}=\frac{1}{4 x \varepsilon_{0}}\left(\frac{-q}{a}\right)+\frac{1}{4 x \varepsilon_{0}}\left(\frac{q}{R}\right)+0\)
\(=\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{q}{R}-\frac{q}{a}\right)\)
\(=\frac{2}{4 \pi \varepsilon 0}\left[\frac{1}{R}-\frac{1}{a}\right]\)
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