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Three concentric metal shells $A, B$ and $C$ of respective radii $a, b$ and $c (a < b < c)$ have surface charge densities $+\sigma,-\sigma$ and $+\sigma$ respectively. The potential of shell $B$ is
$\frac{\sigma}{\epsilon_0} \left[ {\frac{a^2-b^2}{b}+c} \right ]$
$\frac{\sigma}{\epsilon_0} \left[ {\frac{b^2-c^2}{b}+a} \right ]$
$\frac{\sigma}{\epsilon_0} \left[ {\frac{b^2-c^2}{c}+a} \right ]$
$\frac{\sigma}{\epsilon_0} \left[ {\frac{a^2-b^2}{a}+c} \right ]$
Solution
Potential outside the shell, $V_{outside}$ $=\frac{\mathrm{KQ}}{\mathrm{r}}$
where $\mathrm{r}$ is distance of point from the centre of shel Potential inside the shell, $V_{\text {inside }}=\frac{K Q}{R}$
where $'R"$ is radius of the shell
$\mathrm{V}_{\mathrm{B}}=\frac{\mathrm{Kq}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{b}}}+\frac{\mathrm{Kq}_{\mathrm{B}}}{\mathrm{r}_{\mathrm{b}}}+\frac{\mathrm{Kq}_{\mathrm{C}}}{\mathrm{r}_{\mathrm{c}}}$
$\mathrm{V}_{\mathrm{B}}=\frac{1}{4 \pi \epsilon_{0}}\left[\frac{\sigma 4 \pi \mathrm{a}^{2}}{\mathrm{b}}-\frac{\sigma 4 \pi \mathrm{b}^{2}}{\mathrm{b}}+\frac{\sigma 4 \pi \mathrm{c}^{2}}{\mathrm{c}}\right]$
$V_{B}=\frac{\sigma}{\epsilon_{0}}\left[\frac{a^{2}-b^{2}}{b}+c\right]$
