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

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

\(\mathrm{V}_{\mathrm{B}}=\frac{\mathrm{Kq}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{b}}}+\frac{\mathrm{Kq}_{\mathrm{B}}}{\mathrm{r}_{\mathrm{b}}}+\frac{\mathrm{Kq}_{\mathrm{C}}}{\mathrm{r}_{\mathrm{c}}}\)

\(\mathrm{V}_{\mathrm{B}}=\frac{1}{4 \pi \epsilon_{0}}\left[\frac{\sigma 4 \pi \mathrm{a}^{2}}{\mathrm{b}}-\frac{\sigma 4 \pi \mathrm{b}^{2}}{\mathrm{b}}+\frac{\sigma 4 \pi \mathrm{c}^{2}}{\mathrm{c}}\right]\)

\(V_{B}=\frac{\sigma}{\epsilon_{0}}\left[\frac{a^{2}-b^{2}}{b}+c\right]\)