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Three concentric metallic shells A, B and C of radii $a, b$ and $c(a < b < c)$ have surface charge densities $+\sigma,-\sigma$ and $+\sigma$ respectively. The potential of shell B is
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The correct answer is:
$\left(\frac{a^2}{b}-b+c\right) \frac{\sigma}{e_0}$
$V_b=V_{A, b}+V_{B, b}+V_{C, b}$
$=\frac{K \sigma 4 \pi a^2}{b}-\frac{K \sigma 4 \pi b^2}{b}+\frac{K \sigma 4 \pi c^2}{c}$
$=\frac{\sigma}{\varepsilon_0}\left(\frac{a^2}{b}-b+c\right)$
$=\frac{K \sigma 4 \pi a^2}{b}-\frac{K \sigma 4 \pi b^2}{b}+\frac{K \sigma 4 \pi c^2}{c}$
$=\frac{\sigma}{\varepsilon_0}\left(\frac{a^2}{b}-b+c\right)$
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