Three concentric metallic shells A, B and C o | vedclass

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(D) The potential at the surface of shell $B$ is the sum of potentials due to all three shells $A, B$ and $C$.$V_B = V_{A,B} + V_{B,B} + V_{C,B}$Since

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$\left(\frac{a^2}{b}-b+c\right) \frac{\sigma}{\varepsilon_0}$

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(D) The potential at the surface of shell $B$ is the sum of potentials due to all three shells $A, B$ and $C$.$V_B = V_{A,B} + V_{B,B} + V_{C,B}$Since the potential inside a shell is constant and equal to the potential at its surface, we have:$V_{A,B} = \frac{k Q_A}{b} = \frac{1}{4\pi\varepsilon_0} \frac{\sigma(4\pi a^2)}{b} = \frac{\sigma a^2}{\varepsilon_0 b}$$V_{B,B} = \frac{k Q_B}{b} = \frac{1}{4\pi\varepsilon_0} \frac{-\sigma(4\pi b^2)}{b} = -\frac{\sigma b}{\varepsilon_0}$$V_{C,B} = \frac{k Q_C}{c} = \frac{1}{4\pi\varepsilon_0} \frac{\sigma(4\pi c^2)}{c} = \frac{\sigma c}{\varepsilon_0}$Adding these, we get:$V_B = \frac{\sigma a^2}{\varepsilon_0 b} - \frac{\sigma b}{\varepsilon_0} + \frac{\sigma c}{\varepsilon_0} = \frac{\sigma}{\varepsilon_0} \left( \frac{a^2}{b} - b + c \right)$

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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