Three concentric metallic spherical shells A, | vedclass

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(C) The charges on the shells are given by $q = 	ext{surface charge density} 	imes 	ext{area}$.For shell $A$ (radius $a$): $q_A = -\sigma(4\pi a^2)

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$(\sigma/\varepsilon_0) [b - a - c]$

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(C) The charges on the shells are given by $q = 	ext{surface charge density} 	imes 	ext{area}$.For shell $A$ (radius $a$): $q_A = -\sigma(4\pi a^2)$.For shell $B$ (radius $b$): $q_B = +\sigma(4\pi b^2)$.For shell $C$ (radius $c$): $q_C = -\sigma(4\pi c^2)$.The potential at the surface of shell $A$ is the sum of potentials due to all three shells:$V_A = V_{A,A} + V_{A,B} + V_{A,C} = \frac{1}{4\pi\varepsilon_0} [\frac{q_A}{a} + \frac{q_B}{b} + \frac{q_C}{c}]$.Substituting the values:$V_A = \frac{1}{4\pi\varepsilon_0} [\frac{-\sigma(4\pi a^2)}{a} + \frac{\sigma(4\pi b^2)}{b} + \frac{-\sigma(4\pi c^2)}{c}]$.$V_A = \frac{1}{4\pi\varepsilon_0} [-\sigma(4\pi a) + \sigma(4\pi b) - \sigma(4\pi c)]$.$V_A = \frac{\sigma}{\varepsilon_0} [-a + b - c] = \frac{\sigma}{\varepsilon_0} [b - a - c]$.

Three concentric metallic spherical 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 $A$ is:

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