Browse Questions

# Three concentric spherical metallic shells A , B and C of radii a ,b and c $\;(c > b> a)\;$ have charge densities $\;\sigma , - \sigma \;and\; \sigma\;$ respectively . The potential of shell B is

$(a)\;(a+b+c)\;\large\frac{\sigma}{\in_{0}}\qquad(b)\;(\large\frac{a^2}{b}-b+c)\;\large\frac{\sigma}{\in_{0}}\qquad(c)\;(\large\frac{a^2}{c}-\large\frac{b^2}{c}+c)\;\large\frac{\sigma}{\in_{0}}\;\qquad(d)\;\large\frac{\sigma\; c }{\in_{0}}$

Answer : (b) $\;(\large\frac{a^2}{b}-b+c)\;\large\frac{\sigma}{\in_{0}}$
Explanation :
$V_{B}=\large\frac{k\;\sigma\;4\;\pi\;a^2}{b}-\large\frac{k\;\sigma\;4\;\pi\;b^2}{b}+\large\frac{k\;\sigma\;4\;\pi\;c^2}{c}$
$V_{B}=\large\frac{1\times\sigma\times 4 \pi}{4\;\pi\;\in_{0}}\;(\large\frac{a^2}{b}-b+c)$
$V_{B}=(\large\frac{a^2}{b}-b+c)\;\large\frac{\sigma}{\in_{0}}\;.$