Question

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 :

• A. $\frac{\sigma }{{\epsilon }_0}\left[\frac{a^2-b^2}{a}+c\right]$
• B. $\frac{\sigma }{{\epsilon }_0}\left[\frac{a^2-b^2}{b}+c\right]$
• C. $\frac{\sigma }{{\epsilon }_0}\left[\frac{b^2-c^2}{b}+c\right]$
• D. $\frac{\sigma }{{\epsilon }_0}\left[\frac{b^2-c^2}{c}+c\right]$

Answer 1

Answer: (B)

$V_B=\left[\frac{\sigma 4\pi a^2}{4\pi {\epsilon }_{0}b}-\frac{\sigma 4\pi b^2}{4\pi {\epsilon }_{0}b}+\frac{\sigma 4\pi c^2}{4\pi {\epsilon }_{0}c}\right]$
$V_B=\frac{\sigma }{{\epsilon }_0}\left[\frac{a^2-b^2}{b}+c\right]$