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

Answer 1

The correct option is D $\frac{\sigma }{{\epsilon }_0}[\frac{a^2-b^2}{b}+c]$


$V_B=\frac{1}{4\pi {\epsilon }_0}\frac{4\pi a^2\sigma }{b}-\frac{1}{4\pi {\epsilon }_0}\frac{4\pi b^2\sigma }{b}+\frac{1}{4\pi {\epsilon }_0}\frac{4\pi c^2\sigma }{c}$
$=\frac{\sigma }{{\epsilon }_0}(\frac{a^2-b^2}{b}+c)$