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}{ \varepsilon_{0}} \left[\frac{a^{2} -b^{2}}{a} + c\right] $
• B. $\frac{\sigma}{ \varepsilon_{0}} \left[\frac{a^{2} -b^{2}}{b} + c\right] $
• C. $\frac{\sigma}{ \varepsilon_{0}} \left[\frac{b^{2} - c^{2}}{b} + c\right] $
• D. $\frac{\sigma}{ \varepsilon_{0}} \left[\frac{b^{2} - c^{2}}{c} + c\right] $

Answer 1

Answer: (B)

$V_{B}=\left[\frac{\sigma 4 \pi a^{2}}{4 \pi \varepsilon_{0} b}-\frac{\sigma 4 \pi b^{2}}{4 \pi \varepsilon_{0} b}+\frac{\sigma 4 \pi c^{2}}{4 \pi \varepsilon_{0} c}\right]$
$V_{B}=\frac{\sigma}{\varepsilon_{0}}\left[\frac{a^{2}-b^{2}}{b}+c\right]$