Question

Three concentric metallic spherical shells $A,B$ and $C$ having radii $a,b$ and $c(a<b<c)$ has surface charge densities $-\sigma ,+\sigma$ and $-\sigma$ respectively. The potential of shell $A$ is

• A. Zero
• B. $\frac{\sigma }{{ϵ}_0}(a-b+c)$
• C. $\frac{\sigma }{{ϵ}_0}(b-a-c)$
• D. $\frac{\sigma }{{ϵ}_0}(a+b-c)$

Answer 1

The correct option is C $\frac{\sigma }{{ϵ}_0}(b-a-c)$


The potential of shell $A$ is,

$V=V_A+V_B+V_C$

$V=\frac{1}{4\pi {ϵ}_0}(\frac{q_A}{a}+\frac{q_B}{b}+\frac{q_C}{c})...\left(1\right)$

$\because q_A=-\sigma 4\pi a^2,q_B=\sigma 4\pi b^2$ and $q_C=-\sigma 4\pi c^2,$

Putting the values of $q_A,q_B$ and $q_C$ in $\left(1\right)$, we get,

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

$=\frac{\sigma }{{ϵ}_0}(-a+b-c)$

$\therefore V=\frac{\sigma }{{ϵ}_0}(b-a-c)$
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