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# Three concentric metal shells A ,

Question:

Three concentric metal shells $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ of respective radii $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}(\mathrm{a}<\mathrm{b}<\mathrm{c})$ have surface charge densities $+\sigma,-\sigma$ and $+\sigma$ respectively. The potential of shell B is :-

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

2. $\frac{\sigma}{\varepsilon_{0}}\left[\frac{\mathrm{b}^{2}-\mathrm{c}^{2}}{\mathrm{~b}}+\mathrm{a}\right]$

3. $\frac{\sigma}{\varepsilon_{0}}\left[\frac{\mathrm{b}^{2}-\mathrm{c}^{2}}{\mathrm{c}}+\mathrm{a}\right]$

4. $\frac{\sigma}{\varepsilon_{0}}\left[\frac{\mathrm{a}^{2}-\mathrm{b}^{2}}{\mathrm{a}}+\mathrm{c}\right]$

Correct Option: 1

Solution: