A) \[\frac{\sigma }{{{\in }_{0}}}\times \frac{{{r}_{1}}}{{{r}_{2}}}\]
B) \[\frac{\sigma }{{{\in }_{0}}}\times \frac{{{r}_{2}}}{{{r}_{1}}}\]
C) \[\frac{\sigma }{{{\in }_{0}}}({{r}_{1}}-{{r}_{2}})\]
D) \[\frac{\sigma }{{{\in }_{0}}}({{r}_{1}}+{{r}_{2}})\]
Correct Answer: D
Solution :
Electric potential at common centre is, \[v=\frac{{{q}_{1}}}{4\pi {{\in }_{0}}{{r}_{1}}}+\frac{{{q}_{2}}}{4\pi {{\in }_{0}}{{r}_{2}}}\] \[V=\frac{\sigma }{{{\in }_{0}}}{{r}_{1}}+\frac{\sigma }{{{\in }_{0}}}\times {{r}_{2}}=\frac{\sigma }{{{\in }_{0}}}[{{r}_{1}}+{{r}_{2}}]\]\[\left[ \begin{align} & \therefore {{q}_{1}}=4\pi r_{1}^{2}\times \sigma \\ & {{q}_{1}}=4\pi r_{2}^{2}\times \sigma \\ \end{align} \right]\]
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