Two concentric spheres of radii $\mathrm{R}$ and $\mathrm{r}$ have similar charges with equal surface charge densities $(\sigma)$. What is the electric potential at their common centre ?

Question

Aicharya · Accepted Answer

Charge on the outer sphere $=q_{1}=4 \pi R^{2} \sigma$ Charge on the inner sphere $=q_{2}=4 \pi r^{2} \sigma$ $\mathrm{v}=\frac{1}{4 \pi \in_{0}} \frac{\mathrm{q}_{1}}{\mathrm{R}}+\frac{1}{4 \pi \epsilon_{0}} \frac{\mathrm{q}_{2}}{\mathrm{r}}$
$=\frac{1}{4 \pi \epsilon_{0}}\left[\frac{4 \pi \mathrm{R}^{2} \sigma}{\mathrm{R}}+\frac{4 \pi \mathrm{r}^{2} \sigma}{\mathrm{r}}\right]$
$=\frac{4 \pi \sigma}{4 \pi \epsilon_{0}}(\mathrm{R}+\mathrm{r})=\frac{\sigma}{\epsilon_{0}}(\mathrm{R}+\mathrm{r})$

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Two concentric spheres of radii $\mathrm{R}$ and $\mathrm{r}$ have similar charges with equal surface charge…

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