The capacitance of an isolated sphere of radius $r_1$ is increased by 5 times, when it is enclosed by an earthed concentric sphere of radius $r_2$. The ratio of their radii is

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Aicharya · Accepted Answer

$\begin{aligned} & 	ext { } \mathrm{C}_2=5 \mathrm{C}_1 \ & \Rightarrow 4 \pi \varepsilon_0\left(\frac{\mathrm{r}_1 r_2}{\mathrm{r}_2-\mathrm{r}_1}ight)=5\left(4 \pi \varepsilon_0 \mathrm{r}_1ight) \ & \Rightarrow \mathrm{r}_1 \mathrm{r}_2=5 \mathrm{r}_1 \mathrm{r}_2-5 \mathrm{r}_1^2 \ & \Rightarrow 5 \mathrm{r}_1^2=4 \mathrm{r}_1 \mathrm{r}_2 \ & 	herefore \frac{\mathrm{r}_1}{\mathrm{r}_2}=\frac{4}{5}\end{aligned}$

The capacitance of an isolated sphere of radius $r_1$ is increased by 5 times, when it is enclosed by an…

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