Two insulated charged conducting spheres of radii $20 \text{ cm}$ and $15 \text{ cm}$ respectively and having an equal charge of 10 C are connected by a copper wire and then they are separated. Then
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After redistribution, charges on them will be different, but they will acquire common potential
i.e. $k \frac{Q_1}{r_1} = k \frac{Q_2}{r_2}$ ⇒ ⇒ $\frac{Q_1}{Q_2} = \frac{r_1}{r_2}$
As $\sigma = \frac{Q}{4 \pi r^{2}}$ ⇒ ⇒ $\frac{\sigma_1}{\sigma_2} = \frac{Q_1}{Q_2} \times \frac{r_2^2}{r_1^2}$ ⇒ ⇒ $\frac{\sigma_1}{\sigma_2} = \frac{r_2}{r_1}$ ⇒ ⇒ $\sigma \propto \frac{1}{r}$
i.e. surface charge density on smaller sphere will be more.
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