Physics - Electrostatics Question with Solution | TestHub

Let $q_1$ and $q_2$ be charge on two spheres of radius ' $r$ ' and ' $R$ ' respectively As, $q_1+q_2=\mathrm{Q}$ and ${\sigma }_1={\sigma }_2$ [Surface charge density are equal] $$\therefore \frac{q_1}{r\pi r^2}=\frac{q_2}{4\pi R^2}$$ So, $q_1=\frac{Q{r}^2}{R^2+r^2}$ and $q_2=\frac{Q{R}^2}{R^2+r^2}$ Now, potential, $V=\frac{1}{4\pi {\epsilon }_0}\left[\frac{q_1}{r}+\frac{q_2}{R}\right]$ $$\begin{array}{rl}& =\frac{1}{4\pi {\epsilon }_0}\left[\frac{Qr}{R^2+r^2}+\frac{QR}{R^2+r^2}\right]\\ & =\frac{Q(R+r)}{R^2+r^2}\frac{1}{4\pi {\epsilon }_0}\end{array}$$