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Two concentric hollow metallic spheres of radii $r_1$ and $r_2 (r_1 > r_2)$ contain charges $q_1$ and $q_2$ respectively. The potential at a distance $x$ between $r_1$ and $r_2$ will be
$\frac{{{q_1} + {q_2}}}{{4\pi {\varepsilon _0}x}}$
$\frac{{{q_1}}}{{4\pi {\varepsilon _0}{r_1}}} + \frac{{{q_2}}}{{4\pi {\varepsilon _0}{r_2}}}$
$\frac{{{q_1}}}{{4\pi {\varepsilon _0}x}} + \frac{{{q_2}}}{{4\pi {\varepsilon _0}{r_2}}}$
$\frac{{{q_1}}}{{4\pi {\varepsilon _0}{r_1}}} + \frac{{{q_2}}}{{4\pi {\varepsilon _0}x}}$
Solution
Potential at $\mathrm{P}$ due to $\mathrm{A}$ is
$\mathrm{V}_{1}=\frac{\mathrm{q}_{1}}{4 \pi \varepsilon_{0} \mathrm{r}_{1}}$
and due to $\mathrm{B}$ is
$\mathrm{V}_{2}=\frac{\mathrm{q}_{2}}{4 \pi \varepsilon_{0} \mathrm{x}}$
Net potential at $\mathrm{P}$
$\mathrm{V}=\mathrm{V}_{1}+\mathrm{V}_{2}=\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{\mathrm{q}_{2}}{\mathrm{X}}+\frac{\mathrm{q}_{1}}{\mathrm{r}_{1}}\right)$
