• # question_answer Two concentric spheres of radii R and r have similar charges with equal surface densities $(\sigma ).$What is the electric potential at their common center? A) $\frac{\sigma }{{{\varepsilon }_{0}}}$                              B) $\frac{\sigma }{{{\varepsilon }_{0}}}(R-r)$C)  $\frac{\sigma }{{{\varepsilon }_{0}}}(R+r)$                    D)  None of the above.

Let Q and q be the charges on the spheres. The potential at the common center will be $V=\frac{1}{4\pi {{\varepsilon }_{0}}}\times \frac{Q}{R}+\frac{1}{4\pi {{\varepsilon }_{0}}}\times \frac{q}{r}$ $=\frac{1}{{{\varepsilon }_{0}}}\left[ \frac{Q}{4\pi {{R}^{2}}}\times R+\frac{q}{4\pi {{r}^{2}}}\times r \right]$ But $\frac{Q}{4\pi {{R}^{2}}}=\frac{q}{4\pi {{R}^{2}}}=\sigma$ $\therefore$$V=\frac{1}{{{\varepsilon }_{0}}}[\sigma R+\sigma r]=\frac{\sigma }{{{\varepsilon }_{0}}}(R+r)$ Hence, the correction option is [c].