Question

A charge is distributed over two concentric hollow spheres of radii $R$ and $r$, where $R>r$, such that the surface densities of charges are equal $\left(\sigma \right)$. What is the potential at their common centre?

• A. $\frac{\sigma }{{\epsilon }_0}(R+r)$
• B. $\frac{{\epsilon }_0}{\sigma }(R+r)$
• C. $\frac{\sigma }{{\epsilon }_0}R$
• D. $\frac{\sigma }{{\epsilon }_0}r$

Answer 1

The correct option is A $\frac{\sigma }{{\epsilon }_0}(R+r)$

We know potential inside a hollow sphere to be

$V=\frac{Q}{4\pi {ϵ}_{0}R}=\frac{\sigma R}{{ϵ}_0}$

Thus, potential at the common centre of both the spheres

$V_{total}=V_1+V_2$

$V_{total}=\frac{\sigma \cdot R}{{ϵ}_0}+\frac{\sigma \cdot r}{{ϵ}_0}$

$=\frac{\sigma }{{ϵ}_0}(R+r)$