Question

Two concentric spheres of radii $r_1$ and $r_2$ carry charges $q_1$ and $q_2$ respectively. If the surface charge density $\left(\sigma \right)$ is the same for both the spheres, the electric potential at the common centre will be

• A. $\frac{\sigma }{{ϵ}_0}\times \frac{r_1}{r_2}$
• B. $\frac{\sigma }{{ϵ}_0}\times \frac{r_2}{r_1}$
• C. $\frac{\sigma }{{ϵ}_0}(r_1-r_2)$
• D. $\frac{\sigma }{{ϵ}_0}(r_1+r_2)$

Answer 1

The correct option is D $\frac{\sigma }{{ϵ}_0}(r_1+r_2)$

Electric potential of the common centre, is
$V=\frac{q_1}{4\pi {ϵ}_0{r}_1}+V=\frac{q_1}{4\pi {ϵ}_0{r}_2}$
$\Rightarrow V=\frac{\sigma }{{ϵ}_0}\times r_1+\frac{\sigma }{{ϵ}_0}\times r_2=\frac{\sigma }{{ϵ}_0}[r_1+r_2]$
$\left[\begin{array}{ccc}\because q_1& =& \left(4\pi r_1^2\right)\sigma \\ q_2& =& \left(4\pi r_2^2\right)\sigma \end{array}\right]$