Question

Two concentric spheres of radii $R$ and $r$ have similar charges equal surface charge density $\left(\sigma \right)$. What is the electric potential at their common centre?

• A. $\sigma /{\epsilon }_0$
• B. $\frac{\sigma }{{\epsilon }_0}(R-r)$
• C. $\frac{\sigma }{{\epsilon }_0}(R+r)$
• D. None of these

Answer 1

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

Charge on the outer sphere, $q_1=4\pi R^2\sigma$

Charge on the inner sphere, $q_2=4\pi r^2\sigma$

$v=\frac{1}{4\pi {\in }_0}\frac{q_1}{R}+\frac{1}{4\pi {\in }_0}\frac{q_2}{r}$

$=\frac{1}{4\pi {\in }_0}[\frac{4\pi R^2\sigma }{R}+\frac{4\pi r^2\sigma }{r}]$

$=\frac{4\pi \sigma }{4\pi {\in }_0}(R+r)$

$=\frac{\sigma }{{\in }_0}(R+r)$