Q. Two insulated charged conducting spheres of radii $20cm\ and\ 15cm$ respectively and having an equal charge of $10C$ are connected by a copper wire and then they are separated. Then

A) Both the spheres will have the same charge of $10\ C$
B) Surface charge density on the $20cm$ sphere will be greater than that on the $15cm$ sphere
C) Surface charge density on the $15cm$ sphere will be greater than that on the $20cm$ sphere
D) Surface charge density on the two spheres will be equal
Explanation

(c) After redistribution, charges on them will be different, but they will acquire common potential
$i.e.\ k\frac{Q_{1}}{r_{1}} = k\frac{Q_{2}}{r_{2}} \Rightarrow \frac{Q_{1}}{Q_{2}} = \frac{r_{1}}{r_{2}}$
As $\sigma = \frac{Q}{4\pi r^{2}} \Rightarrow \frac{\sigma_{1}}{\sigma_{2}} = \frac{Q_{1}}{Q_{2}} \times \frac{r_{2}^{2}}{r_{1}^{2}} \Rightarrow \frac{\sigma_{1}}{\sigma_{2}} = \frac{r_{2}}{r_{1}} \Rightarrow \sigma \propto \frac{1}{r}$
$i.e.$ surface charge density on smaller sphere will be more

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.