Question

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 $10C$
• 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

Answer 1

Answer: (C)

Surface charge density on the $15cm$ sphere will be greater than that on the $20cm$ sphere

Answer 2

After redistribution, charges on them will be different, but they will acquire common potential i. e

. $k\frac{Q_{1}}{r_{1}} = k\frac{Q_{2}}{r_{2}}$ ⇒ $\frac{Q_{1}}{Q_{2}} = \frac{r_{1}}{r_{2}}$

As $\sigma = \frac{Q}{4\pi r^{2}}$ ⇒ $\frac{\sigma_{1}}{\sigma_{2}} = \frac{Q_{1}}{Q_{2}} \times \frac{r_{2}^{2}}{r_{1}^{2}}$ ⇒ $\frac{\sigma_{1}}{\sigma_{2}} = \frac{r_{2}}{r_{1}}$ ⇒ $\sigma \propto \frac{1}{r}$

i.e. surface charge density on smaller sphere will be more.