Question

Two insulated charged conducting spheres of radii $20\, cm$ and $15\, cm$, respectively, and having an equal charge of $10\, C$ 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 20 cm sphere will be greater than that on the 15 cm sphere
• C. surface charge density on the 15 cm sphere will be greater than that on the 20 cm sphere
• D. surface charge density on the two spheres will be equal

Answer 1

Answer: (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.