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 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.