Question

Two insulated charged spheres of radii $20cm$ and $25cm$ respectively and having equal charge $q$ are connected by a copper wire and then they are separated

• A. Both the spheres will have same charge $q$
• B. The charge on $20cm$ sphere will be greater than on the $25cm$ sphere
• C. The charge on $25cm$ sphere will be greater than on the $20cm$ sphere
• D. Both have same charge density

Answer 1

Answer: (B)

The charge on $20cm$ sphere will be greater than on the $25cm$ sphere

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,

$\sigma =\frac{Q}{4\pi r^2}$

$\frac{{\sigma }_1}{{\sigma }_2}=\frac{Q_1}{Q_2}\times \frac{r_2^2}{r_1^2}\Rightarrow \frac{{\sigma }_1}{{\sigma }_2}=\frac{r_2}{r_1}$

$\sigma \propto \frac{1}{r}$ i.e. surface charge density on smaller sphere will be more.