Question

A conducting sphere of radius $10\text{cm}$ is charged with $10\mu C$. Another uncharged sphere of radius $20\text{cm}$ is allowed to touch it for some time. After that if the spheres are seperated, then surface charge density on the spheres will be in the ratio of

• A. $1:4$
• B. $1:3$
• C. $2:1$
• D. $1:1$

Answer 1

The correct option is C $2:1$

After touching, potential of both the spheres will be equal.
$V_1=V_2$
$\Rightarrow \frac{K{Q}_1}{R_1}=\frac{K{Q}_2}{R_2}$
$\Rightarrow \frac{Q_1}{R_1}=\frac{Q_2}{R_2}$
$\Rightarrow \frac{Q_1}{Q_2}=\frac{R_1}{R_2}$
Surface charge density, $\sigma =\frac{Q}{4\pi R^2}$
$\therefore \frac{{\sigma }_1}{{\sigma }_2}=\frac{\frac{Q_1}{4\pi R_1^2}}{\frac{Q_2}{4\pi R_2^2}}$
=$\frac{Q_1}{Q_2}\times {\left(\frac{R_2}{R_1}\right)}^2$
$\Rightarrow \frac{{\sigma }_1}{{\sigma }_2}=\frac{R_1}{R_2}\times {\left(\frac{R_2}{R_1}\right)}^2=\frac{R_2}{R_1}=\frac{20}{10}$
$\therefore \frac{{\sigma }_1}{{\sigma }_2}=\frac{2}{1}$